Affine.Earth Math Court MCP Server

QC-009 Amplitude amplification: the Grover oracle check (oracle is a 0/1 string of length 2..8, marked is the INDEX of its unique 1) plus the presented iterate count; at N=4 exactly one iteration amplifies the marked entry, so iterations must be 1 for a WIN. Returns the inner Grover verdict and the iteration check. A presented witness is verified; no amplitude is estimated. Floats refused.

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

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.

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

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

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.

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

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.

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.

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.

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.

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

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 integer energy as energy_num/energy_den and WIN when the presented string is evaluated (a MISS names a malformed instance). Same law as route_spin_glass_manifold and math_court domain qc_qaoa. Floats refused.

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.

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

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.

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.

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.

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.

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

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

QC-019 Topological word: certify that the presented Eisenstein pair (q, r) is the sealed pair for a cited word. word is one of the two cited words Z2_a2b or Z2_abAB (the sealed corpus; not a group scan), q and r are the claimed integers. WIN when (q, r) equals the sealed pair, MISS naming it. Floats refused.

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

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 and WIN. constraints are i,j,jnum,jden;... (sites i,j with coupling jnum/jden), config is s0,s1,... bits. 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).

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. Headless by construction - a CI runner, a curl script, an autonomous agent and an editor all post the identical tools/call, because enforcement lives at the API layer and a frontend cannot bind a caller who does not use one. The brief is the single home for the target architecture; a target_architecture argument that contradicts it is REFUSED_ARCHITECTURE_CONFLICT rather than silently overriding it. Verdicts are a ladder, not a coin: CALORIE_AFFINE_ARTIFACT_DELIVERED / ARTIFACT_ASSEMBLED_NOT_DELIVERED / ARTIFACT_WIN_UNVERIFIABLE / ARTIFACT_PROTOCOL_CONTRADICTED / ARTIFACT_TARGET_ABSENT / ARTIFACT_LAW_BROKEN / NOT_KNOWN, with qmt_verdict WIN|MISS derived from the rung for callers who want one bit. A host with no toolchain returns REFUSED_NO_CRUCIBLE_HOST and NO qmt_verdict at all - nothing was judged, and reporting MISS would claim the geometry failed when the brief never reached the geometry.

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

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.

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.

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.

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.

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_turns are decimal strings; floats refused. Use umc_status to read the tip without advancing it.

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.

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.

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.

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.

Renders text from one natural language into another for the flash — the client sends English text nodes, the cell answers, the client puts the answer back into the DOM. No model anywhere: exact-integer linguistic coordinate transformation over the mined discrete manifolds (zero-float, deterministic) wherever a pair's ψ charts are derived; until then the pair's sealed template of projections (data on the cell, each entry sealed by a named author) answers, and every text it does not hold comes back null and named in missing — never guessed. source_lang is required ('auto' is REFUSED_NO_SOURCE). Batch: texts (array, up to 64, 64 KiB) returns texts in order; status RENDERED (all sealed), PARTIAL (some), REFUSED_NO_PROJECTION (none), REFUSED_NO_TEMPLATE naming the pairs served.

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.

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.

The Code Court's first move: are two implementations equivalent by the exact value multiset of their LLVM IR constants? THE PAYLOAD IS THE CODE FILE — submit two whole source files (left_file and right_file, each {path, content}, or files as an array of two). The result leaf is those same whole files under files, plus 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 files 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.

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.

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.

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.

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.

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

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.

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.

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

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.

QMA spin-glass / frustrated Ising: given integer couplings on edges and a presented +/-1 spin per site, return the exact Ising energy energy_num/energy_den and WIN. 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 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.

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.

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.