earth.affine/math-court

Tools

• 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.

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• code_ir_equiv

  The Code Court's first move: are two implementations equivalent by the exact value multiset of their LLVM IR constants? Submit two .ll texts; get WIN (constant-pool digests identical), CODE_IR_DIVERGED (naming the first divergent value), NOT_KNOWN (nothing mineable), or a REFUSED_* refusal. Stateless and content-addressed — the same two inputs rule identically on every cell, so a reviewer re-checks by re-digesting, not by re-reading the diff. Compares the constant pool (a necessary, strong condition for the numeric kernels the corpus is built from), not full behavioural equivalence.

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• 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.

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• 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.

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• 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.

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• 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.

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• execute_2local_hamiltonian

  QMA 2-local Hamiltonian as exact rational Jordan exclusions on the UUM-8D torus. constraints and config are decimal strings. Floats refused. Same law as math_court domain qma_2local.

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• execute_exact_permanent

  #P exact integer permanent, n≤3. matrix is a decimal-string grid. Float permanent refused. Same law as math_court domain qma_permanent.

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• 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.

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• 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.

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• 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.

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• 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.

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• ide_rebuild_mesh

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

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• lattice_op

  UUM-8D lattice algebra. op is verify, shear, add, sub, mul, distance, locking_distance, lane_mask, park, permute_p1, permute_p2, is_zero. A, B, K as x0,x1,x2,x3,x4,x5,x6,x7|z decimal lattices. Empty op lists the ops.

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• math_court

  Affine.Earth math court. 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), and affine_key Q-only expose). 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. Empty domain returns the court catalog. Decimal strings on the wire. Floats refused.

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• membrane_health

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

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• 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.

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• 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: secp256k1 has PRIME group order, so required bond dimension is n itself (~1.16e77) against a ceiling of 4096, and the court answers NOT_KNOWN - not MISS, because nothing was graded. 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.

  shallow
• 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.

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• route_spin_glass_manifold

  QMA spin-glass / frustrated Ising as discrete ±1 torus vectors. edges and spins are decimal strings. Floats refused. Same law as math_court domain qma_spinglass.

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• twin.robotics.evaluate_exact_ik

  Exact integer inverse kinematics over a declared piece chain: compose local frames from the sovereign anchor and report each piece's pose in whole milli-units. Zero floats, one Q16 normalization point, byte-identical on arm64 and wasm32.

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• umc_direct

  Universal Manifold Controller GAV direct: seed (optional) -> decompose -> measure Rational torsion -> shear-correct -> converge. Domains: cinema|aviation|gaming|coding.

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• umc_resume

  Resume UMC Long Play from latest tip (local cache / NATS KV). Domains: cinema|aviation|gaming|coding.

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• umc_status

  UMC tip + documented MCP tool surface + NATS subjects (gaiaftcl.umc.state.> / gaiaftcl.agent.state.>).

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• verify_amplitude_amplification

  QC-009 Amplitude amplification. Grover oracle plus presented iterate count. N=4 requires iterations=1. Floats refused.

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• verify_amplitude_estimation

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

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• verify_bell_measurement

  QC-018 Bell class. class bits must equal the presented pair. Floats refused.

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• verify_bernstein_vazirani

  QC-007 Bernstein-Vazirani. answers[i] = popcount(hidden AND query_i) mod 2. Floats refused.

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• verify_deutsch_jozsa

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

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• 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.

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• verify_hhl

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

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• verify_jordan_bond

  UUM-8D Jordan bond cross-mul admit (cell-local JordanBondTable, integer geometry).

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• 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.

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• verify_period

  Presented period: a^r == 1 (mod N), gcd(a,N)=1. Optional proper_divisors must not themselves be periods. Does not search for r. Floats refused.

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• verify_phase_kickback

  QC-011 Phase kickback. Presented phase equals k/2^m. Floats refused.

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• verify_presented_pair

  QC-021 Presented two-way affine pair. Either face posts the pair: A (or k) is the private face — 64-hex or decimal; Q (or q_hex) is the public face. Hex A legally contains e; a decimal point is the float. Empty on BOTH faces is REFUSED_EMPTY. One face is enough. Does not derive a third value. Does not ECDLP.

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• verify_qaoa_energy

  QC-014 QAOA problem, not the pulse schedule. Same Ising law as route_spin_glass_manifold. Presented spin string. Floats refused.

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• 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.

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• verify_qpe_phase

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

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• verify_quantum_counting

  QC-015 Quantum counting. count equals the number of 1s in the presented oracle. Floats refused.

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• verify_quantum_walk

  QC-012 Quantum walk on C2. Even steps return; odd steps flip. Floats refused.

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• 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.

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• verify_simon

  QC-008 Simon collision. x != y, x XOR y = mask, f(x)=f(y). Floats refused.

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• verify_superdense

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

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• verify_teleport

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

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• verify_topological_word

  QC-019 Topological word. Sealed Eisenstein (q,r) for cited words Z2_a2b and Z2_abAB. Not a group scan. Floats refused.

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• verify_vqe_energy

  QC-013 VQE problem, not the variational search. Same ZZ law as execute_2local_hamiltonian. Presented config energy. Floats refused.

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• 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.

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