{ "reading_this_index": "This file indexes 65 worked examples; each entry names one command, and the matching per-example file holds a runnable problem with the stored answer it reproduces. A title is a label on a reusable encoding shape, not the boundary of what that example solves: every example declares a `shape` and an `also_solves` list of named problems from other industries that submit the identical structure under different names, so the 65 titles are 65 of the 488 named problems in this catalogue and a reader who stops at the titles discards the other 423. Read the top-level `shapes` object next — it groups the 65 titles into 18 encodings and names the example that best teaches each one — then open a per-example file, where every `also_solves` entry carries the field-by-field mapping that turns that problem into this example's input. Canonical recipes explicitly start at `flash`: record that baseline first, then request `medium` or `high` only when deeper search is worth the measured cost. Effort never upgrades a heuristic result into a certificate.", "shapes": { "subset-with-pairwise-interaction": { "what_it_is": "You give every candidate a standalone value and give each pair of candidates a value that applies only when both are taken; the answer is the subset with the best total.", "template_example": "finance_portfolio", "examples": [ "finance_portfolio", "finance_settlement_netting", "bio_epistasis_triple" ], "covers": 24, "which_command": "Send it to optimize: one entry in linear per candidate for its standalone value and one [i, j, w] triple in quadratic per interacting pair, with the size of the chosen subset left free. Three conditions move it elsewhere — a declared shortlist size k is select, a pair relation that is an absolute prohibition rather than a price you would pay is a mutual_exclusion in rules, and any quantity that is an amount rather than a yes/no is milp." }, "assignment-under-conflict": { "what_it_is": "You give the items, the slots each item may take, and for each pair a cost or a prohibition that applies when they share a slot; the answer is one slot per item.", "template_example": "compiler_register_allocation", "examples": [ "compiler_register_allocation", "quantum_error_decoder", "ai_tensor_placement", "cloud_microservice_latency", "logistics_crossdock_hub", "robotics_cell_layout", "music_key_modulation", "infra_workload_placement", "cloud_gpu_scheduler", "cyber_zero_trust", "facility_session_scheduling", "logistics_container_incompat", "supply_bom_sourcing", "robotics_fleet_pathing", "agtech_crop_rotation", "space_maneuver_deconfliction" ], "covers": 130, "which_command": "Send it to qap only when items and slots are equal in number, every slot takes exactly one item, and the entire cost is one flow matrix multiplied by one distance matrix, with no capacity, no forbidden pair and no pin to declare. Otherwise route on the extra structure: design when each of L sites picks one of the same K values and a single KxK table prices every bonded pair (pins and preferences go in bias, a wrap-around value set sets circular true), rules the moment a slot carries a capacity, a pair must share or must split, or a choice is fixed in advance — only rules reports how many declared rules the assignment breaks — and optimize when the yes/no variable is a candidate pairing carrying its own weight rather than an item-in-a-slot." }, "cover-the-requirements": { "what_it_is": "You give the requirements, the candidate items with the requirements each one covers, and what each item costs; the answer is the cheapest family of items that covers every requirement as many times as that requirement demands.", "template_example": "devops_test_selection", "examples": [ "devops_test_selection", "infra_probe_placement", "health_shift_coverage", "bio_therapy_coverage", "security_dual_watch", "assembly_kit_partition", "hub_corridor_coverage", "hpc_solver_ensemble" ], "covers": 55, "which_command": "Send it to cover when each requirement is a FLOOR — covered at least k times — and the objective is the cheapest family of candidates: sets, min_cover and cost, plus max_cover for a ceiling, max_sets for a count cap, conflicts for two candidates that cannot both be chosen, and force/forbid for decisions already made. Send it to rules when the requirement is not a floor — exactly k covers per element is one choose_exactly per element listing only that element's own candidates, at most k is capacity_limit — or when the chosen candidates must also satisfy something that is not about coverage at all, such as an incompatible pair among the selected or a fixed total of k selected; if coverage is measured as a weighted quantity (kilograms, watts, hours) rather than counted in candidates, neither fits and it is milp." }, "satisfy-declared-rules": { "what_it_is": "You give the decisions as yes/no variables and the rules over them — exactly one of these, exactly k of those, at most k, if this then that, the same as, different from, pinned on, pinned off — and the answer is an assignment plus the count of rules it breaks.", "template_example": "agent_action_arbiter", "examples": [ "agent_action_arbiter", "ha_failover_sync", "devops_dependency_resolver", "ops_task_pipeline", "health_icu_roster", "legal_contract_consistency", "edtech_curriculum_path", "museum_exhibit_selection", "energy_microgrid_islanding", "game_procedural_map" ], "covers": 71, "which_command": "Send it to rules: each decision becomes one yes/no variable and each policy becomes one rule from the declared vocabulary — choose_one, choose_exactly, capacity_limit, mutual_exclusion, requires, identical, different, force_true, force_false — and violations comes back as an integer, where 0 certifies the whole set holds together and a positive count is how many rules cannot hold at once. It stays in rules while the relationships are hard and countable: a pair relation that is a price to trade off rather than a prohibition belongs to optimize (subset size free) or select (exactly k), and a cap denominated in an amount — currency, kilograms, tonnes — rather than in a count of items belongs to milp." }, "choose-k-of-m": { "what_it_is": "You give m candidates a score each and every pair a penalty for the overlap between them, and you state k; the answer is a shortlist whose size is exactly k.", "template_example": "bio_biomarker_panel", "examples": [ "bio_biomarker_panel", "rag_context_packing", "cat_item_selection", "conservation_reserve" ], "covers": 32, "which_command": "Send it to select when the shortlist size is exactly k and both terms are numbers: m, k, one affinity per candidate, and a symmetric redundancy penalty charged when two picks are taken together; the returned count is exactly k even when the certainty label reads heuristic. If a pair relation is an absolute veto rather than a penalty, or a candidate must be forced in or out, select has no field for it — state the same exact-k requirement in rules as one choose_exactly over all m plus one mutual_exclusion per forbidden pair and one force_true or force_false per pinned candidate; if k is free rather than declared, it is optimize." }, "partition-into-two": { "what_it_is": "You give a weight to every pair of items that is worth keeping apart; the answer puts each item on one of two sides so that the total weight of the separated pairs is as large as it can be.", "template_example": "infra_fault_domain_split", "examples": [ "infra_fault_domain_split", "telecom_band_assignment", "calibration_polarity_audit" ], "covers": 23, "which_command": "Send it to maxcut when every declared pair is one you want separated and carries a weight: n plus one [i, j, weight] per measured pair, and the answer is the two-way split with the largest separated weight. Send it to rules instead when the claims run both ways — some pairs must land on the same side (identical) and others on opposite sides (different) — because that mixture has no single cut value to maximize, and rules returns the count of claims the returned split breaks." }, "sequence-over-costs": { "what_it_is": "You give one square table holding the cost of going from each item to every other item; the answer is the order that takes every item once and returns to the start for the least total cost.", "template_example": "logistics_last_mile", "examples": [ "logistics_last_mile", "paint_shop_sequencing" ], "covers": 14, "which_command": "Send it to tsp — one square matrix whose [i][j] entry is the cost of placing j immediately after i — and read the returned order as the schedule; a run that need not come back to its start is stated by adding one extra item whose cost to and from every other item is zero. If the cost is paid because two items share a slot rather than because one directly follows the other, the shape is an assignment and not a sequence: qap when it is flow times distance, rules when the slots have capacities." }, "mixed-integer-with-continuous": { "what_it_is": "You declare some variables as yes/no and others as continuous quantities inside stated bounds, then give one objective over both in linear and pairwise terms; the answer sets every variable of both kinds.", "template_example": "recycling_line_dispatch", "examples": [ "recycling_line_dispatch", "robotics_balance_jettison" ], "covers": 14, "which_command": "Send it to milp as soon as one decision is an amount rather than a yes/no — a throughput, an arm position, a dosage — declared in vars as continuous with lo/hi bounds beside the binary ones, with the single objective carried in linear, diag and quadratic over both kinds. milp takes no constraint list, so a hard equality (a balance that must be exactly zero, a total that must hit a target) is folded into the objective by squaring that expression into those same three fields; if every quantity is a count of items rather than a measured amount, stay with rules and capacity_limit." }, "aggregate-noisy-orders": { "what_it_is": "You give the items and the pairwise verdicts collected about them, contradictions included; the answer is one order over all of them that agrees with as many of those verdicts as possible.", "template_example": "ai_judge_consensus", "examples": [ "ai_judge_consensus" ], "covers": 8, "which_command": "Send it to rank when the evidence is bare pairwise verdicts with no numbers attached: items plus one comparison entry per recorded verdict, contradictions and reversed duplicates included, and the answer is the one order that disagrees with fewest of them. If instead every ordered pair carries a numeric cost and the order is a schedule rather than a consensus, it is tsp with one square matrix; if you already hold a single consistent total order, there is nothing to aggregate." }, "spectral-readout": { "what_it_is": "You give the symmetric matrix that describes the system; the answer is its eigenvalues, its ground-state energy and the gap above that energy.", "template_example": "quantum_spin_spectrum", "examples": [ "quantum_spin_spectrum" ], "covers": 7, "which_command": "Send it to spectrum when the question is about the symmetric matrix itself rather than about a choice made over it: one matrix in, the eigenvalue ladder out with the ground energy and the gap above it, and the matrix must be symmetric and small enough to be read exactly. If what you want is an assignment or a subset that the matrix scores, it is a decision problem instead — optimize for a free-size subset over linear and quadratic terms, maxcut for a two-way split priced on edges." }, "verified-scientific-operation": { "what_it_is": "A structured scientific or numerical operation with an independently recomputable invariant; optimality does not apply unless a separate bound says it does.", "template_example": "science_known_entropy", "examples": [ "math_unimodular_reduction", "world_terrain_oracle", "science_known_entropy", "math_golden_ratio_relation", "math_sqrt2_precision", "science_planted_frequency" ], "covers": 18, "which_command": "Route by the observable: entropy for a valid correlation spectrum, frequency for a sampled signal, precision for a supported high-precision scalar operation, relation for an integer witness, reduce for an integer lattice basis, and world for a named geometry/terrain operation." }, "parity-system": { "what_it_is": "Binary variables linked by exclusive-or equations; the returned assignment is checked clause-by-clause over GF(2).", "template_example": "security_gf2_consistency", "examples": [ "security_gf2_consistency" ], "covers": 3, "which_command": "Use xorsat for parity/XOR clauses. Use rules for counts, implications and exclusions that are not parity equations." }, "binary-energy": { "what_it_is": "Binary states with local and pair terms, optionally with fixed outputs; every returned energy is recomputable from the supplied coefficients.", "template_example": "energy_known_ground_state", "examples": [ "energy_known_ground_state", "design_pinned_completion" ], "covers": 6, "which_command": "Use feel for a physical field/coupling model, want when some outputs are pinned, and optimize for a generic QUBO expressed as linear/quadratic coefficients." }, "scientific-hypothesis": { "what_it_is": "A controlled classifier or proxy whose output is explicitly a hypothesis and must be checked with an independent experiment or contrast.", "template_example": "physics_controlled_phase", "examples": [ "physics_controlled_phase" ], "covers": 3, "which_command": "Use phase only for the supported coupled-site phase proxy and preserve hypothesis language; do not present it as a proof." }, "planted-scale-certificate": { "what_it_is": "A seeded construction with a known planted floor used to test scale, precision and transport without generalizing to arbitrary hard instances.", "template_example": "scale_planted_65536", "examples": [ "scale_planted_65536" ], "covers": 3, "which_command": "Use quantum-scale only for its declared planted construction. Use optimize, maxcut or feel for an arbitrary user-supplied objective." }, "empirical-distribution": { "what_it_is": "Many draws and distribution diagnostics from a coupled binary model; the result is empirical evidence, not one proven optimum.", "template_example": "science_enumerable_sampling", "examples": [ "science_enumerable_sampling" ], "covers": 3, "which_command": "Use sample when the output needed is a distribution or diverse draws. Use feel/optimize when the output needed is one low-energy assignment." }, "integrity-roundtrip": { "what_it_is": "A typed protect/recover round-trip whose public assurance comes from byte equality and an independently reproduced digest.", "template_example": "integrity_protect_payload", "examples": [ "integrity_protect_payload", "integrity_recover_payload" ], "covers": 6, "which_command": "Use protect to create symbols and a digest; use recover only with that typed object and require honest refusal when the witness cannot be reproduced." }, "multi-layer-resolution": { "what_it_is": "A bounded dependency graph of supported capabilities and typed external evidence whose public claims are guarded by explicit residual criteria.", "template_example": "simulator_fault_isolation", "examples": [ "simulator_fault_isolation" ], "covers": 3, "which_command": "Use simulator when two or more supported capabilities or a real domain oracle must share one receipt. Use the native command directly when one layer answers the whole bounded question." } }, "count": 65, "categories": [ { "name": "Infrastructure", "ids": [ "ha_failover_sync", "infra_fault_domain_split", "infra_probe_placement", "infra_workload_placement", "simulator_fault_isolation" ] }, { "name": "AI Infrastructure", "ids": [ "agent_action_arbiter", "ai_judge_consensus", "ai_tensor_placement", "cloud_gpu_scheduler", "rag_context_packing" ] }, { "name": "Cloud", "ids": [ "cloud_microservice_latency" ] }, { "name": "DevOps", "ids": [ "compiler_register_allocation", "devops_dependency_resolver", "devops_test_selection" ] }, { "name": "Security", "ids": [ "cyber_zero_trust", "integrity_protect_payload", "integrity_recover_payload", "math_unimodular_reduction", "security_dual_watch", "security_gf2_consistency" ] }, { "name": "Operations", "ids": [ "calibration_polarity_audit", "ops_task_pipeline" ] }, { "name": "Scheduling", "ids": [ "facility_session_scheduling" ] }, { "name": "Healthcare", "ids": [ "health_icu_roster", "health_shift_coverage" ] }, { "name": "Logistics", "ids": [ "logistics_container_incompat", "logistics_crossdock_hub", "logistics_last_mile", "supply_bom_sourcing" ] }, { "name": "Telecom", "ids": [ "telecom_band_assignment" ] }, { "name": "Manufacturing", "ids": [ "assembly_kit_partition", "paint_shop_sequencing" ] }, { "name": "Legal", "ids": [ "legal_contract_consistency" ] }, { "name": "Education", "ids": [ "cat_item_selection", "edtech_curriculum_path" ] }, { "name": "Finance", "ids": [ "finance_portfolio", "finance_settlement_netting" ] }, { "name": "Biotech", "ids": [ "bio_biomarker_panel", "bio_epistasis_triple", "bio_therapy_coverage" ] }, { "name": "Sustainability", "ids": [ "conservation_reserve", "recycling_line_dispatch" ] }, { "name": "Robotics", "ids": [ "robotics_balance_jettison", "robotics_cell_layout", "robotics_fleet_pathing", "world_terrain_oracle" ] }, { "name": "Quantum & Physics", "ids": [ "energy_known_ground_state", "physics_controlled_phase", "quantum_error_decoder", "quantum_spin_spectrum", "science_known_entropy" ] }, { "name": "Agriculture", "ids": [ "agtech_crop_rotation" ] }, { "name": "Culture", "ids": [ "museum_exhibit_selection" ] }, { "name": "Energy", "ids": [ "energy_microgrid_islanding" ] }, { "name": "Engineering", "ids": [ "design_pinned_completion" ] }, { "name": "Gaming", "ids": [ "game_procedural_map" ] }, { "name": "Music", "ids": [ "music_key_modulation" ] }, { "name": "Real Estate", "ids": [ "hub_corridor_coverage" ] }, { "name": "Scientific Computing", "ids": [ "hpc_solver_ensemble", "math_golden_ratio_relation", "math_sqrt2_precision", "scale_planted_65536", "science_enumerable_sampling", "science_planted_frequency" ] }, { "name": "Space", "ids": [ "space_maneuver_deconfliction" ] } ], "examples": [ { "id": "ha_failover_sync", "title": "HA Pair Config Sync & Failover", "category": "Infrastructure", "icon": "🔁", "tagline": "Lockstep is identical on each value pair, so one force_false binds both units; exactly-one-active is different on the two role bits.", "command": "rules", "min_cli": "1.0.0", "effort": "flash", "shape": "satisfy-declared-rules", "scales_to": "At 500 redundant pairs drawn from a 12-value catalogue the identical shape is 2x12 + 2 = 26 variables per pair, 13,000 binary variables in one request, and 15 rules per pair (two choose_one groups, twelve identical links, one different on the role bits) for 7,500 rules. A withdrawn value is stated once per pair as a single force_false because the identical links carry it to the partner, and violations is reported per answer, so zero violations certifies that every declared rule holds rather than leaving an unlabelled guess.", "also_solves": [ { "problem": "Bus-tie transfer between two utility feeders in a substation", "domain": "Energy" }, { "problem": "Main and backup playout chains on one encoding profile with exactly one on air", "domain": "Broadcast" }, { "problem": "Active-passive exchange gateway pair holding a single order-entry session", "domain": "Finance" }, { "problem": "Dual infusion pumps sharing one drug-library revision with a single delivering pump", "domain": "Medical devices" }, { "problem": "Redundant PLC pair on a packaging line with one field-bus write token", "domain": "Manufacturing" }, { "problem": "Dual-channel brake-by-wire controllers on one calibration set with a single arbitration master", "domain": "Automotive" }, { "problem": "Enforced build diversity in a redundant safety pair, where the two channels must NOT run the same build", "domain": "Security" } ], "shipped": { "n": 8, "assurance": "certified_optimal" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": { "n": 100000, "rules": 30000 }, "certainty": "certified", "engine_ms_median": 984.738, "runs": 3, "measured": true } }, { "id": "infra_fault_domain_split", "title": "Fault-Domain Partitioning", "category": "Infrastructure", "icon": "🛡️", "tagline": "Weight a pair by what a shared failure costs; cut_value is coupling separated, and coupling left inside a domain is total minus cut_value.", "command": "maxcut", "min_cli": "1.0.0", "effort": "flash", "shape": "partition-into-two", "scales_to": "The identical shape at 5,000 components is one integer n and one [i, j, weight] triple per measured coupling — 50,000 triples for a mesh averaging 20 couplings each, 12,497,500 for a fully measured matrix — submitted as one request, with the answer still one 0/1 domain label per component. Only the edge count grows, not the structure; certification is proven by exhaustion and reported per answer, so a graph that size returns a labelled heuristic whose cut_value you recheck by summing the weights whose two endpoints carry different labels.", "also_solves": [ { "problem": "Randomizing a matched cohort into treatment and control so each closely matched pair lands on opposite arms", "domain": "Clinical research" }, { "problem": "Dividing a catastrophe-exposed policy book between two reinsurance treaties so correlated policies never concentrate in one treaty", "domain": "Insurance" }, { "problem": "Ground state of an antiferromagnetic Ising spin glass on an arbitrary interaction graph", "domain": "Condensed-matter physics" }, { "problem": "Splitting a review committee into two parallel panels so no pair with a declared conflict of interest sits on the same panel", "domain": "Scientific peer review" }, { "problem": "Assigning redundant line-replaceable units to two independent aircraft channels so units sharing a failure cause are never on one channel", "domain": "Avionics" }, { "problem": "Forming two teams from a lobby so habitual duo partners and same-clan players are placed on opposite sides", "domain": "Gaming" }, { "problem": "Dual-sourcing a component list across two suppliers so parts sharing one upstream fab or port cannot fail together", "domain": "Supply chain" } ], "shipped": { "n": 7, "assurance": "certified_optimal" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": { "n": 8000, "edges": 80000 }, "certainty": "heuristic (labelled)", "engine_ms_median": 5774.875, "runs": 3, "measured": true } }, { "id": "infra_probe_placement", "title": "Redundant Probe Placement", "category": "Infrastructure", "icon": "📡", "tagline": "Booleans are the probes, not the links; redundancy is a per-element floor under a ceiling, so surplus cover is forbidden, not priced.", "command": "cover", "min_cli": "1.0.0", "effort": "flash", "shape": "cover-the-requirements", "scales_to": "At 4,000 candidate placements over 25,000 monitored elements the identical encoding is 4,000 booleans, 4,000 covered-element lists (about 24,000 (candidate, element) incidences at six elements each), a 25,000-entry min_cover array of floors, a 25,000-entry max_cover array of ceilings, a 4,000-entry cost array and one [a,b] row per mutually exclusive pair — one request, the same six fields as the five-element version. Certainty is labelled on every answer and certification is proven by exhaustion, so an instance that size comes back marked heuristic instead of claiming an optimum it did not prove.", "also_solves": [ { "problem": "Safety-instrumented transmitter siting where SIL-rated process variables need two independent measurements", "domain": "Industrial Automation" }, { "problem": "PMU siting so every bus is observable and tie buses carry two independent observations", "domain": "Electric Utilities" }, { "problem": "In-line metrology sampling so every process layer is measured and critical litho layers measured twice", "domain": "Semiconductors" }, { "problem": "Camera position selection where officiating zones need two angles and no zone gets more than two feeds", "domain": "Broadcast Media" }, { "problem": "Surface-surveillance sensor siting so every taxiway segment is seen and runway crossings seen twice", "domain": "Aviation" }, { "problem": "Market-data capture appliance placement with two independent captures on best-execution venues", "domain": "Capital Markets" }, { "problem": "Election observer route assignment where contested precincts need two independent observers", "domain": "Election Administration" } ], "shipped": { "n": 6, "assurance": "certified_optimal" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": { "elements": 12000, "sets": 4000, "incidences": 40408 }, "certainty": "heuristic (labelled)", "engine_ms_median": 872.33, "runs": 3, "measured": true } }, { "id": "infra_workload_placement", "title": "Workload Placement Across Hosts", "category": "Infrastructure", "icon": "🗄️", "tagline": "A multi-way choice is one boolean per item-slot pair plus choose_one; keep-apart is one exclusion per slot, never one rule between items.", "command": "rules", "min_cli": "1.0.0", "effort": "flash", "shape": "assignment-under-conflict", "scales_to": "The identical shape at 400 items across 60 slots is 400x60 = 24,000 binary variables, 400 choose_one groups, 60 capacity_limit rules, and one mutual_exclusion per slot per protected pair, so 150 protected pairs add 150x60 = 9,000 exclusions and 9,460 rules travel in one request. Only the counts grow, not the rule types; items x slots must stay within the declared ceiling of 100,000 variables, which a single request has carried in full, and violations is reported per answer, where zero certifies every declared rule holds and a positive count states how many could not hold at once.", "also_solves": [ { "problem": "Berthing ambulances in station garages so the two units covering one district never share a garage", "domain": "Public safety" }, { "problem": "Distributing a collection across storage vaults so the only two copies of a work are never in one room", "domain": "Cultural heritage" }, { "problem": "Distributing key shares to custodians so no custodian can reach the reconstruction threshold alone", "domain": "Cryptography" }, { "problem": "Seating exam candidates in rooms under a collusion screen", "domain": "Education" }, { "problem": "Assigning inpatients to ward bays under infection-control separation", "domain": "Healthcare" }, { "problem": "Splitting custodians across document-review teams so an ethical wall is never crossed", "domain": "Legal" }, { "problem": "Placing duplicate seed accessions in gene banks so one bank's failure never loses a landrace", "domain": "Agriculture" } ], "shipped": { "n": 12, "assurance": "certified_optimal" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": { "n": 100000, "rules": 30000 }, "certainty": "certified", "engine_ms_median": 984.738, "runs": 3, "measured": true } }, { "id": "simulator_fault_isolation", "title": "Residual-Guarded Fault Isolation", "category": "Infrastructure", "icon": "◎", "tagline": "Two independently checked layers support one bounded claim; missing evidence would withhold it.", "command": "simulator", "min_cli": "1.0.0", "effort": "flash", "shape": "multi-layer-resolution", "scales_to": null, "also_solves": [ { "problem": "Power-grid islanding plus an upstream AC power-flow residual", "domain": "Energy" }, { "problem": "Active-region choice plus an external electronic-structure calculation", "domain": "Quantum chemistry" }, { "problem": "Orbital conjunction screening followed by a trusted propagator", "domain": "Space" } ], "shipped": { "n": 1, "assurance": "operation" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": null, "certainty": null, "engine_ms_median": null, "runs": null, "measured": false } }, { "id": "agent_action_arbiter", "title": "Multi-Agent Action Arbiter", "category": "AI Infrastructure", "icon": "🧩", "tagline": "Exclusive use of a resource is capacity_limit k=1 over all claimants, not g(g-1)/2 pairs; the world's current state enters as force_true.", "command": "rules", "min_cli": "1.0.0", "effort": "flash", "shape": "satisfy-declared-rules", "scales_to": "The identical shape at 20,000 proposed operations is 20,000 binary variables, one requires per dependency edge and one mutual_exclusion per conflicting pair, so 12,000 dependencies plus 30,000 conflicting pairs is 42,000 rules in one request, with one force_true per fact already true. A resource touched by g proposals costs g(g-1)/2 pairwise exclusions or a single capacity_limit with k=1 over all g nodes, so the same exclusivity is stated in one rule instead of thousands, and violations is reported per answer, where zero certifies that every declared rule holds.", "also_solves": [ { "problem": "Approving a substation switching program", "domain": "Utilities" }, { "problem": "Issuing hot-work permits for a refinery turnaround", "domain": "Process safety" }, { "problem": "Releasing a cutoff batch of payment instructions", "domain": "Banking operations" }, { "problem": "Clearing concurrent pad operations during a countdown hold", "domain": "Space operations" }, { "problem": "Choosing which promotions may all run in one circular", "domain": "Retail" }, { "problem": "Deciding which protocol amendments can be enacted at one trial site", "domain": "Clinical research" }, { "problem": "Admitting add-on surgical cases to a theatre list", "domain": "Healthcare" }, { "problem": "Authorising concurrent underground activities on a mine panel plan", "domain": "Mining" } ], "shipped": { "n": 8, "assurance": "certified_optimal" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": { "n": 100000, "rules": 30000 }, "certainty": "certified", "engine_ms_median": 984.738, "runs": 3, "measured": true } }, { "id": "ai_judge_consensus", "title": "LLM Judge Consensus Ranking", "category": "AI Infrastructure", "icon": "🗳️", "tagline": "No scores, only [winner, loser] pairs — repeat a pair to weight it; cycles are legal input, and the answer's unit is verdicts contradicted.", "command": "rank", "min_cli": "1.0.0", "effort": "flash", "shape": "aggregate-noisy-orders", "scales_to": "The identical encoding at 400 items judged by 12 panels is 400 item labels and 957,600 comparison entries — each panel's full set of 79,800 ordered pairs — in one request with the same two fields, items and comparisons. The ordering count is 400 factorial, so above the small certified range the answer carries the heuristic label rather than a proof, and `disagreements` stays an integer you recount against the raw comparison list yourself.", "also_solves": [ { "problem": "Build one product order from a sensory panel where 20 tasters gave paired-preference verdicts that contradict each other", "domain": "Consumer goods" }, { "problem": "Order champion and challenger credit scorecards from head-to-head A/B outcomes across segments that disagree", "domain": "Financial services" }, { "problem": "Seed a 128-player bracket from a season of head-to-head results containing upsets and no common opponents", "domain": "Esports" }, { "problem": "Rank 30 process recipes from split-lot wafer comparisons where different metrology tools named different winners", "domain": "Semiconductor" }, { "problem": "Turn ranked-choice ballots into one committee-wide order when no candidate beats every other candidate pairwise", "domain": "Elections / civic" }, { "problem": "Order 40 catalyst candidates from paired bench runs where duplicate runs reversed the verdict", "domain": "Chemicals" }, { "problem": "Order 25 triage protocols from clinicians' paired preference judgments recorded across shifts that disagree", "domain": "Healthcare operations" }, { "problem": "Rank grasp policies from teleoperator preference votes where operators disagree about which policy emptied a bin better", "domain": "Robotics" } ], "shipped": { "n": 4, "assurance": "certified_optimal" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": { "items": 2000, "comparisons": 119941, "contradiction_rate": "~22%" }, "certainty": "heuristic (labelled)", "engine_ms_median": 135.323, "runs": 3, "measured": true } }, { "id": "ai_tensor_placement", "title": "Tensor / GPU Shard Placement", "category": "AI Infrastructure", "icon": "🧠", "tagline": "Two same-size matrices over different sets: flow over the items, distance over the places. Spare places enter as zero-flow padding items.", "command": "qap", "min_cli": "1.0.0", "effort": "flash", "shape": "assignment-under-conflict", "scales_to": "The identical shape at 128 shards is two 128x128 matrices — 32,768 numbers in one request, 8,128 unordered pairs on each side — and the objective is a sum of 16,256 flow-by-distance products over one assignment out of 128! possible ones. Only the numbers grow; the request still carries exactly the two fields it carries at n=4, and the certainty label is reported per answer, so past the exhaustion cap the response is a labelled heuristic rather than a silent guess.", "also_solves": [ { "problem": "Initial logical-to-physical qubit mapping on a fixed coupling graph", "domain": "Quantum computing" }, { "problem": "Recovering a monoalphabetic substitution key from digram statistics", "domain": "Cryptanalysis" }, { "problem": "Aligning two protein-interaction networks across species", "domain": "Computational biology" }, { "problem": "Thermal-aware server placement inside a rack", "domain": "Data-center facilities" }, { "problem": "Assigning avionics line-replaceable units to equipment-bay slots to shorten the wiring harness", "domain": "Aerospace systems" }, { "problem": "Arranging camera feeds on a live gallery's monitor wall so the director's eyes travel less", "domain": "Broadcast production" }, { "problem": "Placing process units on a refinery plot plan to cut total pipe run", "domain": "Process engineering" }, { "problem": "Zoning a supermarket floor so categories bought together sit within a short walk", "domain": "Retail store planning" }, { "problem": "Seating orchestra sections on the risers of an unfamiliar hall", "domain": "Live performance" }, { "problem": "Assigning species to the enclosures of a new zoo precinct so stress-inducing neighbours are kept apart", "domain": "Zoo husbandry" }, { "problem": "Ordering grave assemblages into a chronological sequence from shared artefact types", "domain": "Archaeology" } ], "shipped": { "n": 4, "assurance": "certified_optimal" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": { "n": 200, "flow_entries": 40000, "dist_entries": 40000 }, "certainty": "heuristic (labelled)", "engine_ms_median": 25.992, "runs": 3, "measured": true } }, { "id": "cloud_gpu_scheduler", "title": "GPU Fleet Scheduling With Tenant Isolation", "category": "AI Infrastructure", "icon": "🖥️", "tagline": "capacity_limit counts requests, not gigabytes: equal slots are native, weighted budgets are not; isolation is one exclusion per node.", "command": "rules", "min_cli": "1.0.0", "effort": "flash", "shape": "assignment-under-conflict", "scales_to": "The identical shape at 2,000 requests across 40 resources is 2,000x40 = 80,000 binary variables, 2,000 choose_one groups, 40 capacity_limit rules, and one mutual_exclusion per resource per separated pair, so 10 separated pairs add 400 exclusions for 2,440 rules in one request. Requests x resources must stay within the declared ceiling of 100,000 variables, which a single request has carried in full, so a fleet past that ceiling is encoded one resource group at a time, and violations is reported per answer, where a positive count is the plain statement that the capacities and separations asked for were over-subscribed.", "also_solves": [ { "problem": "Building commercial breaks under category-exclusivity clauses", "domain": "Advertising" }, { "problem": "Seating a banquet against a do-not-seat list", "domain": "Events" }, { "problem": "Allocating detainees to housing blocks under keep-separate orders", "domain": "Corrections" }, { "problem": "Drawing a tournament group stage under association-protection rules", "domain": "Sport" }, { "problem": "Assigning production lots to cleanroom tools under customer segregation", "domain": "Semiconductor manufacturing" }, { "problem": "Routing claims to adjuster pools without putting both sides of one accident together", "domain": "Insurance" }, { "problem": "Housing animals in enclosures with recorded aggression pairs kept apart", "domain": "Animal management" } ], "shipped": { "n": 10, "assurance": "certified_optimal" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": { "n": 100000, "rules": 30000 }, "certainty": "certified", "engine_ms_median": 984.738, "runs": 3, "measured": true } }, { "id": "rag_context_packing", "title": "RAG Context-Window Packing", "category": "AI Infrastructure", "icon": "🪟", "tagline": "Reward is per item, penalty is per pair, so a near-duplicate keeps only what it adds beyond its twin — which is exactly where top-k fails.", "command": "select", "min_cli": "1.0.0", "effort": "flash", "shape": "choose-k-of-m", "scales_to": "The identical encoding at 1,200 retrieved chunks with a 30-chunk budget is 1,200 affinity values plus a symmetric overlap matrix of up to 719,400 distinct pairs (1,440,000 matrix entries), submitted as one request with the same four fields: m, k, affinity, redundancy. Only the numbers grow, not the structure. Certification is proven by exhaustion and is labelled on every answer, so an instance this size returns a stated heuristic while the returned set still holds exactly 30 chunks.", "also_solves": [ { "problem": "Choose the 12 reinsurance treaty layers to bind for next season from 300 quoted layers, where layers covering the same peril region relieve the same exposure", "domain": "Insurance" }, { "problem": "Pick the 6 creatives to run in one flight from 80 approved assets when creatives sharing a hook fatigue the same audience", "domain": "Advertising" }, { "problem": "Select the 25 documents for a deposition exhibit binder from 4,000 responsive hits, where near-duplicate email threads consume binder slots", "domain": "Legal / eDiscovery" }, { "problem": "Choose the 40 detection rules to enable on a SIEM tier from 600 authored rules when several rules alert on the same attack technique", "domain": "Cybersecurity" }, { "problem": "Choose 8 of 90 inline inspection stations to keep on a line where two stations catch the same defect class", "domain": "Manufacturing QA" }, { "problem": "Select 15 of 400 cell sites for a fibre-backhaul upgrade round where adjacent sites carry the same traffic", "domain": "Telecom" }, { "problem": "Pick the 20 telemetry channels to downlink at full rate from 350 instrumented channels when several channels are derived from one sensor", "domain": "Aerospace" }, { "problem": "Choose the 10 stories for a newsletter front section from 250 filed pieces where two pieces on the same event compete", "domain": "Media / Publishing" } ], "shipped": { "n": 8, "assurance": "certified_optimal" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": { "m": 2000, "k": 80, "redundancy_pairs": 20000 }, "certainty": "heuristic (labelled)", "engine_ms_median": 4.924, "runs": 3, "measured": true } }, { "id": "cloud_microservice_latency", "title": "Microservice Placement for Low Latency", "category": "Cloud", "icon": "🔗", "tagline": "Cost lives in the pairs: set dist to (widest gap - gap) and 'keep these apart' becomes the same minimization as 'put these close'.", "command": "qap", "min_cli": "1.0.0", "effort": "flash", "shape": "assignment-under-conflict", "scales_to": "At 60 placement slots the encoding is two 60x60 matrices — 7,200 numbers, 1,770 unordered pairs per matrix — and the cost is a sum of 3,540 traffic-by-distance products over one assignment out of 60! possible ones. The request keeps the same two fields it has at n=4; only the matrices get bigger. Certification is by exhaustion and is stated per answer, so a large instance returns a heuristic that says it is one.", "also_solves": [ { "problem": "Exam timetabling that spreads conflicting exams apart", "domain": "Education" }, { "problem": "Seeding a knockout bracket so rivalries meet as late as possible", "domain": "Sports" }, { "problem": "Frequency assignment where interference falls off with channel separation", "domain": "Wireless networks" }, { "problem": "Patch-panel port assignment in a data hall", "domain": "Network cabling" }, { "problem": "Laying out the vocabulary tiles on a child's speech-generating communication board", "domain": "Assistive technology" }, { "problem": "Assigning record series to shelf bays in an archive's closed stacks", "domain": "Archives and records management" }, { "problem": "Positioning the prep stations in a new restaurant kitchen", "domain": "Commercial kitchen design" }, { "problem": "Arranging the indicators on a nuclear control-room console", "domain": "Nuclear power operations" }, { "problem": "Placing the orchestra sections on the risers of a new concert hall stage", "domain": "Orchestral performance" }, { "problem": "Assigning compartments to hull zones in a ship's general arrangement", "domain": "Naval architecture" }, { "problem": "Siting the attractions on the plots of a new theme park", "domain": "Theme park design" } ], "shipped": { "n": 4, "assurance": "certified_optimal" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": { "n": 200, "flow_entries": 40000, "dist_entries": 40000 }, "certainty": "heuristic (labelled)", "engine_ms_median": 25.992, "runs": 3, "measured": true } }, { "id": "compiler_register_allocation", "title": "Register Allocation Colorer", "category": "DevOps", "icon": "🎨", "tagline": "One of K values per site natively, no one-hot: the request grows with the conflict count, not L×K, and a pin is just a bias on the rest.", "command": "design", "min_cli": "1.0.0", "effort": "flash", "shape": "assignment-under-conflict", "scales_to": "The identical shape at 5,000 sites and 16 values is one `L`, one `K`, one bond per conflicting pair (a 40,000-edge interference graph is 40,000 entries), one 16x16 = 256-number symmetric `table` no matter how large L grows, and one `bias` triple per pin or preference — over K^L = 16^5000 assignments. The request scales with the CONFLICT COUNT, not with L x K: nothing one-hot is ever transmitted. Certification is by exhaustion and is reported per answer, so a large instance returns a labelled heuristic, and `energy` is recomputable from the returned assignment by summing the table over every bond plus the bias of each chosen value.", "also_solves": [ { "problem": "Gate assignment when flights' ground times overlap", "domain": "Aviation" }, { "problem": "Exam timetabling with shared students", "domain": "Education" }, { "problem": "Spreading a service's replicas across failure zones", "domain": "Cloud infrastructure" }, { "problem": "Assigning PCB net segments to copper layers", "domain": "Electronics (EDA)" }, { "problem": "Placing fixtures into broadcast windows", "domain": "Media" }, { "problem": "Assigning assays to instrument runs with carryover risk", "domain": "Life-science lab operations" } ], "shipped": { "n": 6, "assurance": "certified_optimal" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": { "L": 2000, "K": 8, "bonds": 16000, "bias_terms": 1000 }, "certainty": "heuristic (labelled)", "engine_ms_median": 2.861, "runs": 3, "measured": true } }, { "id": "devops_dependency_resolver", "title": "Dependency Version Resolver", "category": "DevOps", "icon": "📦", "tagline": "One boolean per component-version, choose_one per component: pin one with force_true and the requires edges cascade the whole fleet.", "command": "rules", "min_cli": "1.0.0", "effort": "flash", "shape": "satisfy-declared-rules", "scales_to": "The identical shape at 3,000 components averaging 8 candidate values is 24,000 binary variables and 3,000 choose_one groups, plus one requires per dependency edge and one mutual_exclusion per declared incompatibility, so 60,000 dependencies and 4,000 incompatibilities is 67,000 rules in one request. Only the counts grow, not the rule types, and violations is reported per answer: zero certifies that a coherent set of choices exists, while a positive count is a real unsatisfiable conflict surfaced before the change is applied.", "also_solves": [ { "problem": "Validating a vehicle option configuration before it reaches the order bank", "domain": "Automotive" }, { "problem": "Assembling a multi-agent therapy regimen with one agent per drug class", "domain": "Clinical pharmacology" }, { "problem": "Specifying products so every tested fire and acoustic assembly stays certified", "domain": "Construction" }, { "problem": "Choosing modification variants so a set of supplemental type certificates stays valid", "domain": "Aviation" }, { "problem": "Choosing accounting method elections so a return stays internally consistent", "domain": "Tax and accounting" }, { "problem": "Choosing ingredient grades so every label claim survives the formulation", "domain": "Food manufacturing" }, { "problem": "Resolving IP-block releases across an SoC so interface and process-kit revisions agree", "domain": "Chip design" } ], "shipped": { "n": 6, "assurance": "certified_optimal" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": { "n": 100000, "rules": 30000 }, "certainty": "certified", "engine_ms_median": 984.738, "runs": 3, "measured": true } }, { "id": "devops_test_selection", "title": "CI Test Suite Selection", "category": "DevOps", "icon": "🧷", "tagline": "The cap counts chosen sets, not their weight: cheapest-first can strand a requirement, so the floor and the cap are one problem.", "command": "cover", "min_cli": "1.0.0", "effort": "flash", "shape": "cover-the-requirements", "scales_to": "At 2,500 candidate sets over 12,000 requirements the identical encoding is 2,500 booleans, 2,500 covered-element lists (50,000 (candidate, element) incidences at twenty each), one min_cover integer, a 2,500-entry cost array and a single max_sets integer — the count cap stays one number however large the universe gets, which is exactly why it cannot stand in for a weighted budget. Certainty is labelled on every answer, so a universe that size returns a marked heuristic, and `uncovered` still reports precisely how many requirements a cap that tight leaves unmet.", "also_solves": [ { "problem": "Tool crib loadout so every machined feature can be cut by a loaded tool within the turret's pockets", "domain": "Manufacturing" }, { "problem": "Asserted-claim selection for trial so every accused feature is read on, under the court's limit on asserted claims", "domain": "Legal / IP" }, { "problem": "Batch release-testing plan so every registered specification attribute is determined by a validated method", "domain": "Pharmaceutical QC" }, { "problem": "Flight-test sortie selection so every certification requirement is demonstrated across the funded sorties", "domain": "Aerospace" }, { "problem": "Planogram fill so every demand category is present on a fixture with a fixed number of facings", "domain": "Retail" }, { "problem": "Crop protection program so every scouted pest is controlled, with the program limited to a set number of products", "domain": "Agriculture" } ], "shipped": { "n": 6, "assurance": "certified_optimal" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": { "elements": 12000, "sets": 4000, "incidences": 40408 }, "certainty": "heuristic (labelled)", "engine_ms_median": 872.33, "runs": 3, "measured": true } }, { "id": "cyber_zero_trust", "title": "Zero-Trust Segment Assignment", "category": "Security", "icon": "🛡️", "tagline": "A policy is one rule per segment on the pair's same-segment variables: identical for must-share, mutual_exclusion for must-separate.", "command": "rules", "min_cli": "1.0.0", "effort": "flash", "shape": "assignment-under-conflict", "scales_to": "At 300 workload classes and 8 segments the identical encoding is 2,400 binary variables, 300 choose_one rules (one per class), 8 capacity_limit rules (one per segment) and 8 pairwise rules per policy, so 120 must-share plus 400 must-keep-apart policies add 4,160 rules — 4,468 rules submitted as one request, with the rule types unchanged. A returned 0 violations certifies the whole policy set holds together; a nonzero count is the number of declared rules the returned assignment breaks, recomputable from the problem by arithmetic.", "also_solves": [ { "problem": "Hazmat storage bay assignment where incompatible chemical classes may not share a bay", "domain": "Chemical logistics" }, { "problem": "Placing ad creatives into break pods with competitive brand separation", "domain": "Advertising operations" }, { "problem": "Assigning process steps to chambers so metal-bearing and photoresist steps never share one", "domain": "Semiconductor manufacturing" }, { "problem": "Assigning client matters to practice teams under conflict-of-interest walls", "domain": "Legal services" }, { "problem": "Penning livestock groups so different disease-status groups never share a pen", "domain": "Livestock agriculture" }, { "problem": "Drawing clubs into competition groups with stadium-sharing and travel-cluster rules", "domain": "Professional sports" }, { "problem": "Assigning trial cohorts to investigator sites so blinded arms never share a site", "domain": "Clinical research" } ], "shipped": { "n": 12, "assurance": "certified_optimal" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": { "n": 100000, "rules": 30000 }, "certainty": "certified", "engine_ms_median": 984.738, "runs": 3, "measured": true } }, { "id": "integrity_protect_payload", "title": "Protected Payload Envelope", "category": "Security", "icon": "⌁", "tagline": "The digest is a public integrity witness for an exact future recovery.", "command": "protect", "min_cli": "1.0.0", "effort": "flash", "shape": "integrity-roundtrip", "scales_to": null, "also_solves": [ { "problem": "Checkpoint protection", "domain": "HPC" }, { "problem": "Telemetry packet protection", "domain": "IoT" }, { "problem": "Model-state transport", "domain": "AI infrastructure" } ], "shipped": { "n": null, "assurance": "verified_operation" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": null, "certainty": null, "engine_ms_median": null, "runs": null, "measured": false } }, { "id": "integrity_recover_payload", "title": "Byte-Exact Recovery", "category": "Security", "icon": "↺", "tagline": "Recovery succeeds only when the restored bytes reproduce the sealed digest.", "command": "recover", "min_cli": "1.0.0", "effort": "flash", "shape": "integrity-roundtrip", "scales_to": null, "also_solves": [ { "problem": "Corrupted checkpoint restoration", "domain": "HPC" }, { "problem": "Noisy link recovery", "domain": "Networking" }, { "problem": "Archive integrity restoration", "domain": "Storage" } ], "shipped": { "n": null, "assurance": "verified_operation" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": null, "certainty": null, "engine_ms_median": null, "runs": null, "measured": false } }, { "id": "math_unimodular_reduction", "title": "Unimodular Lattice Reduction", "category": "Security", "icon": "ℤ", "tagline": "The output must span the identical integer lattice and satisfy reduction checks.", "command": "reduce", "min_cli": "1.0.0", "effort": "flash", "shape": "verified-scientific-operation", "scales_to": null, "also_solves": [ { "problem": "Integer-lattice conditioning", "domain": "Cryptography" }, { "problem": "Diophantine preprocessing", "domain": "Mathematics" }, { "problem": "Integer feature decorrelation", "domain": "Data science" } ], "shipped": { "n": null, "assurance": "operation" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": null, "certainty": null, "engine_ms_median": null, "runs": null, "measured": false } }, { "id": "security_dual_watch", "title": "Dual-Watcher Camera Plan", "category": "Security", "icon": "📹", "tagline": "The quota sits on each covered element's candidate group, not on the devices; at-most-2 is satisfied by zero watchers, exactly-2 is not.", "command": "rules", "min_cli": "1.0.0", "effort": "flash", "shape": "cover-the-requirements", "scales_to": "At 4,000 candidate devices and 1,200 covered elements the encoding is 4,000 binary variables and 1,200 choose_exactly rules, one per element listing only that element's own candidates — at an average of 6 candidates per element that is 7,200 index references and zero rules between elements, since all of the coupling comes from candidates that appear in several groups. A returned 0 violations means every quota is met exactly; a nonzero count is how many quotas are off. If an element's requirement is a floor of k rather than exactly k, that regime is the companion command cover with min_cover, not choose_exactly.", "also_solves": [ { "problem": "Powering flight-control sensor units so every measured parameter is read by exactly two units", "domain": "Aerospace avionics" }, { "problem": "Rostering duty officers so each account has exactly two authorised release approvers on shift", "domain": "Banking compliance" }, { "problem": "Choosing which axle-counter units to commission so each interlocking area is sensed by exactly two", "domain": "Rail signalling" }, { "problem": "Selecting gas-detector positions so every compartment is monitored by exactly two independent heads", "domain": "Offshore energy safety" }, { "problem": "Energising branch circuits so every rack is fed by exactly two live feeds", "domain": "Data centre infrastructure" }, { "problem": "Keeping exactly two sectors active per coverage area during a low-demand window", "domain": "Telecommunications" }, { "problem": "Designating exactly two market makers per listed instrument from the firms qualified to quote it", "domain": "Capital markets infrastructure" } ], "shipped": { "n": 4, "assurance": "certified_optimal" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": { "n": 100000, "rules": 30000 }, "certainty": "certified", "engine_ms_median": 984.738, "runs": 3, "measured": true } }, { "id": "security_gf2_consistency", "title": "GF(2) Consistency Check", "category": "Security", "icon": "⊕", "tagline": "Every parity clause is checked independently over GF(2).", "command": "xorsat", "min_cli": "1.0.0", "effort": "flash", "shape": "parity-system", "scales_to": null, "also_solves": [ { "problem": "XOR consistency diagnosis", "domain": "Data integrity" }, { "problem": "Binary sensor reconciliation", "domain": "IoT" }, { "problem": "Constraint puzzle", "domain": "Education" } ], "shipped": { "n": 6, "assurance": "certified_optimal" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": null, "certainty": null, "engine_ms_median": null, "runs": null, "measured": false } }, { "id": "calibration_polarity_audit", "title": "Calibration Polarity Audit", "category": "Operations", "icon": "🧭", "tagline": "Same-polarity and opposite-polarity claims form a signed graph — the minimum violations IS the number of irreducible contradictions.", "command": "rules", "min_cli": "1.0.0", "effort": "flash", "shape": "partition-into-two", "scales_to": "At 5,000 instruments and 40,000 claims the encoding is 5,000 binary variables and 40,000 pairwise rules, one rule per claim — different for an opposition, identical for an agreement — and no other structure. The reported count is exactly the number of claims the returned assignment breaks, at any size; whether it is also certified as the minimum is stated by the certainty label on that answer, so read the label rather than inferring it from the instance size, and recompute the count from the raw claim list whenever the count itself is the deliverable.", "also_solves": [ { "problem": "Haplotype phasing from read evidence, where the broken-claim count is the frustration of the read graph", "domain": "Genomics" }, { "problem": "Recovering binary labels from annotators who supplied only relative judgments of same or opposite class", "domain": "Machine learning data operations" }, { "problem": "Trace-polarity reconciliation across overlapping seismic surveys before a merge", "domain": "Seismic surveying" }, { "problem": "Multi-microphone polarity audit from measured pairwise correlation on a live rig", "domain": "Audio engineering" }, { "problem": "Splitting a rack's devices across the A and B power feeds when high-availability pairs must be split and a device must share a feed with the switch that manages it", "domain": "Data centre electrical design" }, { "problem": "Assigning a housing unit's residents to two wings when keep-separate orders and must-stay-together pairings collide", "domain": "Corrections" }, { "problem": "Assigning field parcels to the two halves of a rotation when adjoining parcels must be out of phase and parcels on one irrigation valve must be in phase", "domain": "Agriculture" }, { "problem": "Splitting a season's SKUs across two production lines under allergen segregation and single-copy tooling rules", "domain": "Food manufacturing" }, { "problem": "Labelling retained batches of a chiral intermediate as one enantiomer or the other from pairwise comparison assays", "domain": "Pharmaceutical quality control" } ], "shipped": { "n": 4, "assurance": "certified_optimal" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": { "n": 100000, "rules": 30000 }, "certainty": "certified", "engine_ms_median": 984.738, "runs": 3, "measured": true } }, { "id": "ops_task_pipeline", "title": "Task Pipeline Promotion", "category": "Operations", "icon": "⚙️", "tagline": "requires [X,Y] means X implies Y: forcing one item forces its whole chain, and the cap counts items, not money.", "command": "rules", "min_cli": "1.0.0", "effort": "flash", "shape": "satisfy-declared-rules", "scales_to": "At 2,000 candidate items the encoding is 2,000 binary variables and one rule per stated relationship: 3,500 prerequisite edges are 3,500 requires rules (a chain of length L contributes L-1 of them), 600 conflicting pairs are 600 mutual_exclusion rules, 40 mandatory items are 40 force_true rules, and the count cap is a single capacity_limit over all 2,000 — 4,141 rules in one request. A budget measured in currency, kilograms or crew capacity is not a count of items and belongs to milp rather than capacity_limit.", "also_solves": [ { "problem": "Choosing which dossier modules enter the next rolling regulatory submission", "domain": "Pharmaceutical regulatory affairs" }, { "problem": "Selecting valid rider combinations for a policy quote", "domain": "Insurance" }, { "problem": "Shortlisting capital projects for a fiscal programme", "domain": "Public infrastructure planning" }, { "problem": "Choosing which instruments are powered during an observation block", "domain": "Spacecraft operations" }, { "problem": "Listing therapies on a formulary tier under tender and protocol constraints", "domain": "Health payer formulary management" }, { "problem": "Selecting which stopes enter the quarter's mine plan", "domain": "Mining" } ], "shipped": { "n": 6, "assurance": "certified_optimal" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": { "n": 100000, "rules": 30000 }, "certainty": "certified", "engine_ms_median": 984.738, "runs": 3, "measured": true } }, { "id": "facility_session_scheduling", "title": "Facility Session Scheduling", "category": "Scheduling", "icon": "🗓️", "tagline": "One variable per (item, slot): together is identical per slot, apart is mutual_exclusion per slot — different only works at 2 slots.", "command": "rules", "min_cli": "1.0.0", "effort": "flash", "shape": "assignment-under-conflict", "scales_to": "At 500 sessions and 12 rooms the same encoding is 6,000 binary variables, 500 choose_one rules, 12 capacity_limit rules and 12 rules per related pair, so 200 must-share and 150 must-split pairs add 4,200 rules — 4,712 in all. One structural note as the room count grows: a must-share pair stays identical paired per room, while a must-split pair is one mutual_exclusion per room; different per room states the same thing only when there are exactly 2 rooms.", "also_solves": [ { "problem": "Berth allocation for a tide window where two vessels must not draw on the same shore crane", "domain": "Port operations" }, { "problem": "Assigning scenes to sound stages when one standing set cannot be struck", "domain": "Film and television production" }, { "problem": "Placing exam sections into halls so a paper and its resit never share a hall", "domain": "Higher education" }, { "problem": "Splitting product campaigns across packaging lines to keep an allergen product off the shared line", "domain": "Food and beverage manufacturing" }, { "problem": "Assigning simultaneous emergency drills to training grounds", "domain": "Emergency services" }, { "problem": "Assigning product categories to display islands with a cross-merchandising pair and two anchors", "domain": "Retail merchandising" }, { "problem": "Placing language queues across two sites so a disaster-recovery pair is never co-located", "domain": "Contact centre operations" } ], "shipped": { "n": 8, "assurance": "certified_optimal" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": { "n": 100000, "rules": 30000 }, "certainty": "certified", "engine_ms_median": 984.738, "runs": 3, "measured": true } }, { "id": "health_icu_roster", "title": "ICU Roster With Supervision & Fatigue Rules", "category": "Healthcare", "icon": "🏥", "tagline": "One variable per (person, slot): supervision is the same implication as precedence, fatigue an exclusion on one person's adjacent slots.", "command": "rules", "min_cli": "1.0.0", "effort": "flash", "shape": "satisfy-declared-rules", "scales_to": "The identical shape at 120 clinicians across 21 shifts is 2,520 binary variables: fatigue is one `mutual_exclusion` per clinician per consecutive-shift pair (120 x 20 = 2,400 rules), plus one `requires` per supervision link and one `force_true` per pre-committed slot, all in a single request. Only the counts grow — the rule vocabulary stays at the same nine types — and `violations` is recomputed rule by rule from the returned assignment, so zero still certifies that every declared rule holds together.", "also_solves": [ { "problem": "Line-maintenance rostering where a mechanic may only be assigned a task if the licensed certifying engineer is on the same shift", "domain": "Aviation MRO" }, { "problem": "Court listing where a trainee magistrate may only sit a session the presiding judge also sits", "domain": "Justice" }, { "problem": "Plant permit-to-work scheduling where valve work in a window is authorised only if the upstream isolation is tagged out in that window", "domain": "Energy" }, { "problem": "Shooting-day scheduling where a minor's call day is legal only if the on-set tutor and chaperone are booked that day", "domain": "Film and TV production" }, { "problem": "Port transit planning where a deep-draft transit in a tide window is permitted only if an escort tug is booked for that window", "domain": "Maritime ports" }, { "problem": "Site works sequencing where a concrete pour in a week is released only if the rebar inspection is booked that week", "domain": "Construction" } ], "shipped": { "n": 6, "assurance": "certified_optimal" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": { "n": 100000, "rules": 30000 }, "certainty": "certified", "engine_ms_median": 984.738, "runs": 3, "measured": true } }, { "id": "health_shift_coverage", "title": "Clinical Shift Coverage", "category": "Healthcare", "icon": "🩺", "tagline": "A squared penalty punishes surplus as hard as shortfall, so the floor is declared per element; the family size is an output, not an input.", "command": "cover", "min_cli": "1.0.0", "effort": "flash", "shape": "cover-the-requirements", "scales_to": "At 3,000 candidate patterns over 9,000 coverage requirements the identical encoding is 3,000 booleans, 3,000 covered-element lists, a 9,000-entry min_cover array of per-requirement demands and a 3,000-entry cost array, submitted as one request; because each candidate is chosen at most once, a pattern that may be staffed by several teams is listed as that many candidate rows, so the boolean count is the number of fillable slots rather than the number of distinct templates. Certification is proven by exhaustion and labelled per answer, so a roster that size returns a marked heuristic with `uncovered` naming exactly how many requirements are still short.", "also_solves": [ { "problem": "Conductor crew pairing where hazmat runs require a second qualified conductor", "domain": "Rail" }, { "problem": "Follow-the-sun on-call staffing where tier-1 payment blocks need two responders", "domain": "Software Operations" }, { "problem": "Harbour pilot duty patterns where LNG and deep-draft movements require two licensed pilots", "domain": "Maritime" }, { "problem": "Branch shift patterns where dual-control vault operations require two authorized staff", "domain": "Retail Banking" }, { "problem": "Steward deployment where the away-supporter segregation block needs two stewards", "domain": "Live Events" }, { "problem": "Engine and lookout staffing where red-flag districts need two crews on cover", "domain": "Wildland Fire" }, { "problem": "Court interpreter assignment where capital proceedings require team interpreting", "domain": "Court Administration" }, { "problem": "Ground-station pass coverage where commissioning windows need two stations", "domain": "Space Operations" } ], "shipped": { "n": 5, "assurance": "certified_optimal" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": { "elements": 12000, "sets": 4000, "incidences": 40408 }, "certainty": "heuristic (labelled)", "engine_ms_median": 872.33, "runs": 3, "measured": true } }, { "id": "logistics_container_incompat", "title": "Container Loading With Incompatible Goods", "category": "Logistics", "icon": "📦", "tagline": "Items are groups of variables, not variables, so keep-apart is one mutual_exclusion per container, never a single rule between two items.", "command": "rules", "min_cli": "1.0.0", "effort": "flash", "shape": "assignment-under-conflict", "scales_to": "The identical shape at 900 items and 40 containers is 900 x 40 = 36,000 binary variables and 3,340 rules in one request: 900 `choose_one` rules (one per item, over its 40 container variables), 40 `capacity_limit` rules, and one `mutual_exclusion` per container per forbidden pair (60 declared pairs x 40 containers = 2,400). Only the item-by-container product grows, not the rule types; `violations` is recounted rule by rule from the returned plan, so zero certifies that every separation and capacity rule holds at once.", "also_solves": [ { "problem": "Placing tenant virtual machines on hypervisor hosts under anti-affinity policies", "domain": "Cloud infrastructure" }, { "problem": "Loading unit load devices into aircraft holds under dangerous-goods segregation", "domain": "Air cargo" }, { "problem": "Assigning client accounts to trading desks across an information barrier", "domain": "Financial services" }, { "problem": "Allocating prisoners to wings under keep-apart orders", "domain": "Corrections" }, { "problem": "Scheduling product campaigns into shared bioreactor suites under cross-contamination rules", "domain": "Pharmaceutical manufacturing" }, { "problem": "Assigning inpatients to bays under infection-control separation", "domain": "Healthcare" } ], "shipped": { "n": 8, "assurance": "certified_optimal" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": { "n": 100000, "rules": 30000 }, "certainty": "certified", "engine_ms_median": 984.738, "runs": 3, "measured": true } }, { "id": "logistics_crossdock_hub", "title": "Cross-Dock Door Assignment", "category": "Logistics", "icon": "🏭", "tagline": "A bijection that prices closeness but cannot forbid it: one item per location; hard separations and shared locations move to `rules`.", "command": "qap", "min_cli": "1.0.0", "effort": "flash", "shape": "assignment-under-conflict", "scales_to": "A 90-door hub is the same request with two 90x90 matrices: 16,200 numbers, 4,005 unordered pairs on each side, and 8,010 flow-by-distance products in the objective, over one assignment out of 90! possible ones. Nothing about the encoding changes with n except the size of the two matrices, and each answer states its own certainty — certified below the exhaustion cap, explicitly heuristic above it.", "also_solves": [ { "problem": "Hospital department layout across a floor plan", "domain": "Healthcare facilities" }, { "problem": "Gate assignment for one departure bank at an airport", "domain": "Aviation" }, { "problem": "Slotting SKUs into pick faces by co-pick frequency", "domain": "Warehousing" }, { "problem": "Assigning reactive chemicals to storage bays that keep hazardous pairs apart", "domain": "Industrial safety" }, { "problem": "Assigning broadcast channels to the transmitters of a regional radio network", "domain": "Telecommunications spectrum planning" }, { "problem": "Slotting component reels into the feeder bank of a pick-and-place machine", "domain": "Electronics manufacturing" }, { "problem": "Assigning scenes to the days of a shooting schedule so cast standby is minimized", "domain": "Film and television production" }, { "problem": "Placing acts into the stage-and-time slots of a two-stage festival day", "domain": "Live events programming" }, { "problem": "Placing avionics boxes on the equipment panel of a satellite bus", "domain": "Spacecraft integration" }, { "problem": "Redistributing specialist companies across a city's firehouses", "domain": "Emergency services deployment" }, { "problem": "Seating orchestra sections on the risers of a concert platform", "domain": "Performing arts" } ], "shipped": { "n": 4, "assurance": "certified_optimal" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": { "n": 200, "flow_entries": 40000, "dist_entries": 40000 }, "certainty": "heuristic (labelled)", "engine_ms_median": 25.992, "runs": 3, "measured": true } }, { "id": "logistics_last_mile", "title": "Last-Mile Delivery Route", "category": "Logistics", "icon": "🚚", "tagline": "Only `length` is the answer's real unit - reverse or rotate the order and it's the same optimum; a zero-cost dummy stop opens the loop.", "command": "tsp", "min_cli": "1.0.0", "effort": "flash", "shape": "sequence-over-costs", "scales_to": "The identical shape at 200 stops is one 200x200 integer matrix - 40,000 entries holding 19,900 distinct pairwise costs - and the answer is one order of 200 indices whose length is the sum of 200 look-ups around the closed sequence. The count of distinct closed orders over 200 items is 199!/2, so only the matrix grows, not the structure; the certainty label marks the order as proven by exhaustion or as a labelled heuristic you recheck with those same 200 look-ups.", "also_solves": [ { "problem": "Ordering a night's observing target list so total telescope slew between consecutive pointings is least", "domain": "Astronomy" }, { "problem": "Sequencing the drill hits of a printed-circuit-board panel so total head travel is least", "domain": "Electronics manufacturing" }, { "problem": "Ordering the locations a shooting unit visits in one production day so total unit-move distance is least", "domain": "Film and TV production" }, { "problem": "Ordering a batch of queued disk reads so total head travel across cylinders is least", "domain": "Storage systems" }, { "problem": "Ordering the closed contours a laser cutter or 3D printer traverses so total rapid travel between them is least", "domain": "Additive manufacturing" }, { "problem": "Ordering the orbital targets a servicing spacecraft visits so total delta-v is least", "domain": "Space systems" }, { "problem": "Ordering the sampling plots a soil crew covers in one field pass so total machine travel including headland turns is least", "domain": "Agriculture" } ], "shipped": { "n": 8, "assurance": "certified_optimal" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": { "n": 600, "matrix_entries": 360000 }, "certainty": "heuristic (labelled)", "engine_ms_median": 102.684, "runs": 3, "measured": true } }, { "id": "supply_bom_sourcing", "title": "Geopolitical Multi-Sourcing Rules", "category": "Logistics", "icon": "🌐", "tagline": "An if/then contract clause is one implication between two (item, option) variables; choose_one is all that stops zero or several picks.", "command": "rules", "min_cli": "1.0.0", "effort": "flash", "shape": "assignment-under-conflict", "scales_to": "The identical shape at 1,200 components with 12 approved options each is 14,400 binary variables and 1,200 `choose_one` rules, one per component over its 12 option variables. Every contractual if/then clause is exactly one `requires` over two (component, option) variables, so 3,000 clauses bring the request to 4,200 rules plus one `force_true` per decision already committed; `violations` is recomputed clause by clause from the returned plan, and zero certifies that all of them hold together.", "also_solves": [ { "problem": "Placing reinsurance layers with carriers where taking one carrier on a layer obliges a different carrier on the layer above", "domain": "Insurance" }, { "problem": "Vehicle build configuration where selecting the towing package obliges the heavy-duty alternator variant", "domain": "Automotive" }, { "problem": "Choosing a hosting jurisdiction per service where placing the data store in one jurisdiction obliges the audit-log service into the matching one", "domain": "Data residency" }, { "problem": "Assigning a fuel contract type per generating unit where taking spot supply at one plant obliges a fixed-price contract at its paired plant", "domain": "Energy" }, { "problem": "Assigning a release window per territory where licensing a title to one platform obliges a holdback window in the paired territory", "domain": "Media rights" }, { "problem": "Booking each trade to a legal entity where booking a swap to the EU entity obliges an EU-authorised clearing route", "domain": "Banking" } ], "shipped": { "n": 6, "assurance": "certified_optimal" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": { "n": 100000, "rules": 30000 }, "certainty": "certified", "engine_ms_median": 984.738, "runs": 3, "measured": true } }, { "id": "telecom_band_assignment", "title": "Interference-Aware Band Assignment", "category": "Telecom", "icon": "📡", "tagline": "A cost paid only when a pair shares a bucket inverts: maximize the cut, minimize the cost — what you pay is total weight minus cut_value.", "command": "maxcut", "min_cli": "1.0.0", "effort": "flash", "shape": "partition-into-two", "scales_to": "The identical shape at 1,200 transmitters is one edge per interfering pair: 18,000 [i, j, cost] triples when each unit interferes with 30 others, 719,400 for the full pairwise matrix, and the answer is still one band bit per transmitter. The residual co-band cost stays a single subtraction, total edge weight - cut_value, over those same weights; the certainty label states per answer whether the split was exhausted and proven or returned as a labelled heuristic.", "also_solves": [ { "problem": "Splitting a departure bank between two runways so pairs that need wake-turbulence separation do not share a runway", "domain": "Aviation" }, { "problem": "Distributing reagents between two storage cabinets so incompatible chemicals are never stored together", "domain": "Laboratory safety" }, { "problem": "Placing spots into the two ad pods of one commercial break so directly competing brands never run in the same pod", "domain": "Advertising" }, { "problem": "Allocating admitted patients to two ward bays so pairs carrying a cross-transmission risk are not housed together", "domain": "Healthcare" }, { "problem": "Splitting an exam cohort into two sittings so candidates with a collusion risk do not sit at the same time", "domain": "Education" }, { "problem": "Placing a deal team on the two sides of an information barrier so conflicted individuals never share a side", "domain": "Legal" }, { "problem": "Drawing a tournament field into two pools so entrants from the same club or nation avoid an early clash", "domain": "Sports" } ], "shipped": { "n": 6, "assurance": "certified_optimal" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": { "n": 8000, "edges": 80000 }, "certainty": "heuristic (labelled)", "engine_ms_median": 5774.875, "runs": 3, "measured": true } }, { "id": "assembly_kit_partition", "title": "Assembly Kit Exact Partition", "category": "Manufacturing", "icon": "🧰", "tagline": "Inverted encoding: the booleans are the kits, one exactly-once rule lives on every part — the rules sit on the universe, not on the sets.", "command": "rules", "min_cli": "1.0.0", "effort": "flash", "shape": "cover-the-requirements", "scales_to": "The identical shape at 20,000 candidate sets covering 6,000 required elements is 20,000 binary variables and 6,000 `choose_exactly` k=1 rules — one per element, never one per set — whose node lists together carry one entry per (set, element) membership: at 8 elements per set that is 160,000 references in a single request. Raising k to 2 states doubled coverage without adding a variable, and `violations` is recounted element by element from the returned selection, so zero certifies a partition with no element short and none double-covered.", "also_solves": [ { "problem": "Crew pairing where every scheduled flight leg is flown by exactly one selected pairing", "domain": "Aviation" }, { "problem": "Redistricting where every precinct falls inside exactly one adopted district", "domain": "Government" }, { "problem": "Ad inventory packaging where every sellable slot is sold inside exactly one package", "domain": "Advertising" }, { "problem": "Technology mapping where every node of a logic netlist is covered by exactly one library-cell match", "domain": "Semiconductor design" }, { "problem": "Polyomino tiling and Sudoku, where every cell is filled by exactly one placement", "domain": "Puzzles and games" }, { "problem": "Cash application where every open invoice is cleared by exactly one remittance batch", "domain": "Accounting" } ], "shipped": { "n": 5, "assurance": "certified_optimal" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": { "n": 100000, "rules": 30000 }, "certainty": "certified", "engine_ms_median": 984.738, "runs": 3, "measured": true } }, { "id": "paint_shop_sequencing", "title": "Paint-Shop Batch Sequencing", "category": "Manufacturing", "icon": "🎨", "tagline": "Put 0 on every same-class pair and batching stops being a rule you enforce - the cost matrix is any changeover, not a distance.", "command": "tsp", "min_cli": "1.0.0", "effort": "flash", "shape": "sequence-over-costs", "scales_to": "The identical shape at 120 bodies is a 120x120 integer matrix - 14,400 entries covering 7,140 distinct job pairs - but it is generated rather than typed: with 12 colors the whole matrix comes from a 12x12 changeover table, 66 distinct color-pair costs plus 0 on every same-color pair. The answer is one order of 120 job indices and length is the sum of 120 look-ups around the closed sequence, so only the matrix grows, not the structure; certification is reported per answer, and above the exact cap the order arrives labelled as a heuristic whose length you recompute from those same look-ups.", "also_solves": [ { "problem": "Sequencing product campaigns on a shared tablet line so total cleaning-validation effort between consecutive products is least", "domain": "Pharmaceutical manufacturing" }, { "problem": "Sequencing flavour runs on a filling line so the total product flushed at changeovers is least", "domain": "Food and beverage" }, { "problem": "Ordering the segments of a studio rundown so total set, lighting and camera reconfiguration between consecutive segments is least", "domain": "Broadcast media" }, { "problem": "Ordering an operating room's elective case list so total instrument-tray and room turnover between consecutive cases is least", "domain": "Healthcare" }, { "problem": "Ordering coils in a hot-rolling campaign so total width-jump and grade-change cost between consecutive coils is least", "domain": "Steel and metals" }, { "problem": "Ordering a CI suite's test classes so total fixture teardown and rebuild between consecutive tests is least", "domain": "Software delivery" }, { "problem": "Ordering an LC-MS sample batch so total column re-equilibration between consecutive methods is least", "domain": "Analytical chemistry" } ], "shipped": { "n": 8, "assurance": "certified_optimal" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": { "n": 600, "matrix_entries": 360000 }, "certainty": "heuristic (labelled)", "engine_ms_median": 102.684, "runs": 3, "measured": true } }, { "id": "legal_contract_consistency", "title": "Contract & Policy Consistency Check", "category": "Legal", "icon": "⚖️", "tagline": "The answer's unit is a count of clauses that must give, not a yes/no: zero means consistent, a certified count is the smallest fix.", "command": "rules", "min_cli": "1.0.0", "effort": "flash", "shape": "satisfy-declared-rules", "scales_to": "The identical shape at 40,000 extracted clause terms is 40,000 binary variables, and each declared relation costs exactly one rule rather than a term-by-term product: 12,000 `mutual_exclusion` contradictions, 9,000 `requires` implications, 400 `choose_one` families and 5,000 `force_true` assertions total 26,400 rules in a single request. Zero `violations` certifies that all 26,400 can hold at once; a positive count is how many rules the returned assignment breaks, and the per-answer certainty label says how to read it — labelled certified, that count is the proven minimum; labelled heuristic, it is an upper bound on the minimum, tightest when every rule is pairwise so a single miss can only cost one.", "also_solves": [ { "problem": "Auditing an access-policy bundle for allow and deny statements that contradict on the same principal", "domain": "Cybersecurity" }, { "problem": "Polypharmacy review asking whether every guideline-recommended drug can be prescribed together", "domain": "Healthcare" }, { "problem": "Machine safety interlock audit asking whether every declared interlock can hold in one control program", "domain": "Industrial automation" }, { "problem": "Collective-agreement audit asking whether a proposed shift pattern satisfies every union clause", "domain": "Labour relations" }, { "problem": "Planning-condition audit asking whether one design can meet every condition attached to a permission", "domain": "Real estate development" }, { "problem": "Branching-narrative state audit asking whether every declared world-state flag can hold at one save point", "domain": "Game development" } ], "shipped": { "n": 6, "assurance": "certified_optimal" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": { "n": 100000, "rules": 30000 }, "certainty": "certified", "engine_ms_median": 984.738, "runs": 3, "measured": true } }, { "id": "cat_item_selection", "title": "Adaptive Test Item Selection", "category": "Education", "icon": "📝", "tagline": "Exposure control and content balance aren't extra constraints — both are the same pairwise penalty, so one overlap matrix buys you both.", "command": "select", "min_cli": "1.0.0", "effort": "flash", "shape": "choose-k-of-m", "scales_to": "The identical encoding at a 3,000-item bank with a 25-item form is 3,000 affinity values and up to 4,498,500 distinct pairwise penalties (a 9,000,000-entry symmetric matrix) in one request whose field list is unchanged: m, k, affinity, redundancy. The selected count is exactly 25 at any size, while certification is proven by exhaustion and is stated per answer, so a bank this large returns a labelled heuristic rather than a silent claim of optimality.", "also_solves": [ { "problem": "Choose 30 of 500 screened investigator sites for a phase III protocol where sites drawing on the same referral catchment compete for the same patients", "domain": "Pharma / Clinical trials" }, { "problem": "Pick 6 of 120 screened applicants for an onsite loop so the shortlist spans distinct skill profiles rather than six near-copies", "domain": "Recruiting / HR" }, { "problem": "Pick the 5 opponent plays to drill in one practice block from 200 filmed plays when several plays exercise the same defensive read", "domain": "Sports analytics" }, { "problem": "Choose 20 of 400 wastewater sampling points for a pathogen surveillance network where points on one trunk sewer sample the same population", "domain": "Public health surveillance" }, { "problem": "Select 8 of 150 drafted survey questions for a short instrument where several questions load on the same latent construct", "domain": "Market research" }, { "problem": "Pick 12 of 300 wafer test patterns for a production screen when patterns sensitize the same fault set", "domain": "Semiconductor test" }, { "problem": "Choose 4 of 60 approved simulator scenarios for a recurrent check when scenarios exercise the same failure mode", "domain": "Aviation training" }, { "problem": "Pick 5 of 90 authored quests for a weekly event rotation when quests reuse the same zone and reward loop", "domain": "Game live-ops" } ], "shipped": { "n": 8, "assurance": "certified_optimal" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": { "m": 2000, "k": 80, "redundancy_pairs": 20000 }, "certainty": "heuristic (labelled)", "engine_ms_median": 4.924, "runs": 3, "measured": true } }, { "id": "edtech_curriculum_path", "title": "Adaptive Curriculum Sequencing", "category": "Education", "icon": "🎓", "tagline": "Do not list the plan: force the goal only — its requires closure is implied, and the count cap decides whether that closure fits.", "command": "rules", "min_cli": "1.0.0", "effort": "flash", "shape": "satisfy-declared-rules", "scales_to": "The identical shape at 2,000 modules and 5,000 prerequisite links is 2,000 booleans, 5,000 `requires` rules, one `capacity_limit` over all 2,000 nodes and one `force_true` per goal — 5,002 rules in a single request, with the rule vocabulary unchanged from the 6-variable instance. Only the counts grow: a returned violations count of 0 certifies the plan breaks none of the declared rules, and a positive count identifies the budget as smaller than the forced prerequisite closure rather than reporting a silent guess.", "also_solves": [ { "problem": "Choosing which packages go into a hardened container base image when each package pulls in its declared dependencies", "domain": "Software supply chain" }, { "problem": "Scoping the minimum control set that closes a named audit finding this quarter", "domain": "Security compliance" }, { "problem": "Validating a configure-price-quote order for a machine with option interdependencies", "domain": "Industrial manufacturing" }, { "problem": "Assembling a pre-operative workup that fits the appointments available before the operating date", "domain": "Healthcare delivery" }, { "problem": "Selecting which assembly, integration and test activities fit one cleanroom campaign before a shipment readiness review", "domain": "Aerospace" }, { "problem": "Scoping a capital works programme where projects depend on enabling infrastructure", "domain": "Public infrastructure" }, { "problem": "Planning a plasmid construct build where each construct depends on its intermediates", "domain": "Biotech laboratory" }, { "problem": "Auto-generating a skill-tree build that reaches a target ability within the points the level grants", "domain": "Game systems" } ], "shipped": { "n": 6, "assurance": "certified_optimal" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": { "n": 100000, "rules": 30000 }, "certainty": "certified", "engine_ms_median": 984.738, "runs": 3, "measured": true } }, { "id": "finance_portfolio", "title": "Portfolio Selection", "category": "Finance", "icon": "📈", "tagline": "Every reward is a negative weight and every correlation a positive pair penalty, so concentration is priced without any 'pick k' rule.", "command": "optimize", "min_cli": "1.0.0", "effort": "flash", "shape": "subset-with-pairwise-interaction", "scales_to": "The identical shape at 1,500 assets is 1,500 linear terms and, if every pair carries a penalty, 1,124,250 quadratic terms submitted as one request; real covariance inputs are thresholded, so keeping only the strongest 2% of pairs sends about 22,485 pair terms instead. Nothing about the structure changes with n — only how many numbers it holds — and the per-answer certainty label states whether the result was certified by exhaustion or is a heuristic to recompute with the free verify call.", "also_solves": [ { "problem": "Media mix: choosing which paid channels to fund when two channels reach the same audience", "domain": "Advertising" }, { "problem": "Feature selection for a credit scorecard whose predictors are multicollinear", "domain": "Machine learning" }, { "problem": "Choosing which drug programs to fund when two share a biological target and fail together", "domain": "Pharmaceutical R&D" }, { "problem": "Siting wind farms when neighbouring sites generate and idle together", "domain": "Energy" }, { "problem": "Selecting reinsurance treaties when two treaties are exposed to the same catastrophe peril", "domain": "Insurance" }, { "problem": "Choosing which exploration targets to drill when two test the same geological model", "domain": "Mining and exploration" }, { "problem": "Awarding a grant round when two proposals duplicate the same line of work", "domain": "Research funding" }, { "problem": "Choosing store sites when two locations draw on the same catchment", "domain": "Retail" } ], "shipped": { "n": 8, "assurance": "certified_optimal" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": { "n": 20000, "linear_terms": 20000, "quadratic_terms": 200000 }, "certainty": "heuristic (labelled)", "engine_ms_median": 111.956, "runs": 3, "measured": true } }, { "id": "finance_settlement_netting", "title": "Settlement Netting Under Collateral Clashes", "category": "Finance", "icon": "🏦", "tagline": "A forbidden pair is one positive weight larger than the smaller reward it guards; the settled value is minus the returned energy.", "command": "optimize", "min_cli": "1.0.0", "effort": "flash", "shape": "subset-with-pairwise-interaction", "scales_to": "A book of 5,000 transactions is 5,000 linear terms plus exactly one quadratic term per forbidden pair — conflicts are sparse, so 12,000 recorded clashes send 12,000 pair terms rather than the 12,497,500 a dense matrix would hold. The big-M rule is scale-free (each penalty only has to outweigh the smaller reward in the pair it guards, never a function of n), and each answer carries a certainty label saying whether it was certified by exhaustion or is a heuristic whose chosen pairs should be re-checked with the free verify call.", "also_solves": [ { "problem": "Filling a commercial break when two advertisers hold exclusivity against each other", "domain": "Broadcast media" }, { "problem": "Choosing which elective cases take one theatre day when two need the same single robot at overlapping slots", "domain": "Hospital operations" }, { "problem": "Picking which satellite passes a ground station records when passes overlap on one antenna", "domain": "Space operations" }, { "problem": "Choosing which product batches run in one reactor campaign when two cross-contaminate", "domain": "Chemical manufacturing" }, { "problem": "Accepting client mandates under conflict-of-interest rules", "domain": "Legal services" }, { "problem": "Approving which maintenance outages run in one window when two jointly break N-1 security", "domain": "Electric utility" }, { "problem": "Releasing orders into one pick wave when two orders claim the last unit of a SKU", "domain": "E-commerce fulfillment" }, { "problem": "Allocating one night of telescope time among competing observing proposals", "domain": "Astronomy" } ], "shipped": { "n": 6, "assurance": "certified_optimal" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": { "n": 20000, "linear_terms": 20000, "quadratic_terms": 200000 }, "certainty": "heuristic (labelled)", "engine_ms_median": 111.956, "runs": 3, "measured": true } }, { "id": "bio_biomarker_panel", "title": "Biomarker Panel Selection", "category": "Biotech", "icon": "🧬", "tagline": "The value returned is signal minus redundancy paid, so a weaker uncorrelated marker can outrank a stronger one that duplicates a pick.", "command": "select", "min_cli": "1.0.0", "effort": "flash", "shape": "choose-k-of-m", "scales_to": "The identical encoding at 2,500 candidate markers with a 20-slot panel is 2,500 affinity values and up to 3,123,750 distinct pairwise penalties (a 6,250,000-entry symmetric matrix), carried in one request still described by m, k, affinity, redundancy. Certification is proven by exhaustion and is stated on every answer, so at this size the result carries the heuristic label, while the returned panel contains exactly 20 markers.", "also_solves": [ { "problem": "Choose 15 of 800 factor signals for a live trading model where factors built on one data source explain the same return", "domain": "Finance" }, { "problem": "Pick 30 of 1,200 substation PMU locations for a state-estimation network when units on the same bus observe the same state", "domain": "Energy / grid" }, { "problem": "Choose 8 of 140 durability road-test routes for a validation programme when two routes load the chassis the same way", "domain": "Automotive" }, { "problem": "Pick 6 of 90 wheat breeding lines to advance to multi-location yield trials when lines from one cross carry the same trait package", "domain": "Agriculture" }, { "problem": "Choose 12 of 400 spectral bands for a hyperspectral crop-stress product when adjacent bands carry the same reflectance information", "domain": "Earth observation" }, { "problem": "Select 9 of 300 online analyzer measurements as inputs to an advanced process control model when analyzers on one column tray move together", "domain": "Chemicals / process" }, { "problem": "Pick 25 of 600 hydrant and junction nodes for pressure-logger deployment when loggers in one district metered area record the same transient", "domain": "Water utility" }, { "problem": "Choose 16 of 500 candidate alloy compositions for a synthesis campaign when compositions near each other test the same hypothesis", "domain": "Materials R&D" } ], "shipped": { "n": 12, "assurance": "certified_optimal" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": { "m": 2000, "k": 80, "redundancy_pairs": 20000 }, "certainty": "heuristic (labelled)", "engine_ms_median": 4.924, "runs": 3, "measured": true } }, { "id": "bio_epistasis_triple", "title": "Three-Way Epistasis Reduction", "category": "Biotech", "icon": "🧬", "tagline": "An auxiliary means 'A and B both on', so a three-way reward rides on one pair; the gadget scores 0, so energy is the true 3-body value.", "command": "optimize", "min_cli": "1.0.0", "effort": "flash", "shape": "subset-with-pairwise-interaction", "scales_to": "Each three-way term costs exactly one auxiliary variable, one linear entry and four quadratic entries (three for the gadget, one for the reward), so 200 real decisions carrying 500 declared triples submit as n=700 with 700 linear entries and 2,000 quadratic entries. A k-way term chains to k-2 auxiliaries, k-2 linear entries and 3(k-2)+1 quadratic entries — a five-way term is 3 auxiliaries and 10 quadratic entries — and because auxiliaries count toward n, they count toward whether the answer comes back certified by exhaustion or labelled heuristic.", "also_solves": [ { "problem": "Choosing dopants for a catalyst whose activity only appears with one ternary combination", "domain": "Materials science" }, { "problem": "Selecting process changes when a yield gain only appears if three ship together", "domain": "Semiconductor manufacturing" }, { "problem": "Fitting avionics channels when a certification credit requires three dissimilar channels together", "domain": "Aerospace" }, { "problem": "Planning an intercropped plot where the yield bonus needs all three species", "domain": "Agriculture" }, { "problem": "Choosing security controls when an audit clause only credits three deployed together", "domain": "Security and compliance" }, { "problem": "Choosing pipe segments to renew when pressure only recovers if all three in the corridor are replaced", "domain": "Water infrastructure" }, { "problem": "Composing a field crew when the job is only billable with all three certifications present", "domain": "Field service" }, { "problem": "Buying software modules when a rebate only unlocks on a three-module bundle", "domain": "Enterprise procurement" } ], "shipped": { "n": 4, "assurance": "certified_optimal" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": { "n": 20000, "linear_terms": 20000, "quadratic_terms": 200000 }, "certainty": "heuristic (labelled)", "engine_ms_median": 111.956, "runs": 3, "measured": true } }, { "id": "bio_therapy_coverage", "title": "Resistance Pathway Coverage", "category": "Biotech", "icon": "💊", "tagline": "Hitting set is set cover read from the other side: list what each candidate covers. Pinned and barred are parameters, not costs.", "command": "cover", "min_cli": "1.0.0", "effort": "flash", "shape": "cover-the-requirements", "scales_to": "At 1,500 candidate agents over 6,000 requirements the identical encoding is 1,500 booleans, 1,500 covered-element lists, one min_cover integer (or a 6,000-entry array of per-requirement demands) and a 1,500-entry cost array; `force` and `forbid` are index lists that subtract from the undecided set rather than add terms, so pinning 200 candidates and excluding 300 leaves 1,000 free booleans in the same request. Certainty is labelled per answer and certification is proven by exhaustion, so an instance that size returns a marked heuristic, and `total_cost` still carries the forced candidates at their real price.", "also_solves": [ { "problem": "Fortification blend covering every declared micronutrient with the mandated fortificant locked in and an allergen-bearing premix excluded", "domain": "Food Science" }, { "problem": "Cryptographic suite covering every protocol requirement with the mandated primitive forced in and a deprecated cipher excluded", "domain": "Cryptography" }, { "problem": "Newborn screening panel covering every notifiable condition with the statutory assay forced in and a withdrawn kit excluded", "domain": "Public Health" }, { "problem": "Homologation lab selection covering every market regulation with the captive emissions lab forced in and a de-accredited lab excluded", "domain": "Automotive" }, { "problem": "Ancillary service procurement covering every reliability product with a must-run unit forced in and an outaged unit excluded", "domain": "Power Markets" }, { "problem": "Translation vendor selection covering every target locale with the legal-terminology vendor forced in and one excluded by data residency", "domain": "Localization" }, { "problem": "Region set covering every residency and recovery requirement with the contracted primary region forced in and a sovereignty-barred region excluded", "domain": "Cloud Infrastructure" } ], "shipped": { "n": 6, "assurance": "certified_optimal" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": { "elements": 12000, "sets": 4000, "incidences": 40408 }, "certainty": "heuristic (labelled)", "engine_ms_median": 872.33, "runs": 3, "measured": true } }, { "id": "conservation_reserve", "title": "Conservation Reserve Selection", "category": "Sustainability", "icon": "🌱", "tagline": "Overlap is a penalty on the pair, so a negative entry rewards adjacency instead — one matrix expresses both spread-out and clustered picks.", "command": "select", "min_cli": "1.0.0", "effort": "flash", "shape": "choose-k-of-m", "scales_to": "The identical encoding at 4,000 candidate parcels with 120 protected is 4,000 affinity values and up to 7,998,000 distinct pair penalties (a 16,000,000-entry symmetric matrix) in a single request, with the same four fields: m, k, affinity, redundancy. Certification is proven by exhaustion and is labelled on the answer, so an instance this size returns a stated heuristic while the chosen count remains exactly 120.", "also_solves": [ { "problem": "Choose 30 of 700 available sites for a new store network where two sites inside one drive-time isochrone draw the same customers", "domain": "Retail real estate" }, { "problem": "Select 25 of 400 candidate park-and-ride lots where two lots on one corridor capture the same commuters", "domain": "Public transit" }, { "problem": "Choose 40 of 900 planned drill collars for a season when collars inside one hole spacing test the same ore block", "domain": "Mining / exploration" }, { "problem": "Pick 14 of 220 candidate radar sites for an air-surveillance network where sites with overlapping lobes watch the same volume", "domain": "Defense / ISR" }, { "problem": "Choose 12 of 180 city blocks for a street-tree planting round where adjacent blocks relieve the same heat-island cell", "domain": "Municipal government" }, { "problem": "Select 9 of 130 candidate fire-station relocations where two stations inside one response-time contour reach the same incidents", "domain": "Public safety" }, { "problem": "Pick 22 of 350 candidate edge PoP cities where two PoPs on one transit path serve the same users", "domain": "Cloud infrastructure" }, { "problem": "Choose 14 of 200 candidate depot locations for cyclone pre-positioning where two depots inside one road-access window supply the same districts", "domain": "Humanitarian logistics" } ], "shipped": { "n": 8, "assurance": "certified_optimal" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": { "m": 2000, "k": 80, "redundancy_pairs": 20000 }, "certainty": "heuristic (labelled)", "engine_ms_median": 4.924, "runs": 3, "measured": true } }, { "id": "recycling_line_dispatch", "title": "Recycling Line Dispatch & Sizing", "category": "Sustainability", "icon": "♻️", "tagline": "No slack variable for off-means-zero: linear +38 per tonne, binary×tonnage pair −50, so an idle line pays 38 a tonne and snaps to 0.", "command": "milp", "min_cli": "1.0.0", "effort": "flash", "shape": "mixed-integer-with-continuous", "scales_to": "The identical shape at 200 candidate units is 400 variables (one binary and one bounded continuous each), 400 `linear` coefficients, 200 `diag` curvature entries, 200 on/off link pairs and C(200,2) = 19,900 cross terms — 20,100 quadratic triples in one request, over 2^200 on/off patterns. Only the counts grow; the four term families do not. `milp` labels the answer heuristic, so with the returned binaries held fixed the remaining continuous part is convex and you re-derive its optimum yourself to confirm.", "also_solves": [ { "problem": "Unit commitment for a peaking generator fleet over one dispatch interval", "domain": "Energy" }, { "problem": "Splitting a large parent order across execution venues under market impact", "domain": "Finance" }, { "problem": "Which pumps to start and their flow setpoints on a shared trunk main", "domain": "Utilities (Water)" }, { "problem": "Which carriers to bring into service on a cell site and at what transmit power", "domain": "Telecom" }, { "problem": "Channel budget allocation where two channels reach the same audience", "domain": "Marketing" }, { "problem": "Autoscaling an inference pool across instance types sharing one rack power budget", "domain": "Cloud infrastructure" }, { "problem": "Which batch reactors to charge and at what batch rate", "domain": "Chemicals" }, { "problem": "Which pits to mobilise and how many tonnes to haul from each to one concentrator", "domain": "Mining" } ], "shipped": { "n": 4, "assurance": "heuristic" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": { "binary_vars": 1500, "continuous_vars": 1500, "quadratic_terms": 12000 }, "certainty": "heuristic (labelled)", "engine_ms_median": 36.502, "runs": 3, "measured": true } }, { "id": "robotics_balance_jettison", "title": "Counterweight Jettison & Balance", "category": "Robotics", "icon": "⚖️", "tagline": "An equality becomes (Σaᵢxᵢ − T)² in the objective: cross terms 2aᵢaⱼ to quadratic, a²y² doubled into diag, binary a²x² into linear.", "command": "milp", "min_cli": "1.0.0", "effort": "flash", "shape": "mixed-integer-with-continuous", "scales_to": "The identical shape at 60 discrete items, 3 continuous trims and 2 target equalities is 63 variables: 60 `linear` entries (each binary's a_i^2 x_i^2 collapses there because x^2 = x), 3 `diag` entries, and at most C(60,2) = 1,770 binary-binary + 60x3 = 180 binary-continuous + C(3,2) = 3 continuous-continuous = 1,953 quadratic pairs. A second equality adds no new pairs — its coefficients are summed into the same 1,953 — so the request grows with the item count, not with the number of targets. `milp` labels this heuristic: a zero balance term in the returned objective is the statement that the equality is met exactly, and you re-derive the continuous optimum for the returned pattern and its one-flip neighbours to confirm.", "also_solves": [ { "problem": "Trimming a spacecraft's mass properties before a burn", "domain": "Aerospace" }, { "problem": "Meeting a truck's axle-load split by choosing pallets to leave behind and setting the sliding tandem", "domain": "Logistics" }, { "problem": "Rebalancing a book to zero net factor exposure", "domain": "Finance" }, { "problem": "Blending a scrap charge to an exact alloy specification", "domain": "Metals" }, { "problem": "Trimming an analog network to a target conductance", "domain": "Electronics" }, { "problem": "Placing balance weights on a rotor", "domain": "Rotating machinery" } ], "shipped": { "n": 3, "assurance": "heuristic" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": { "binary_vars": 1500, "continuous_vars": 1500, "quadratic_terms": 12000 }, "certainty": "heuristic (labelled)", "engine_ms_median": 36.502, "runs": 3, "measured": true } }, { "id": "robotics_cell_layout", "title": "Robotic Cell Layout", "category": "Robotics", "icon": "🤖", "tagline": "\"Distance\" is any number per pair of places - pocket index cost, acoustic delay in ms, spectral overlap; the answer stays one-to-one.", "command": "qap", "min_cli": "1.0.0", "effort": "flash", "shape": "assignment-under-conflict", "scales_to": "The same two matrices at 45 machines and 45 stations hold 2,025 entries each — 4,050 numbers in one request, 990 unordered station pairs — and the layout cost sums 1,980 flow-by-distance products over one permutation out of 45! possible ones. The fields are identical to the 5-machine instance; only n moves. Each answer carries its own certainty label, which states whether the optimum was proven by exhaustion.", "also_solves": [ { "problem": "Tool-magazine pocket assignment on a CNC machining center", "domain": "Machining" }, { "problem": "Keyboard layout for a language corpus", "domain": "Human-computer interaction" }, { "problem": "PCB component placement for the shortest total trace length", "domain": "Electronics hardware" }, { "problem": "Assigning signal groups to package balls to keep crosstalk-prone pairs apart", "domain": "Semiconductor packaging" }, { "problem": "Landmark correspondence between two 3-D scans", "domain": "Computer vision" }, { "problem": "Placing each airline's gate block along an airport concourse", "domain": "Airport operations" }, { "problem": "Laying out seed-trial varieties across a grid of field plots so cross-pollinating pairs sit far apart", "domain": "Agronomy and plant breeding" }, { "problem": "Assigning transmitters in a dense cell cluster to the channel slots of a fixed plan, one slot each", "domain": "Wireless network planning" }, { "problem": "Seating the orchestra's sections on the risers of a concert shell", "domain": "Performing arts and live sound" }, { "problem": "Shelving closed-stack collections in a repository so a day's paging run walks the least", "domain": "Libraries and archives" }, { "problem": "Assigning outbound blocks to classification tracks in a rail hump yard", "domain": "Rail freight operations" } ], "shipped": { "n": 5, "assurance": "certified_optimal" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": { "n": 200, "flow_entries": 40000, "dist_entries": 40000 }, "certainty": "heuristic (labelled)", "engine_ms_median": 25.992, "runs": 3, "measured": true } }, { "id": "robotics_fleet_pathing", "title": "Warehouse Fleet Path De-confliction", "category": "Robotics", "icon": "🤖", "tagline": "One boolean per (agent, cell, tick); excluding non-adjacent cell pairs across consecutive ticks leaves 'wait or move to a neighbour'.", "command": "rules", "min_cli": "1.0.0", "effort": "flash", "shape": "assignment-under-conflict", "scales_to": "The identical shape for 12 agents on a 150-cell floor over a 6-step rolling horizon is 12 × 150 × 6 = 10,800 booleans and 12 × 6 = 72 `choose_one` rules; shared-cell conflicts add 6 × 150 × C(12,2) = 59,400 exclusions, and the motion rules add one exclusion per agent, per consecutive step pair, per non-adjacent cell pair — the term that dominates the count, which is why the horizon is kept to a few steps and resubmitted as the fleet advances. The structure is byte-for-byte the same grammar as the 32-variable junction; a violations count of 0 certifies the whole joint plan rather than one agent's path.", "also_solves": [ { "problem": "Meet-and-pass planning for two trains on a single-track branch line with passing loops", "domain": "Rail operations" }, { "problem": "Dispatching two elevator cars that share one shaft without letting them close on each other", "domain": "Building systems" }, { "problem": "Sequencing wafer lots through a cluster tool so the handler never double-books a chamber", "domain": "Semiconductor manufacturing" }, { "problem": "Transit scheduling through one-way canal reaches with passing bays", "domain": "Maritime operations" }, { "problem": "Camera and crane blocking for a live studio running order", "domain": "Broadcast production" }, { "problem": "Building a slotframe schedule for a time-slotted industrial wireless mesh", "domain": "Industrial networking" }, { "problem": "Charting a marching-band drill so no two performers land on the same field position", "domain": "Live performance" }, { "problem": "De-conflicting haul trucks in a single-lane underground decline with cut-outs", "domain": "Mining" } ], "shipped": { "n": 32, "assurance": "certified_optimal" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": { "n": 100000, "rules": 30000 }, "certainty": "certified", "engine_ms_median": 984.738, "runs": 3, "measured": true } }, { "id": "world_terrain_oracle", "title": "Deterministic Terrain Oracle", "category": "Robotics", "icon": "⌖", "tagline": "A seeded terrain point returns a height and normal that can be finite-difference checked.", "command": "world", "min_cli": "1.0.0", "effort": "flash", "shape": "verified-scientific-operation", "scales_to": null, "also_solves": [ { "problem": "Robot foothold query", "domain": "Robotics" }, { "problem": "Game-world level-of-detail probe", "domain": "Gaming" }, { "problem": "Synthetic terrain regression", "domain": "Simulation" } ], "shipped": { "n": null, "assurance": "operation" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": null, "certainty": null, "engine_ms_median": null, "runs": null, "measured": false } }, { "id": "energy_known_ground_state", "title": "Known Coupled Ground State", "category": "Quantum & Physics", "icon": "E", "tagline": "A planted coupled system has a recomputable global energy floor.", "command": "feel", "min_cli": "1.0.0", "effort": "flash", "shape": "binary-energy", "scales_to": null, "also_solves": [ { "problem": "Binary material configuration", "domain": "Materials science" }, { "problem": "Coupled on/off policy", "domain": "Operations" }, { "problem": "Small Ising audit", "domain": "Physics" } ], "shipped": { "n": 8, "assurance": "certified_optimal" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": null, "certainty": null, "engine_ms_median": null, "runs": null, "measured": false } }, { "id": "physics_controlled_phase", "title": "Controlled Phase Hypothesis", "category": "Quantum & Physics", "icon": "φ", "tagline": "Phase output stays explicitly hypothetical and requests a boundary-condition check.", "command": "phase", "min_cli": "1.0.0", "effort": "flash", "shape": "scientific-hypothesis", "scales_to": null, "also_solves": [ { "problem": "SSH-chain screening", "domain": "Condensed-matter physics" }, { "problem": "Coupled-mode transition", "domain": "Photonics" }, { "problem": "Network regime indicator", "domain": "Systems science" } ], "shipped": { "n": null, "assurance": "heuristic" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": null, "certainty": null, "engine_ms_median": null, "runs": null, "measured": false } }, { "id": "quantum_error_decoder", "title": "Quantum Error-Correction Decoder", "category": "Quantum & Physics", "icon": "🧊", "tagline": "One boolean per pair, not per item: 'covered exactly once' expands to -M on each incident pairing and +2M wherever two share an item.", "command": "optimize", "min_cli": "1.0.0", "effort": "flash", "shape": "assignment-under-conflict", "scales_to": "Variables are candidate pairings, not items: 60 items with every pairing allowed is 1,770 booleans and 102,660 quadratic terms, because each item contributes C(59,2) = 1,711 mutually exclusive pairs of its own incident pairings. Candidate lists are normally gated by a distance cutoff, so keeping the six nearest partners per item sends roughly 180 booleans and 900 quadratic terms; the reported objective sits one M per item below the physical total, so add 60M back to read total weight, and the certainty label states whether that pairing was certified by exhaustion.", "also_solves": [ { "problem": "Kidney paired donation: choosing which two-way swaps to run", "domain": "Transplant medicine" }, { "problem": "Backhaul pairing: matching each outbound load with a return load so no truck runs empty", "domain": "Freight" }, { "problem": "Flip-flop banking: pairing single-bit registers into two-bit cells that share a clock driver", "domain": "Chip design" }, { "problem": "Building one round of fixtures so every team plays exactly once", "domain": "Sports league operations" }, { "problem": "Selective assembly: pairing shafts with bushings so each fitted clearance is closest to nominal", "domain": "Precision manufacturing" }, { "problem": "Data association: attaching this scan's detections to the existing tracks", "domain": "Radar and air-traffic tracking" }, { "problem": "Pairing officers into two-person patrol units for a roster", "domain": "Public safety" }, { "problem": "Assigning dormitory roommates from a compatibility survey", "domain": "Education" } ], "shipped": { "n": 6, "assurance": "certified_optimal" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": { "n": 20000, "linear_terms": 20000, "quadratic_terms": 200000 }, "certainty": "heuristic (labelled)", "engine_ms_median": 111.956, "runs": 3, "measured": true } }, { "id": "quantum_spin_spectrum", "title": "Spin Hamiltonian Spectrum", "category": "Quantum & Physics", "icon": "⚛️", "tagline": "Any symmetric matrix is a Hamiltonian: the answer is N levels, not 2^N states, and when the ground level is 0 the gap IS the connectivity.", "command": "spectrum", "min_cli": "1.0.0", "effort": "flash", "shape": "spectral-readout", "scales_to": "The identical shape at N = 800 is one symmetric matrix of 640,000 numbers — 320,400 of them independent — submitted as a single 2,160 KB request, and the answer is a ladder of exactly 800 levels with the lowest of them and the gap above it named. The response length is N, never 2^N: the readout is over the operator, not over its state space. It comes back as an operation result — optimality does not apply to a spectrum, and no independent proof is attached, so the check to run is det(H - lambda I) = 0. Two scoping facts follow from the shape: the matrix is dense, so all N^2 numbers are transmitted rather than only the upper triangle; and eigenVECTORS are not part of the response, so a question about WHICH state rather than which level is a different encoding.", "also_solves": [ { "problem": "Screening a structure's natural frequencies against a known forcing frequency", "domain": "Structural engineering" }, { "problem": "Molecular orbital levels of a conjugated ring", "domain": "Chemistry" }, { "problem": "Checking whether an estimated covariance matrix is usable before it drives an allocation", "domain": "Finance" }, { "problem": "Measuring how hard a network is to disconnect", "domain": "Network engineering" }, { "problem": "Conditioning a kernel/Gram matrix before it is inverted in a fit", "domain": "Machine learning" }, { "problem": "Whether a modelled ecological community returns to equilibrium after a shock", "domain": "Ecology" }, { "problem": "Locating a power network's slow inter-area oscillation modes", "domain": "Energy" } ], "shipped": { "n": 4, "assurance": "operation" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": { "n": 800, "matrix_entries": 640000 }, "certainty": "operation result", "engine_ms_median": 8151.937, "runs": 3, "measured": true } }, { "id": "science_known_entropy", "title": "Known Entropy Spectrum", "category": "Quantum & Physics", "icon": "∑", "tagline": "A diagonal correlation spectrum gives an independently recomputable entropy.", "command": "entropy", "min_cli": "1.0.0", "effort": "flash", "shape": "verified-scientific-operation", "scales_to": null, "also_solves": [ { "problem": "Entanglement entropy of a Gaussian subsystem", "domain": "Quantum information" }, { "problem": "Diversity of a two-class mixture", "domain": "Statistics" }, { "problem": "Information content of independent modes", "domain": "Signal processing" } ], "shipped": { "n": null, "assurance": "operation" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": null, "certainty": null, "engine_ms_median": null, "runs": null, "measured": false } }, { "id": "agtech_crop_rotation", "title": "Crop Rotation & Adjacency Planner", "category": "Agriculture", "icon": "🌱", "tagline": "One exclusion primitive stamped on two axes: adjacent plots in one season, consecutive seasons in one plot — space and time, same rule.", "command": "rules", "min_cli": "1.0.0", "effort": "flash", "shape": "assignment-under-conflict", "scales_to": "The identical lattice at 400 plots, 6 periods and 12 families is 400 × 6 × 12 = 28,800 booleans with 2,400 `choose_one` rules. On a 20 × 20 field there are 760 adjacent plot pairs, so each conflicting family costs 760 × 6 = 4,560 spatial exclusions, and each non-repeatable family costs 400 × 5 = 2,000 temporal exclusions — one exclusion per pair per axis, exactly as in the 18-variable instance. The rule vocabulary never changes with size, and a violations count of 0 certifies the whole board rather than one period of it.", "also_solves": [ { "problem": "Phased channel-group refarm across a cellular network without neighbour interference", "domain": "Telecom" }, { "problem": "Bay-level planogram theming across promotional cycles", "domain": "Retail" }, { "problem": "Stocking and fallowing plan for net pens on a shared mooring grid", "domain": "Aquaculture" }, { "problem": "Assigning firmware rollout waves to rack rows without exceeding a failure domain's blast radius", "domain": "Cloud infrastructure" }, { "problem": "Insecticide-class rotation across districts to delay vector resistance", "domain": "Public health" }, { "problem": "Adjacency-constrained harvest block scheduling under a green-up rule", "domain": "Forestry" }, { "problem": "Campaign allocation on parallel lines sharing an air-handling zone under allergen segregation", "domain": "Food and pharma manufacturing" }, { "problem": "Street-works permit windows under junction conflicts and a reinstatement moratorium", "domain": "Municipal works" } ], "shipped": { "n": 18, "assurance": "certified_optimal" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": { "n": 100000, "rules": 30000 }, "certainty": "certified", "engine_ms_median": 984.738, "runs": 3, "measured": true } }, { "id": "museum_exhibit_selection", "title": "Gallery Exhibit Selection", "category": "Culture", "icon": "🖼️", "tagline": "Conflicts are hard vetoes here, not prices — and without the exactly-k pin the empty set satisfies every one of them.", "command": "rules", "min_cli": "1.0.0", "effort": "flash", "shape": "satisfy-declared-rules", "scales_to": "The identical shape at 5,000 candidates, 40,000 conflict pairs and 300 shared-resource groups is 5,000 booleans, one `choose_exactly` over all 5,000 nodes, 40,000 `mutual_exclusion` rules and 300 `capacity_limit` rules — 40,301 rules in one request, the same four rule types as the 6-variable gallery. The declared cardinality k stays exact at any size; a violations count of 0 certifies the chosen k break no conflict and no shared-resource cap, and a positive count is the diagnosis that the conflict graph admits no k-set, not an engine fault.", "also_solves": [ { "problem": "Choosing which arms a site runs concurrently in a platform trial", "domain": "Clinical research" }, { "problem": "Assembling a reinsurance panel for one treaty layer", "domain": "Insurance" }, { "problem": "Loading one air-cargo deck under dangerous-goods segregation rules", "domain": "Air cargo" }, { "problem": "Selecting which subcontractor packages run inside one plant shutdown window", "domain": "Construction" }, { "problem": "Picking reagents for a one-pot combinatorial screen", "domain": "Chemistry" }, { "problem": "Seating a reviewer panel for a manuscript under a conflict-of-interest policy", "domain": "Scholarly publishing" }, { "problem": "Choosing which detection rules an endpoint agent enables within its rule budget", "domain": "Security engineering" }, { "problem": "Selecting guide RNAs for a multiplex edit", "domain": "Genomics" } ], "shipped": { "n": 6, "assurance": "certified_optimal" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": { "n": 100000, "rules": 30000 }, "certainty": "certified", "engine_ms_median": 984.738, "runs": 3, "measured": true } }, { "id": "energy_microgrid_islanding", "title": "Microgrid Fault Islanding Reflex", "category": "Energy", "icon": "⚡", "tagline": "Measured reality enters as force_false, not a preference; the requires chain then eliminates every mode that needed it, unlisted.", "command": "rules", "min_cli": "1.0.0", "effort": "flash", "shape": "satisfy-declared-rules", "scales_to": "The identical shape on a campus with 600 switchable elements and 40 four-mode assets is 600 + 160 = 760 booleans and 40 `choose_one` rules; with 1,500 documented preconditions, 200 shared-section pairs, 40 generation groups and 30 measured pins that is 1,810 rules submitted as one request, using the same seven rule types as the 8-variable instance. The rule file is fixed for the site — between events only the `force_true`/`force_false` pins change — and a violations count of 0 certifies the returned configuration breaks none of the declared rules, while a positive count names the over-constraint, such as a must-serve load with no admissible mode.", "also_solves": [ { "problem": "Isolating a district metered area after a trunk main bursts", "domain": "Water utilities" }, { "problem": "Choosing the safe state of a process unit after a compressor trip", "domain": "Oil and gas operations" }, { "problem": "Electrical reconfiguration and load shedding after an in-flight generator loss", "domain": "Aviation systems" }, { "problem": "Selecting a degraded drive configuration after an EV battery module isolates", "domain": "Automotive" }, { "problem": "Choosing an egress policy and traffic-class survival set after a transit circuit fails", "domain": "Network operations" }, { "problem": "Reconfiguring an operating-theatre suite after a chiller loss", "domain": "Hospital facilities" }, { "problem": "Switching a payment switch to degraded authorization after an acquirer link drops", "domain": "Payments infrastructure" }, { "problem": "Deciding which stations keep running after a robot cell faults on an assembly line", "domain": "Discrete manufacturing" } ], "shipped": { "n": 8, "assurance": "certified_optimal" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": { "n": 100000, "rules": 30000 }, "certainty": "certified", "engine_ms_median": 984.738, "runs": 3, "measured": true } }, { "id": "design_pinned_completion", "title": "Pinned Inverse Completion", "category": "Engineering", "icon": "◎", "tagline": "Pinned outputs remain fixed while the remaining variables minimize a recomputable objective.", "command": "want", "min_cli": "1.0.0", "effort": "flash", "shape": "binary-energy", "scales_to": null, "also_solves": [ { "problem": "Inverse material design", "domain": "Materials" }, { "problem": "Policy completion", "domain": "Operations" }, { "problem": "Boundary-conditioned model", "domain": "Physics" } ], "shipped": { "n": 8, "assurance": "certified_optimal" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": null, "certainty": null, "engine_ms_median": null, "runs": null, "measured": false } }, { "id": "game_procedural_map", "title": "Procedural Map Tile Consistency", "category": "Gaming", "icon": "🎮", "tagline": "A grammar rule is a template, not a constraint: stamp it on every adjacent pair in both directions, or unstamped pairs go unconstrained.", "command": "rules", "min_cli": "1.0.0", "effort": "flash", "shape": "satisfy-declared-rules", "scales_to": "The identical shape on a 128x128 chunk with 6 tile types is 98,304 booleans and 16,384 choose_one rules; its 32,512 four-neighbour cell pairs carry 65,024 mutual_exclusion rules for each forbidden label pair in the grammar (every pair stamped in both directions), plus one force_true per pinned cell and one capacity_limit per label quota — one request, same structure, larger numbers. Certification is reported per answer and is not decided by board size: a 100,000-boolean rule set carrying 30,000 rules has come back certified, so read the label the answer carries rather than assuming a bigger board must be a labelled heuristic.", "also_solves": [ { "problem": "Exam timetabling where two exams sharing a student cannot land in the same slot", "domain": "Education" }, { "problem": "Frequency assignment across transmitters with co-channel and adjacent-channel interference", "domain": "Telecom" }, { "problem": "Hazardous-goods bay layout where incompatible chemical classes may not occupy neighbouring bays", "domain": "Warehousing" }, { "problem": "Routing-layer assignment where two crossing nets cannot share a layer", "domain": "Electronics" }, { "problem": "Season planting plan where bordering parcels must not carry crops that bridge the same pest", "domain": "Agriculture" }, { "problem": "Register allocation where two simultaneously live values cannot share a physical register", "domain": "Compilers" }, { "problem": "Zoning a block where heavy industry may not abut residential without a commercial buffer", "domain": "Urban Planning" } ], "shipped": { "n": 18, "assurance": "certified_optimal" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": { "n": 100000, "rules": 30000 }, "certainty": "certified", "engine_ms_median": 984.738, "runs": 3, "measured": true } }, { "id": "music_key_modulation", "title": "Harmonic Modulation Planner", "category": "Music", "icon": "🎼", "tagline": "Choose one of K cyclic values per slot with the anchors pinned — the cost wraps, so value 11 sits next to value 0.", "command": "design", "min_cli": "1.0.0", "effort": "flash", "shape": "assignment-under-conflict", "scales_to": "The identical shape at 64 slots and 12 cyclic values is `L` = 64, `K` = 12, one bond per coupled pair (63 for a chain), a SINGLE number `j`, and one `bias` triple per anchor — over K^L = 12^64 assignments. The KxK cost is built from `j` at the far end and never transmitted, so raising K from 12 to 360 one-degree steps adds nothing at all to the request while taking the assignment count to 360^64; a hand-written `table` would have grown to 129,600 numbers to say the same thing. Certification is by exhaustion and is reported per answer, and `energy` is recomputable by summing floor(-j*1000*cos(2*pi*delta/K)+0.5) over the bonds plus each chosen bias.", "also_solves": [ { "problem": "Torsion-angle (rotamer) assignment on a flexible molecule", "domain": "Computational chemistry" }, { "problem": "Interleaving the switching phases of a multiphase converter", "domain": "Power electronics" }, { "problem": "A colorway across a garment's panels", "domain": "Product design" }, { "problem": "Ground-state orientations of a K-state clock model with a pinned boundary", "domain": "Condensed-matter physics" }, { "problem": "Setting the leg phases of a walking robot's gait cycle", "domain": "Robotics" }, { "problem": "Rotation angle of every shading fin on a tower facade", "domain": "Architecture and facade engineering" }, { "problem": "Driving direction for the machine passes on each parcel of a farm", "domain": "Precision agriculture" }, { "problem": "Which month each policy cohort renews in, across one underwriting book", "domain": "Insurance operations" }, { "problem": "Angular phasing of the shaped charges along a perforating gun string", "domain": "Oil and gas well completion" } ], "shipped": { "n": 4, "assurance": "certified_optimal" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": { "L": 2000, "K": 8, "bonds": 16000, "bias_terms": 1000 }, "certainty": "heuristic (labelled)", "engine_ms_median": 2.861, "runs": 3, "measured": true } }, { "id": "hub_corridor_coverage", "title": "Maintenance Hub Coverage", "category": "Real Estate", "icon": "🏢", "tagline": "Activate exactly k hubs so every corridor has an active endpoint — 'at least one of the pair' built from complements.", "command": "rules", "min_cli": "1.0.0", "effort": "flash", "shape": "cover-the-requirements", "scales_to": "The identical gadget on 5,000 items and 40,000 pairwise requirements is 10,000 booleans — one active flag plus one complement shadow per item — with 5,000 different rules, 40,000 mutual_exclusion rules (one per requirement pair), and a single choose_exactly for the budget, sent as one request. Counts follow the item and pair totals only. k is declared rather than minimized: sweep k downward and re-solve, or price the items in this command's optional linear objective. A requirement over more than two items (at least 2 of these 7) is outside the pairwise gadget and belongs to the cover command. Certification is reported per answer and is not decided by graph size: a 100,000-boolean rule set carrying 30,000 rules has come back certified, so read the label the answer carries rather than assuming a bigger graph must be a labelled heuristic.", "also_solves": [ { "problem": "Contact-tracing triage where every recorded contact pair must have at least one of the two people tested", "domain": "Public Health" }, { "problem": "Rolling out hardened endpoint controls so every trust relationship has at least one hardened end", "domain": "Cybersecurity" }, { "problem": "Contract testing where every service-to-service boundary needs a suite on at least one side", "domain": "Software Testing" }, { "problem": "Pressure-sensor placement so every pipe is instrumented at one of its two end junctions", "domain": "Water Utilities" }, { "problem": "Staffing inspection posts so every trade lane is inspected at one of its two ports", "domain": "Customs and Trade" }, { "problem": "Fitting detection equipment so every track section between two interlockings is monitored from one end", "domain": "Rail" }, { "problem": "Buying habitat parcels so every wildlife corridor has at least one protected endpoint patch", "domain": "Conservation" } ], "shipped": { "n": 10, "assurance": "certified_optimal" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": { "n": 100000, "rules": 30000 }, "certainty": "certified", "engine_ms_median": 984.738, "runs": 3, "measured": true } }, { "id": "hpc_solver_ensemble", "title": "Numerical Scheme Ensemble Cover", "category": "Scientific Computing", "icon": "🧪", "tagline": "choose_exactly k=1 per requirement, listing only the bundles that serve it; the exclusions go on the covering sets, not the elements.", "command": "rules", "min_cli": "1.0.0", "effort": "flash", "shape": "cover-the-requirements", "scales_to": "The identical shape at 3,000 candidate bundles over 1,200 requirements is 3,000 booleans and 1,200 choose_exactly k=1 rules — each listing only the bundles that serve that one requirement — plus one mutual_exclusion per recorded incompatible bundle pair, bounded above by the 4,498,500 pairs a fully hostile portfolio would have. Only the counts change: both rule families still travel in one request, because a cover chosen first and conflict-checked afterwards is a different and weaker problem. Exactly-once is choose_exactly k=1; at-least-once with per-bundle costs is the cover command; the cheapest exact partition puts per-bundle prices in this command's optional linear objective. Certification is reported per answer and is not decided by portfolio size: a 100,000-boolean rule set carrying 30,000 rules has come back certified, so read the label the answer carries rather than assuming a bigger portfolio must be a labelled heuristic.", "also_solves": [ { "problem": "Crew pairing where every flight leg must be flown by exactly one published pairing", "domain": "Airlines" }, { "problem": "Placing a reinsurance programme so every risk layer is ceded to exactly one treaty", "domain": "Insurance" }, { "problem": "Assay panel selection where every biomarker is measured on exactly one panel", "domain": "Diagnostics" }, { "problem": "Multiplex primer pooling where every target region is amplified by exactly one pool", "domain": "Genomics" }, { "problem": "Tooling-package selection where every part feature is produced by exactly one package", "domain": "Manufacturing" }, { "problem": "Buying a security stack where every control requirement is met by exactly one product", "domain": "IT Procurement" }, { "problem": "Media plan where every audience segment is reached by exactly one campaign flight", "domain": "Advertising" } ], "shipped": { "n": 7, "assurance": "certified_optimal" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": { "n": 100000, "rules": 30000 }, "certainty": "certified", "engine_ms_median": 984.738, "runs": 3, "measured": true } }, { "id": "math_golden_ratio_relation", "title": "Golden-Ratio Relation Witness", "category": "Scientific Computing", "icon": "ƒ", "tagline": "A high-precision constant yields a residual-checked polynomial witness, not a theorem.", "command": "relation", "min_cli": "1.0.0", "effort": "flash", "shape": "verified-scientific-operation", "scales_to": null, "also_solves": [ { "problem": "Minimal-polynomial discovery", "domain": "Experimental mathematics" }, { "problem": "Identity audit", "domain": "Numerical computing" }, { "problem": "Symbolic-regression seed", "domain": "Scientific computing" } ], "shipped": { "n": null, "assurance": "certified_feasible" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": null, "certainty": null, "engine_ms_median": null, "runs": null, "measured": false } }, { "id": "math_sqrt2_precision", "title": "High-Precision Square Root", "category": "Scientific Computing", "icon": "√", "tagline": "The returned digits are checked by squaring at higher precision.", "command": "precision", "min_cli": "1.0.0", "effort": "flash", "shape": "verified-scientific-operation", "scales_to": null, "also_solves": [ { "problem": "Reference constant generation", "domain": "Metrology" }, { "problem": "Numerical regression oracle", "domain": "Software testing" }, { "problem": "Precision-loss diagnosis", "domain": "Scientific computing" } ], "shipped": { "n": null, "assurance": "operation" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": null, "certainty": null, "engine_ms_median": null, "runs": null, "measured": false } }, { "id": "scale_planted_65536", "title": "65,536-Variable Planted Floor", "category": "Scientific Computing", "icon": "2ⁿ", "tagline": "A 2^65536 space reaches a construction-known floor without claiming arbitrary NP-hardness.", "command": "quantum-scale", "min_cli": "1.0.0", "effort": "flash", "shape": "planted-scale-certificate", "scales_to": null, "also_solves": [ { "problem": "Scale-path validation", "domain": "HPC" }, { "problem": "Serialization stress", "domain": "Infrastructure" }, { "problem": "Receipt reproducibility", "domain": "Audit" } ], "shipped": { "n": 65536, "assurance": "certified_optimal" }, "sandbox": { "runnable": false, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": null, "certainty": null, "engine_ms_median": null, "runs": null, "measured": false } }, { "id": "science_enumerable_sampling", "title": "Enumerable Distribution Sample", "category": "Scientific Computing", "icon": "∿", "tagline": "An empirical distribution is checked as a distribution, never mislabeled as an optimum.", "command": "sample", "min_cli": "1.0.0", "effort": "flash", "shape": "empirical-distribution", "scales_to": null, "also_solves": [ { "problem": "Scenario generation", "domain": "Risk" }, { "problem": "Configuration diversity", "domain": "Engineering" }, { "problem": "Uncertainty exploration", "domain": "Science" } ], "shipped": { "n": 6, "assurance": "heuristic" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": null, "certainty": null, "engine_ms_median": null, "runs": null, "measured": false } }, { "id": "science_planted_frequency", "title": "Planted Dominant Frequency", "category": "Scientific Computing", "icon": "≈", "tagline": "A signal with a planted period returns the exact dominant bin.", "command": "frequency", "min_cli": "1.0.0", "effort": "flash", "shape": "verified-scientific-operation", "scales_to": null, "also_solves": [ { "problem": "Rotor vibration diagnosis", "domain": "Mechanical engineering" }, { "problem": "Seasonality detection", "domain": "Finance" }, { "problem": "Clock-jitter inspection", "domain": "Hardware" } ], "shipped": { "n": null, "assurance": "operation" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": null, "certainty": null, "engine_ms_median": null, "runs": null, "measured": false } }, { "id": "space_maneuver_deconfliction", "title": "Satellite Conjunction De-confliction", "category": "Space", "icon": "🛰️", "tagline": "The exclusion binds two candidate choices, not the two actors; a fix creates new conflicts, so screen and exclude those pairs too.", "command": "rules", "min_cli": "1.0.0", "effort": "flash", "shape": "assignment-under-conflict", "scales_to": "The identical shape for 2,000 actors with 8 candidate options each is 16,000 booleans and 2,000 choose_one rules; every screened pair of actors contributes one mutual_exclusion per forbidden combination of their options, so 5,000 flagged pairs averaging 3 bad combinations is 15,000 exclusions, and one flagged pair can carry at most 8 x 8 = 64. Add one force_false per option ruled out in advance. That is the same structure as the 12-boolean instance here, in one request. Certification is reported per answer and is not decided by the size of the screening set: a 100,000-boolean rule set carrying 30,000 rules has come back certified, so read the label the answer carries rather than assuming a bigger screening set must be a labelled heuristic. Either way the label covers the encoding, and this example's notes require an independent re-check of the physical world before any plan is acted on.", "also_solves": [ { "problem": "Assigning each departure a standard route so no two chosen routes lose separation at a shared merge fix", "domain": "Aviation" }, { "problem": "Choosing a switching state per substation so no chosen combination overloads a line under an N-1 contingency", "domain": "Energy" }, { "problem": "Picking one version per service so no chosen pair of versions has an incompatible contract", "domain": "Release Engineering" }, { "problem": "Selecting an operating mode per unit so no chosen pair of modes trips a safety interlock", "domain": "Process Manufacturing" }, { "problem": "Choosing one precomputed route per mobile robot so no two chosen routes claim the same aisle segment in the same window", "domain": "Warehouse Robotics" }, { "problem": "Scheduling maintenance jobs into change windows so no chosen pair takes down both halves of a redundant path", "domain": "IT Operations" }, { "problem": "Assigning each tower crane an operating sector so no two chosen sectors sweep the same airspace", "domain": "Construction" } ], "shipped": { "n": 12, "assurance": "certified_optimal" }, "sandbox": { "runnable": true, "default_effort": "flash", "limits_endpoint": "/api/v1/sandbox" }, "how_to_adapt": "Use mapping_template as a worksheet; preserve keep_fixed, deliberately edit change, do not inherit cannot_carry, and follow if_you_need_that when the required semantics are outside this command.", "at_scale": { "instance": { "n": 100000, "rules": 30000 }, "certainty": "certified", "engine_ms_median": 984.738, "runs": 3, "measured": true } } ] }