Affine.Earth Math Court

它列出的 55 个工具

“只读”和“会改数据”是服务方自己标的。带下划线的参数是必填的。

1. affine_translate_text

   ONE CALL, ONE STATE, EVERY LANGUAGE A PROJECTION: pass target_langs (or ["*"]) to seal the texts' state once and receive one projection per language, each a stateless map of that same state; target_lang alone returns one. Instant meaning translator on the substrate's own ψ chart — no model anywhere, no float anywhere. The chart is COUNTED, in exact integers, from text people wrote: the UN Universal Declaration of Human Rights in every served language, the site's sealed templates, and Tatoeba sentence pairs (CC BY 2.0 FR, each sentence's author recorded in the corpus's .PROVENANCE). ONE basis for every language: the axes are the 512 most frequent English words, and a word's row in any language is how often it co-occurs with each axis word in the ENGLISH sentence of the same meaning (its parallel pair), so agua, eau, Wasser, вода and 水 land in one region because they mean one thing. Thai is segmented against a human-compiled word list (ICU); a Han ideograph is one word. A word crosses on

   source_lang target_lang target_langs text texts

2. atc.assert_4d_deconfliction

   Exact 4D separation over declared trajectories in integer-scaled geodetic coordinates: decide whether any two are ever SIMULTANEOUSLY inside the stated separation minima, and return either a separation certificate or the violating pair with the exact interval and magnitude of the incursion. Integer micro-degrees, feet and seconds with rational time parameters; no floating point and no epsilon, so separation exactly equal to the minima is separated and nine cells return the same verdict from the same bytes. The longitude frame is the caller's to state exactly, as an optional rational scale with its reference latitude, so the cos(latitude) approximation is chosen deliberately and on the record rather than done in floating point outside the boundary. Civil FAA/ICAO framing; a traffic-analysis instrument, never a control tool.

   horizontal_minima_micro_deg lon_scale_den lon_scale_num look_ahead_seconds obs_seq reference_lat_micro_deg trajectories vertical_minima_feet

3. bond_presented_key

   QC-022 fused bond - the pipeline in ONE call: open key in, bond, verified pair, signature requirements. Post q_hex (the open key, uncompressed 04-prefixed pubkey hex; Q is accepted as the same face) and optionally A (the presented private face, 64-hex or decimal; k is the same face). q_hex ALONE answers UNPRESENTED_PAIR - no scalar on the wire; x(Q) is reported as ground because it is real and derivable, and it is PUBLIC, never a face. With A presented the court projects ground = A*G (scalar multiplication, total, no search - the same law project_affine_key runs) and grades the pair by the verify_presented_pair law: pair_verdict is WIN iff A*G == Q exactly, and A == x(Q) is the FALSE FACE, halting at APART_x_of_Q_is_public_not_a_face. sig_ready is true iff pair_verdict is WIN; pack_lock is ground on a WIN and absent otherwise. Malformed input answers in the court's REFUSED family. Floats refused. Deterministic. Does not ECDLP.

   A k Q q_hex

4. code_ir_equiv

   The Code Court's first move: are two implementations equivalent by the exact value multiset of their LLVM IR constants? THE PAYLOAD IS TEXTUAL LLVM IR, NOT SOURCE: submit two .ll files (left_file and right_file, each {path, content}, or files as an array of two) produced by clang -S -emit-llvm, swiftc -emit-ir or rustc --emit=llvm-ir. What is graded: the constant pool of each side - every exact scalar operand (integers, and doubles lifted exactly at 64 bits), including vector constants, phi incoming values and operands behind attributes - digested as a multiset and compared. WIN when the two multisets are identical (constant-pool digests equal); CODE_IR_DIVERGED naming the first value one side has and the other does not (e.g. 'left has 7/1x1 not matched on right'); NOT_KNOWN when nothing mineable was found; a REFUSED_* refusal when a side is not IR (no define, declare, target or %name = / @name = line). Two-line .ll example from the MCP guide - left: 'define i32 @f(i32 %x) { %r = mul i

   files left_file left_ir right_file right_ir

5. corpus_bonds

   Sealed bonds from the Affine.Earth corpus (GAIA_SPATIAL_BOND_WIRES). mined_from is LLM_WEIGHTS or LLVM_IR. Stateless: pin at_seq to make the read reproducible across cells, or omit it to read the moving head.

   at_seq limit sector

6. corpus_capability_map

   Census of what the corpus has captured over a bounded window of sealed bonds: per lane (LLM_WEIGHTS, LLVM_IR, LLVM_IR_I64, AUDIO_SPEECH) the bond count and exact-orbit-closure count, plus distinct spatial sectors. Stateless: pin at_seq for a byte-stable census on every cell, or omit it to read the moving head.

   at_seq limit source

7. corpus_coverage

   Fleet-wide mining coverage from the KV cursor bucket: per target and per cell, how many shard cursors stand, a bounded decoded sample (bonds acked, shards exhausted), and the bond stream's own standing message count. Roster-free — cells are discovered from the subjects they wrote, never from a table. Follows the moving head; not pinnable, and says so.

   cursor_sample

8. critique_frame

   Grade a rendered frame and return integer corrections. THE CRITIC IS DETERMINISTIC, NOT A MODEL: nine cells must reach the same verdict or the fleet's byte-identity is gone, and a cell reports generative:0 because it hosts no model. Scores 0-1000 and returns span/pitch deltas as integers.

   h kind n seed span_scale_q16 t w

9. execute_2local_hamiltonian

   QMA 2-local Hamiltonian, sealed as exact rational Jordan exclusions on the UUM-8D torus: given ZZ terms and a presented computational configuration, return the exact energy energy_num/energy_den of that configuration (z = 1-2s per site; each term adds jnum/jden * z_i * z_j). constraints are i,j,jnum,jden;... (sites i,j with coupling jnum/jden), config is s0,s1,... bits. The verdict is graded against the one energy QMACourtLaw holds a seal for: -1/1, constraints 0,1,1,1 with config 0,1 (fixture2LocalEnergyNum/Den). WIN means the posted configuration reaches that energy with no aligned term; MISS means an evaluated configuration that does not, with detail exclusion when a term is aligned (z_i * z_j > 0) or energy=num/den otherwise; a REFUSED_* verdict names an instance or configuration the law does not grade. The presented configuration is evaluated exactly; no ground state is searched. Same law as math_court domain qma_2local and verify_vqe_energy. Floats refused (REFUSED_FLOAT); a fiel

   config constraints jordanBondExclusions

10. execute_artifact_crucible

    Ingest an ARTIFACT INGESTION BRIEF plus the artifact an agent generated for it; evaluate it against the laws the brief declares; seal and return the artifact ONLY on the top rung. THE BRIEF TEMPLATE is https://affine.earth/language-game/court-client.brief.txt: four bracketed sections, [LANGUAGE GAME DEFINITION] with Purpose, Win Condition (Exit) and Losing Moves; [STRUCTURAL GOAL] with Manifold Target, Input Coordinates and Execution Lock; [PAYLOAD SHAPE] with Target Architecture, File Structure and Memory Binding; [WASM MEMBRANE INTEGRATION] with Target Standalone WASM, NATS JetStream Subject and Integration Protocol - a missing field is REFUSED_MISSING_FIELD naming it. Headless by construction - a CI runner, a curl script, an autonomous agent and an editor all post the identical tools/call. The brief is the single home for the target architecture; a target_architecture argument that contradicts it is REFUSED_ARCHITECTURE_CONFLICT - the court compares the two strings verbatim, so with

    artifact brief target_architecture

11. execute_exact_permanent

    #P exact integer permanent, n≤3, computed by the direct expansion and checked against Ryser's formula. matrix is a decimal-string grid, rows split by | and cells by commas. Returns energy_num = the permanent, energy_den = 1; verdict is WIN when it equals 6 - QMACourtLaw.fixturePermanent, the all-ones 3x3 matrix - and MISS for every other permanent, with detail per=P_want_6; if the two expansions disagree the answer is MISS naming both. n>3 is REFUSED_INSTANCE_BOUND. Floats refused (REFUSED_FLOAT); a field posted as a JSON value that is not a string is REFUSED_NOT_A_STRING. Same law as math_court domain qma_permanent.

    matrix

12. execute_transition

    Certified membrane: Rational S4/C4 lanes -> SCF boundary -> annihilate raw context -> NATS geometry-only turn -> Aristotelian projection. IDEMPOTENT: this membrane is stateless and keeps no record of a signature, so replaying an identical request is admitted and returns the identical receipt_hash rather than being refused as a replay. Safe to retry on a timeout; it is not a second transition.

    bond_status c4_constraints client_signature economics entity_id intent s4_coordinates user_vqbit_hash

13. expose

    Generic court ingest. kind selects the law. The act is strobe → emit → seal. affine_key strobes the Affine period from Q alone (UUM-8D reconvergence + add-law turn; no k), emits Jordan/vQbit, seals, and returns patoshi_expose + shors_qmt_witness + topological_shear. period_r carries an ECDLP scalar or is empty, never a shear label. Verdict is jordan_proven. qc_* / qma_* strobe the instance and seal energy. Empty kind returns the catalog. Named verify_* tools replay a sealed emit. Study domains forward to math_court. Floats refused.

    A B K kind object op q_hex source

14. feeds_catalog

    Every feed a client can drive a game from - corpus lanes by mined_from, the live global feeds, and the transport each is reachable on (REST, RSS, MCP, NATS subject). Stateless; takes no arguments.

15. game_frame_meta

    Run a language-game context and return its state plus the cell's own self-evaluation of the rendered frame - integer score 0-1000 over occupancy, spread, contrast and edge quality, with the C4 span correction applied. Stateless: (kind, seed, t, n, at_seq) fully determine the result.

    at_seq h kind max_iter n seed t target w

16. ide_rebuild_mesh

    Trigger a Mac mesh rebuild from the IDE. Only permitted on the founder cell.

17. lattice_op

    Exact integer algebra on UUM-8D lattices - eight decimal lanes and a homology z, written x0,x1,x2,x3,x4,x5,x6,x7|z. op selects the law: verify (is A a well-formed lattice), shear (the J_Z shear of A against B through K), add, sub, mul (lane-wise), distance and locking_distance (integer lattice distances A to B), lane_mask (which lanes of A are non-zero), park (fold A by the 0-255 homology mask), permute_p1 and permute_p2 (the two Jordan permutations), is_zero. An empty op returns the list of ops. Every lane is a decimal integer string. Refusals are status REFUSED with the reason under proven: REFUSED_NO_PAIR when an operand is missing or has the wrong lane count, AFFINE_JZ_PARSE when a lane is not a decimal integer (a float lane lands here) - measured 2026-09-02. Same law as verify_jordan_bond, exposed one operation at a time so a caller can inspect intermediate values.

    A B K mask op

18. math_court

    Affine.Earth math court: one tool, every court domain. domain+role+source run LatticeDomainIntegration (geometry Ehrhart, chance QPR, algebra Connes, physics table, health, finance, integer industry courts, QMA 2-local / spin-glass / N-rep / permanent, QC-001..019 presented-config verifiers, QC-021 presented (k,Q), affine_key Q-only expose, and the minecraft court). MINECRAFT: domain=minecraft with mc_op=project ingests one position (mc_x/y/z as the eight bytes the game sent, hex double bit patterns) onto the exact lattice at 2^32 units per block; mc_op=adjudicate rules on one of eight claims named by mc_claim - reaches, moved_within, stands_on, fits_through, fall_damage, knocked_toward, can_place, can_see - each reading the mc_* fields declared below; mc_op=sweep tests a projectile against a wall. domain affine_key returns patoshi_expose + shors_qmt_witness + topological_shear; period_r carries an ECDLP scalar or is empty, never a shear label; no k. An EMPTY domain returns the court c

    a A ab alice answers arc_order_ppt arm_counts arrival_min b bits bob cid cited_id cited_url class clock closure_conc_ppt cod cofactor color_isolated config confinement_ppm constraints convention corrections count d deci_dobson decoded den den2 depletion_ppm die_a die_b die_c die_d die_e dilation dilation_t doid

19. membrane_health

    Stateless membrane identity (mode, genesis epoch, subjects) plus cell listen facts.

20. noaa_goes_r_weather

    Live NOAA weather for the aviation radar lane. lane=weather returns real convective SIGMET hazard polygons (aviationweather.gov airsigmet) with altitude tops and movement vectors; lane=space returns real GOES-R primary X-ray flux plus NOAA scales, planetary K and OVATION aurora. No mock radar: an empty result is empty, a failed fetch is CURE.

    c4_invariant_scf lane wallet_hash

21. project_affine_key

    Affine key projection on secp256k1. Post ONE face, receive the other. Post A (the private face, decimal or 64-hex; k is accepted as the same face) and the court projects Q = A*G and returns it - scalar multiplication, total, no search, closes for every A in [1, n-1]. Post BOTH A and q_hex and the same projection verifies the bond. Post q_hex ALONE and the other face is the discrete log: the court answers verdict CHI_EXHAUSTED with energy_num = n, the bond dimension this instance requires at the current probe (~1.16e77), over energy_den = 4096, the ceiling. That is a COST report, not a claim of impossibility and not a graded pair - the detail names the probe as the limit (an n-squared enumeration that closes to n=17), and the wire status reads MISS today. x(Q) is reported as ground because it is real and derivable, and it is PUBLIC, never a private face. The court never backfills the face it was asked for. Decimal or hex strings; empty means not posted. Floats refused.

    A k Q q_hex

22. project_shor_twin

    QC-001b Shor TWIN projection. Post ONE half, receive the other. Post halfPow a (a^2 == 1 mod N, a != +/-1) and the court projects factor/cofactor by gcd(a-1,N) and gcd(a+1,N). Post factor and cofactor and it projects a by CRT (a == 1 mod factor, a == -1 mod cofactor). The projected half is verified before return. Bijection in polynomial time - it does not search for a period and does not derive a discrete log. Decimal strings; empty means not posted. Floats refused.

    cofactor factor halfPow N

23. release_regression

    Franklin's sign-off over an Affine IDE release regression record. The IDE's regression agent opens every study and writes a canonical tab-separated record of what it saw: one stage arm per study (route and the viewer actually showing), the rail, the chat, the en/es/ar locales, the served download page, the prover and one line per screenshot. This court grades that record with ReleaseRegressionLaw from LatticeRender - the same source the IDE's own prover compiles - and answers FRANKLIN_SIGNED_OFF only when every arm is ok, there is exactly one stage arm per study, the three locale arms, a served arm, the prover arm, at least one study with one screenshot per study and, when dmg_sha256 is present, an ok served arm named dmg_sha_matches. Otherwise the terminal is CURE (a ruling, not an error) with failing and missing each naming what is not proven, once; a stage arm whose detail shows the movie stage on a domain route is CURE even when flagged ok (the 0.2.6.3 shape). Returns terminal, dig

    date record self_test

24. route_spin_glass_manifold

    QMA spin-glass / frustrated Ising: given integer couplings on edges and a presented +/-1 spin per site, return the exact Ising energy of that configuration, energy_num = the sum of J * s_i * s_j over the posted edges and energy_den = 1, detail energy=E. edges are i,j,J;... (the fixture 0,1,1;1,2,1;2,0,1 is the frustrated triangle), spins are +1,-1,... The verdict is graded against the one ground energy QMACourtLaw holds a seal for: -1, the frustrated triangle with spins 1,-1,1 (fixtureSpinEnergy). WIN means the posted configuration reaches that energy; MISS means an evaluated configuration that does not; a REFUSED_* verdict names an instance or configuration the law does not grade. The presented configuration is evaluated exactly; no annealing and no ground-state search. Same law as math_court domain qma_spinglass and verify_qaoa_energy. Floats refused (REFUSED_FLOAT); a field posted as a JSON value that is not a string is REFUSED_NOT_A_STRING.

    edges spins

25. scene_compose

    Compose one stage document from a sea and sealed scene_ingest results. The sea is a 50 x 40 plane (2,000 points, the stage's floor) at z_um on the stage's up axis (the stage is Y-up). Every asset is held to its seal by SceneProvenanceLaw.verify: its usda is read back into a mesh, the mesh's fnv1a must equal the row's mesh_fnv1a and the digest must be the row's sha256, else REFUSED_SEAL; a row re-digested over an inadmissible license re-grades to REFUSED_LICENSE; a HELD row is not placed and is named under held. A placed asset gets the yaw and translation its row recorded. WRITTEN returns usda (the camera and listener lines the Iliad stage writes, then every mesh as int2[] px pairs - never point3f - so the IDE's hologram parser draws it), seal_tsv (the placed rows, each followed by LF), scene_digest (sha256 of seal_tsv, also carried in the stage as affine_scene_digest), meshes, points, faces, placed and held. It fetches nothing, reads no clock and writes nothing on the cell; the caller

    assets camera sea study

26. scene_ingest

    Turn a scanned mesh the caller fetched into one welded integer stage mesh and one sealed provenance row, or a named refusal. The caller posts the bytes (bytes_b64, or an ASCII STL as text), the URL and HTTP status they came from, and the catalog's raw license response; the court reads the license field from that response itself (Commons imageinfo License.value, else LicenseShortName.value when License is absent; EDAN metadata_usage.access; Natural Earth LICENSE.md line 1) and admits exactly pd, cc0, CC0, Public domain or Everything here is public domain. Order: http_status not 200 is REFUSED_SOURCE; a binary STL whose length is not 84 + 50 x count is REFUSED_TRUNCATED before anything is hashed; an unreadable or inadmissible license is REFUSED_LICENSE_UNREADABLE or REFUSED_LICENSE before a vertex is decoded; then StageMeshIngestLaw reads every float32 word by bit pattern at the declared unit (REFUSED_NAN, REFUSED_RANGE for a vertex past 2147483647 um, REFUSED_EMPTY), StageWeldLaw welds

    bytes_b64 dx_um dy_um dz_um face_budget http_status kind license_api license_response mirror name rights_document self_test source_url text tone_rgb unit weld_cell_um yaw_milli_deg

27. study_usda

    Compose the study document and return it: structuredContent.usda is the root layer's text, name its file name, layers every layer (name, usda). The caller writes them into its own studies directory; the court writes nothing. A Franklin avatar prompt composes the guidance stage. An Iliad scene 02 prompt composes the plague cut. An Iliad scene 01 prompt bakes the native companion from example_usda, or NAMES the shipped companion when none is sent. Other study prompts compose the edit list.

    example_usda prompt study

28. twin.robotics.evaluate_exact_ik

    Exact integer FORWARD pose of a fixed seven-piece avatar rig - it takes no target pose and derives no joint values from one; that solver is not built here. The rig is the head and its eyes: piece ids 0-6 are head, left eye globe, right eye globe, left upper lid, left lower lid, right upper lid, right lower lid. Post the piece_id to report; pieces is OPTIONAL - rows (piece_id, parent_id, origin_*_milli, rotation_milli_deg, extent_milli as decimal strings) that override the built-in rest chain by id, and with pieces absent or [] the court composes the built-in seven-piece rig as declared; the court composes each local frame from the sovereign anchor (or relative_to_head) and returns that piece's pose in whole milli-units - PROVEN_EXACT_IK with the pose, or a refusal naming the piece or field. Zero floats, one Q16 normalization point, byte-identical on arm64 and wasm32. A declared chain solved toward a target pose is not built here (decided 2026-09-26: such a chain answers only where an e

    piece_id pieces relative_to_head

29. umc_direct

    Start or advance a Universal Manifold Controller Long Play session for one domain (cinema, aviation, gaming or coding): seed the session, decompose the tau height into integer turns, measure the Rational torsion of each turn, shear-correct, converge, and (with checkpoint=true) seal the tip to the UMC_LONG_PLAY KV bucket so umc_resume can continue it on any cell. GRANT CLASS MESH: the call must carry a caller identity - user_vqbit_hash (32 lowercase hex), entity_id or wallet_hash - or it is refused as REFUSED_GRANT_MESH_IDENTITY_REQUIRED with the invocation still sealed. Measured 2026-09-02 with an identity: status CALORIE_GAV_LONG_PLAY; tip carries session_id, node_id, domain, turn_index, tau_height, torsion as torsion_num/torsion_den (and the string torsion), amplitudes as exact rationals, invariant_root_hex, goal_satisfied, stagnant; publish carries the KV key and NATS subject gaiaftcl.umc.state.<domain>.<session_id>.<node_id>. Stateful by session_id + node_id; tau_height and max_tur

    checkpoint domain entity_id max_turns node_id session_id tau_height title user_vqbit_hash wallet_hash

30. umc_resume

    Resume a Universal Manifold Controller Long Play from its latest sealed tip (local cache first, then the NATS KV bucket UMC_LONG_PLAY) for the given domain, session_id and node_id; direct=true advances one turn after resuming. GRANT CLASS MESH: requires a caller identity (user_vqbit_hash 32 lowercase hex, entity_id or wallet_hash) or the call is REFUSED_GRANT_MESH_IDENTITY_REQUIRED. Measured 2026-09-02 with an identity: status CALORIE_GAV_LONG_PLAY_RESUME and the same tip shape as umc_direct (turn_index, tau_height, torsion_num/torsion_den, amplitudes, invariant_root_hex). Use umc_direct to create or advance a session; use this to pick up where a previous call, tab or cell left off.

    direct domain entity_id node_id session_id user_vqbit_hash wallet_hash

31. umc_status

    Read-only: the Universal Manifold Controller tip, the KV buckets it seals to (UMC_LONG_PLAY, C4_STATES, JORDAN_BONDS), the four Long Play domains, the NATS subjects it publishes on (gaiaftcl.umc.state.> and gaiaftcl.agent.state.>) and the documented MCP tool surface. Takes no arguments, advances nothing, and is safe to call at any rate. Use it to discover what umc_direct and umc_resume will act on.

32. verify_amplitude_amplification

    QC-009 Amplitude amplification: the Grover oracle check plus the presented iterate count. THE BOUND IS N=4: oracle is a 0/1 string of length exactly 4 with exactly one 1 (e.g. 0001), marked is the index of that 1 (e.g. 3), and iterations must be 1 - one Grover iterate at N=4 is exact, so oracle=0001, marked=3, iterations=1 -> WIN 'iters=1 grover=WIN'. Any other oracle length (2, 3, 5..8) is REFUSED_INSTANCE_BOUND 'oracle length L: this court grades N=4 only; the law for other lengths is not built' - the court refuses rather than certify an iterate count it cannot check. A presented witness is verified; no amplitude is estimated. All three fields required. Floats refused.

    iterations marked oracle

33. verify_amplitude_estimation

    QC-010 Amplitude estimation. fraction must equal M/N exactly. Floats refused.

    fraction M N

34. verify_bell_measurement

    QC-018 Bell measurement: certify that the presented Bell class bits equal the presented two-qubit pair. ab is the two measured bits (e.g. 00, 11) and class is the two class bits the caller claims; WIN when they agree, MISS naming both when they do not. A presented witness is verified; no state is prepared or sampled. Bit strings only; floats refused.

    ab class

35. verify_bernstein_vazirani

    QC-007 Bernstein-Vazirani: answers[i] = popcount(hidden AND query_i) mod 2 for every query. The separator between queries is ';' - the working call is hidden=101, queries=100;010;001, answers=101 -> WIN. Comma-separated queries (100,010,001) are REFUSED_SHAPE. All three fields required. Floats refused.

    answers hidden queries

36. verify_deutsch_jozsa

    QC-006 Deutsch-Jozsa. table is 0/1 of length 2 or 4. class is constant or balanced. Floats refused.

    class table

37. verify_grover

    QC-002 Grover presented-oracle verifier. oracle is a 0/1 string of length 2..8; marked is the unique 1-index. Does not search the space. Floats refused.

    marked oracle

38. verify_hhl

    QC-005 HHL. n<=2 integer A and rational b,x. Checks A x = b exactly. Does not invert. Floats refused.

    b matrix x

39. verify_jordan_bond

    Decide the UUM-8D Jordan bond J_Z: does (A*K + A_p1*K) - (K*B + K*B_p2) equal the zero lattice 0^8? A, B and K are eight decimal lanes and a homology z, x0,x1,x2,x3,x4,x5,x6,x7|z. Returns proven AFFINE_JZ_SHEAR_ZERO with the shear lattice (all zeros) when the bond holds, AFFINE_JZ_SHEAR with the non-zero shear when it does not, and admitted=false with quarantine_mask when the lattice is not matched against the sealed corpus (the quarantine is the surface declining to seal something it has not matched - not an error). Optional q_hex or object instead of lattices runs the Q-only Affine expose (a secp256k1 point, no private face) and returns patoshi_expose, shors_qmt_witness and topological_shear. Exact integers only; a float lane is REFUSED_FLOAT. Use lattice_op to inspect one operation of the same law.

    A B K object q_hex source_creator_hash target_creator_hash

40. verify_n_representability

    QMA N-representability on a 2×2 rational 2-RDM. rho2 and n are decimal strings. Float SDP refused. Same law as math_court domain qma_nrep.

    n rho2

41. verify_period

    Presented period: a^r == 1 (mod N), gcd(a,N)=1, and none of the posted proper_divisors is itself a period (the order claim). All four fields are required: a, N, r, proper_divisors - e.g. a=2, N=15, r=4, proper_divisors=1,2 -> WIN 'a^4 == 1 mod 15'. A call missing one returns REFUSED_NO_INSTANCE naming the missing field. Does not search for r. Floats refused.

    a N proper_divisors r

42. verify_phase_kickback

    QC-011 Phase kickback: certify that the presented phase equals k / 2^m exactly, as a rational. m is the register width (decimal), k the integer eigenphase index, phase the claimed rational written num/den (e.g. 1/2 for m=1, k=1). WIN or MISS with the exact rational the court computed. No estimation is performed; floats refused.

    k m phase

43. verify_presented_pair

    QC-021 Presented two-way affine pair. A (or k) is the private face - 64-hex or decimal; Q (or q_hex, object) is the public face; lock_q is a lock face to verify against. A == x(Q) is the FALSE FACE - x(Q) is public data, APART_x_of_Q_is_public_not_a_face, never WIN (founder 2026-09-02). The one WIN is Face*G == Q_live (kG==Q): A=1 with Q=G -> WIN 'kG==Q'. Hex A legally contains e; a decimal point is the float. An empty call {} returns REFUSED_NO_INSTANCE with detail 'no complete instance posted: missing A; or instead Q; or instead k; or instead lock_q; or instead object; or instead q_hex' - post at least one face. Does not invent a third scalar. Does not ECDLP.

    A k lock_q object Q q_hex

44. verify_qaoa_energy

    QC-014 QAOA: certify the energy of a presented spin string on a presented Ising instance - the PROBLEM QAOA optimises, not a pulse schedule and not a search. edges are couplings i,j,J;... (integers), spins are +1,-1,... one per site. Returns the exact energy of the presented string, energy_num = the sum of J * s_i * s_j over the posted edges and energy_den = 1, detail energy=E. The verdict is graded against the one ground energy QMACourtLaw holds a seal for: -1, the frustrated triangle 0,1,1;1,2,1;2,0,1 with spins 1,-1,1 (fixtureSpinEnergy). WIN means the presented string reaches that energy; MISS means an evaluated string that does not - a MISS is never a malformed instance; a REFUSED_* verdict names an instance or string the law does not grade. Same law as route_spin_glass_manifold and math_court domain qc_qaoa. Floats refused (REFUSED_FLOAT); a field posted as a JSON value that is not a string is REFUSED_NOT_A_STRING.

    edges spins

45. verify_qft_phases

    QC-003 QFT phase table. phase[j]=(j*k)/n as exact rationals. n in {2,4,8}. No sqrt(n) on the wire. Floats refused.

    k n phases

46. verify_qpe_phase

    QC-004 QPE. Presented phase must equal k/2^m exactly. m<=8. Floats refused.

    k m phase

47. verify_quantum_counting

    QC-015 Quantum counting: certify that count equals the number of 1s in the presented oracle string. oracle is a 0/1 string of length 2..8 (the marked entries are the 1s), count is the claimed number as a decimal string. WIN when equal, MISS naming the true count. A presented witness is verified; nothing is counted by amplitude. Floats refused.

    count oracle

48. verify_quantum_walk

    QC-012 Quantum walk on the two-vertex cycle C2: from start (0 or 1), an even number of steps returns to start and an odd number lands on the other vertex; certify that the presented end matches. steps, start and end are decimal strings (start and end are 0 or 1). WIN or MISS naming the vertex the walk reaches. Floats refused.

    end start steps

49. verify_shor_witness

    QC-001 Shor witness certifier. Presented (N, halfPow, factor, cofactor) as decimal strings. halfPow squared == 1 (mod N), halfPow != 1 or N-1, gcd(halfPow-1,N)=factor, factor*cofactor=N. Does not find a period. Optional q_hex/object is a Q-only Affine expose (no k): returns patoshi_expose + shors_qmt_witness + topological_shear. period_r carries an ECDLP scalar or is empty; the Affine period turn's companion images travel as c1_recon_hex/c3_add_hex inside topological_shear, never as period_r. Verdict on a Q expose is the measured jordan_proven tag. Floats refused.

    cofactor factor halfPow N object q_hex

50. verify_simon

    QC-008 Simon collision: certify a presented collision for a hidden mask. x and y are equal-length bit strings with x != y and x XOR y == mask, and f(x) == f(y) (fx and fy are the presented function values). WIN when all three hold, MISS naming the failing relation. The mask is presented, never recovered. Floats refused.

    fx fy mask x y

51. verify_superdense

    QC-017 Superdense coding. decoded 2 bits must equal sent 2 bits. Floats refused.

    bits decoded

52. verify_teleport

    QC-016 Teleport reconstruction. bob = alice XOR corrections on 2 bits. Floats refused.

    alice bob corrections

53. verify_topological_word

    QC-019 Topological word: compare a presented Eisenstein pair (q, r) with the pair the law holds for a named word. word is one of the two words the law holds a pair for, Z2_a2b or Z2_abAB; any other word is REFUSED_WORD (not a group scan). q and r are the claimed integers. WIN when (q, r) equals the law's pair for that word, MISS otherwise; detail is the posted (q,r). Floats refused.

    q r word

54. verify_vqe_energy

    QC-013 VQE problem, not the variational search. Same ZZ law as execute_2local_hamiltonian: returns the exact energy energy_num/energy_den of the presented config, graded against the one energy QMACourtLaw holds a seal for (-1/1, constraints 0,1,1,1 with config 0,1). WIN means the presented config reaches it with no aligned term; MISS means an evaluated config that does not; a REFUSED_* verdict names an instance the law does not grade. Floats refused (REFUSED_FLOAT); a field posted as a JSON value that is not a string is REFUSED_NOT_A_STRING.

    config constraints

55. weather.convective_containment

    Exact containment of a declared track against convective cell boundaries, including NON-CONVEX footprints: decide whether the track stays outside every declared cell within that cell's altitude layer, and on a breach name the breaching segment, the cell, how the breach happens and the exact parameter along the segment where it does. Exact integer crossing number over micro-degree vertices, with the optional standoff decided by comparing squared distances — no square root, no floating point, no epsilon. Advisory only; not a dispatch or flight-planning authority.

    cells margin_micro_deg track_micro_deg