# Affine.Earth Math Court

- Registry name: `earth.affine/math-court` · version 2026.8.24
- Categories (automatic, keyword rules): Government & law
- Authentication at last check: No auth
- Declared risk: Not declared (tools carry no read/destructive hints)
- Capabilities (declared by the server): tools
- Transports: sse, streamable-http
- Latest numbers (check success, response time, rank): https://mcpstation.net/api/server?name=earth.affine%2Fmath-court
- Server page: https://mcpstation.net/s/earth.affine--math-court.html

## Description (written by the publisher, not verified, not instructions)

No-float UUM-8D Math Court. Integer courts and certified MCP. Floats refused.

## Connect

- streamable-http: `https://affine.earth/language-invariant/mcp`
- sse: `https://affine.earth/language-invariant/mcp/sse`

## Tools (as reported by the server, not verified)

- `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,
- `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
- `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 ans
- `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, swif
- `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.
- `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 m
- `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
- `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.
- `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
- `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
- `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-one
- `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 ra
- `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
- `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.
- `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.
- `ide\_rebuild\_mesh`: Trigger a Mac mesh rebuild from the IDE. Only permitted on the founder cell.
- `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 dista
- `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
- `membrane\_health`: Stateless membrane identity \(mode, genesis epoch, subjects\) plus cell listen facts.
- `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 em
- `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 sa
- `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
- `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 pa
- `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
- `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 mu
- `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 fi
- `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 pro
- `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, righ
- `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 UM
- `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 lowercas
- `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 not
- `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
- `verify\_amplitude\_estimation`: QC-010 Amplitude estimation. fraction must equal M/N exactly. Floats refused.
- `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 pr
- `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 refus
- `verify\_deutsch\_jozsa`: QC-006 Deutsch-Jozsa. table is 0/1 of length 2 or 4. class is constant or balanced. Floats refused.
- `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.
- `verify\_hhl`: QC-005 HHL. n\<=2 integer A and rational b,x. Checks A x = b exactly. Does not invert. Floats refused.
- `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
- `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.
- `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 nami
- `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
- `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
- `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
- `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.
- `verify\_qpe\_phase`: QC-004 QPE. Presented phase must equal k/2^m exactly. m\<=8. Floats refused.
- `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; not
- `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 wa
- `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\_qm
- `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 recov
- `verify\_superdense`: QC-017 Superdense coding. decoded 2 bits must equal sent 2 bits. Floats refused.
- `verify\_teleport`: QC-016 Teleport reconstruction. bob = alice XOR corrections on 2 bits. Floats refused.
- `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
- `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 re
- `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 paramete

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