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 only when its round trip closes over the exact 256-bit order; a word that does not is CARRIED verbatim in the source language and named — never replaced by a nearest-row guess. The receipt names its lattice: lattice.source is human-text (with digest, axes, rows, dimension, network=none, languages) or model (digest, model, revision, tensor) — read it, do not assume which chart a cell is on — and engine ends in /human-text when the human chart answered. A sealed sentence (a projection sealed by a named author into the append-only language ledger; GET /language-invariant/translate/templates lists them) is taken before the chart. NUMBERS FOLLOW THE SOURCE: a sealed sentence answers every numeric variant of its text; where it writes {n} the text's numbers go in, in order; where it writes numbers literally, each number the text changes is replaced where the sealed wording carries it as digits; when the sealed wording cannot carry the text's number (spelled out, another script's digits, a different count) the sealed sentence is NOT used and numbers[i] names why — the court prints no number the text does not say. status, single target (target_lang): RENDERED (every word crossed), PARTIAL (some texts carry words, or some texts are null and named in missing), REFUSED_NO_PROJECTION (nothing crossed), REFUSED_NO_CHART (no chart and no sealed sentence for the pair; names the chart languages and the pairs served), REFUSED_NO_SOURCE ('auto' or empty source_lang), REFUSED_NO_TARGET (neither key sent, or the one key sent names no language: an empty string or an empty array, named in detail), REFUSED_AMBIGUOUS_TARGET (both KEYS sent, whatever their values — a string, null, an array of anything; refused at the top naming each value exactly as sent, nothing projected — the court does not choose), REFUSED_BAD_TARGET (the one key sent is not its declared type — target_lang not a string, target_langs not an array of strings, including an array with one non-string element; names the value as sent, nothing dropped or coerced), REFUSED_EMPTY, REFUSED_BATCH_TOO_LARGE (more than 64 texts or 64 KiB; checked before anything is sealed, on both forms, and on the one-call form refused at the top with no projections). status, one call (target_langs): PROJECTED — shape {state:{status,digest,steps,torsion,turns,dimension}, projections:{<lang>:<a single-target receipt carrying state_digest>}, targets, rendered, partial, refused, templates, lattice}; every projection is one of RENDERED / PARTIAL / a REFUSED_* by name, and rendered+partial+refused == targets.length; REFUSED_NO_PROJECTION when no language rendered or partially rendered. Every single-target receipt also carries, aligned with texts: provenance[i] — when a sealed sentence answered, {key, entry_digest, row_digest (the ledger row that sealed it), ledger_row (the route that returns that row), sealed_by, sealed_at, status: sealed|verified, verified, verified_by, verified_at, verifications, supersedes (the entry_digest of the sealed sentence it replaced), template_digest (sha256 of the pair's ledger projection), source: ledger|file, numbers}; null when the chart answered or nothing did. words[i] — [{src, dst|null, crossed, reason: closed|shared|shear|margin|oov|particle, runner_up, best_dot, best_n, second_dot, second_n}], the exact integers the separability law compared, so the verdict is recomputable at any margin; empty when a sealed sentence answered. reading[i] — one English sentence a person can read without the source, e.g. "4 of 9 words crossed; water, nine, the stayed in English — the chart could not tell water from esponja". numbers[i] — when a sealed sentence matched, {mode: none|same|slots|digits|refused, sealed, source, substituted, refused?}; null otherwise; verdicts[i] is REFUSED_TEMPLATE_NUMBERS when a sealed sentence was refused on its numbers and no chart could read the text. The older verdicts strings stay for compatibility. Every receipt carries templates {pairs, entries, verified, superseded} — the sealed store's four integers, the same healthz serves in translate_chart.templates — and lattice.templates beside the chart digest when the chart answered. exact is a JSON boolean. source_lang is required — the court does not infer a source. Exactly one of target_lang or target_langs, judged on the KEYS sent: both keys is REFUSED_AMBIGUOUS_TARGET whatever the values, neither is REFUSED_NO_TARGET, the wrong type is REFUSED_BAD_TARGET. Batch: texts (array, up to 64 texts, 64 KiB total) returns texts in order, one line each; text renders one.

Argument	Type	Description
text	string	one source text to render. e.g. Book
texts	array	up to 64 source texts; rendered in order, one line each. e.g. ["Book","Water"]
source_lang*	string	ISO 639-1 source language; required, 'auto' refused. e.g. en
target_lang	string	exactly one of target_lang or target_langs (both keys sent, whatever their values, is REFUSED_AMBIGUOUS_TARGET; sent as anything but a string is REFUSED_BAD_TARGET; sent empty is REFUSED_NO_TARGET). ISO 639-1 target language for a single projection. Declared: ar bn de en es fa fr he hi id it ja ko ms nl pl pt ru sw th tr uk ur vi zh. The pairs a cell can actually answer are what its warmed chart reports (healthz translate_chart.languages, the receipt's lattice.languages); a pair outside them is REFUSED_NO_CHART naming the languages served. e.g. es
target_langs	array	exactly one of target_lang or target_langs (both keys sent, whatever their values, is REFUSED_AMBIGUOUS_TARGET; sent as anything but an array of strings is REFUSED_BAD_TARGET; sent empty is REFUSED_NO_TARGET). ONE CALL, ONE STATE: an array of ISO 639-1 codes, or ["*"] for every language the chart serves; the texts' state is sealed once and returned as one projection per language under `projections`, each carrying the same `state_digest`; status PROJECTED. e.g. ["es","fr"]

Input schema (JSON)

{
  "type": "object",
  "required": [
    "source_lang"
  ],
  "properties": {
    "text": {
      "type": "string",
      "description": "one source text to render. e.g. Book"
    },
    "texts": {
      "type": "array",
      "items": {
        "type": "string"
      },
      "description": "up to 64 source texts; rendered in order, one line each. e.g. [\"Book\",\"Water\"]"
    },
    "source_lang": {
      "type": "string",
      "description": "ISO 639-1 source language; required, 'auto' refused. e.g. en"
    },
    "target_lang": {
      "type": "string",
      "description": "exactly one of target_lang or target_langs (both keys sent, whatever their values, is REFUSED_AMBIGUOUS_TARGET; sent as anything but a string is REFUSED_BAD_TARGET; sent empty is REFUSED_NO_TARGET). ISO 639-1 target language for a single projection. Declared: ar bn de en es fa fr he hi id it ja ko ms nl pl pt ru sw th tr uk ur vi zh. The pairs a cell can actually answer are what its warmed chart reports (healthz translate_chart.languages, the receipt's lattice.languages); a pair outside them is REFUSED_NO_CHART naming the languages served. e.g. es"
    },
    "target_langs": {
      "type": "array",
      "items": {
        "type": "string"
      },
      "description": "exactly one of target_lang or target_langs (both keys sent, whatever their values, is REFUSED_AMBIGUOUS_TARGET; sent as anything but an array of strings is REFUSED_BAD_TARGET; sent empty is REFUSED_NO_TARGET). ONE CALL, ONE STATE: an array of ISO 639-1 codes, or [\"*\"] for every language the chart serves; the texts' state is sealed once and returned as one projection per language under `projections`, each carrying the same `state_digest`; status PROJECTED. e.g. [\"es\",\"fr\"]"
    }
  }
}

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.

Argument	Type	Description
obs_seq	string	decimal string; a sealed AirspaceObservationSeal sequence is ONE INSTANT of sky and carries no time base, so supplying it alone returns NOT_MEASURED_OBSERVATION_SET_HAS_NO_TIME_BASE rather than a fabricated verdict. e.g. 1
trajectories*	array	declared 4D paths: id plus waypoints as decimal strings, strictly advancing in time. e.g. [{"id":"AAA","waypoints":[{"lat_micro_deg":"0","lon_micro_deg":"-100000","alt_feet":"30000","t_seconds":"0"},{"lat_micro_deg":"0","lon_micro_deg":"100000","alt_feet":"30000","t_seconds":"600"}]}]
lon_scale_den	string	OPTIONAL, denominator of the longitude scale as decimal string. RECOMMENDED: six digits or fewer. Cosine to 1e-6 is far below any error that could change a verdict about aircraft, and a six-digit denominator clears every segment-pair time base up to 8589 seconds; a three-digit one clears any time base at all. The hard ceiling is 1000000000, but the binding limit is per-request: 8589934592 divided by the segment pair time base, which is the least common multiple of the two segment durations. Above it the pair returns NOT_MEASURED_SCALED_TIME_BASE_EXCEEDS_EXACT_RANGE naming the exact denominator ceiling that clears at that time base, so the remedy is read off the refusal rather than found by bisection. Reduce the ratio to lowest terms or round it to fewer digits. e.g. 1000000

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.

Argument	Type	Description
A	string	presented private face, 64-hex or decimal. e.g. 1
Q	string	same face as q_hex, old label. e.g. 0479be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8
k	string	same face as A, old label. e.g. 1
q_hex	string	open key, uncompressed 04-prefixed pubkey hex (required). e.g. 0479be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8

Input schema (JSON)

{
  "type": "object",
  "anyOf": [
    {
      "required": [
        "A"
      ]
    },
    {
      "required": [
        "Q"
      ]
    },
    {
      "required": [
        "k"
      ]
    },
    {
      "required": [
        "q_hex"
      ]
    }
  ],
  "required": [],
  "properties": {
    "A": {
      "type": "string",
      "description": "presented private face, 64-hex or decimal. e.g. 1"
    },
    "Q": {
      "type": "string",
      "description": "same face as q_hex, old label. e.g. 0479be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8"
    },
    "k": {
      "type": "string",
      "description": "same face as A, old label. e.g. 1"
    },
    "q_hex": {
      "type": "string",
      "description": "open key, uncompressed 04-prefixed pubkey hex (required). e.g. 0479be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8"
    }
  }
}

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 i32 %x, 3 ret i32 %r }' (one line per instruction) and right the same with 'mul i32 %x, 4' -> CODE_IR_DIVERGED; identical constants -> WIN. Stateless and content-addressed - the same two files rule identically on every cell. Compares the constant pool (a necessary, strong condition for numeric kernels), not full behavioural equivalence.

Argument	Type	Description
files	array	Exactly two whole files when left_file/right_file are not used. The payload IS the files. e.g. [{"path":"left.ll","content":"define i32 @f() { ret i32 143 }"},{"path":"right.ll","content":"define i32 @f() { ret i32 143 }"}]
left_ir	string	LEGACY fragment of the first implementation. Still accepted and lifted into a whole file with a defaulted path; prefer left_file. e.g. define i32 @f() { ret i32 143 }
right_ir	string	LEGACY fragment of the second implementation. Still accepted and lifted into a whole file with a defaulted path; prefer right_file. e.g. define i32 @f() { ret i32 143 }

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.

Argument	Type	Description
limit	string	decimal string, rows up to 8192; JSON numbers still admitted. e.g. 64
at_seq	string	decimal string, caller-pinned stream position; same value = same bytes. e.g. 1
sector	string	hex sector prefix: the four hex digits of the top 16 bits of a bond's Morton key, e.g. 0a3f

Input schema (JSON)

{
  "type": "object",
  "required": [],
  "properties": {
    "limit": {
      "type": "string",
      "description": "decimal string, rows up to 8192; JSON numbers still admitted. e.g. 64"
    },
    "at_seq": {
      "type": "string",
      "description": "decimal string, caller-pinned stream position; same value = same bytes. e.g. 1"
    },
    "sector": {
      "type": "string",
      "description": "hex sector prefix: the four hex digits of the top 16 bits of a bond's Morton key, e.g. 0a3f"
    }
  }
}

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.

Argument	Type	Description
limit	string	decimal string, window size up to 8192. e.g. 256
at_seq	string	decimal string, caller-pinned stream position; same value = same bytes. e.g. 1
source	string	optional lane filter: LLM_WEIGHTS, LLVM_IR, LLVM_IR_I64, AUDIO_SPEECH. e.g. LLVM_IR

Input schema (JSON)

{
  "type": "object",
  "required": [],
  "properties": {
    "limit": {
      "type": "string",
      "description": "decimal string, window size up to 8192. e.g. 256"
    },
    "at_seq": {
      "type": "string",
      "description": "decimal string, caller-pinned stream position; same value = same bytes. e.g. 1"
    },
    "source": {
      "type": "string",
      "description": "optional lane filter: LLM_WEIGHTS, LLVM_IR, LLVM_IR_I64, AUDIO_SPEECH. e.g. LLVM_IR"
    }
  }
}

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.

Argument	Type	Description
cursor_sample	string	decimal string, cursors to decode, up to 1024; the bound is stated in the reply. e.g. 256

Input schema (JSON)

{
  "type": "object",
  "required": [],
  "properties": {
    "cursor_sample": {
      "type": "string",
      "description": "decimal string, cursors to decode, up to 1024; the bound is stated in the reply. e.g. 256"
    }
  }
}

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.

Argument	Type	Description
h	string	decimal string. e.g. 128
n	string	decimal string. e.g. 16
t	string	decimal string. e.g. 0
w	string	decimal string. e.g. 128
kind	string	the language-game context kind: atc, proteins or materials, e.g. atc
seed	string	decimal string; JSON numbers still admitted. e.g. 7
span_scale_q16	string	decimal string, framing to grade; 65536 = unity. e.g. 65536

Input schema (JSON)

{
  "type": "object",
  "required": [],
  "properties": {
    "h": {
      "type": "string",
      "description": "decimal string. e.g. 128"
    },
    "n": {
      "type": "string",
      "description": "decimal string. e.g. 16"
    },
    "t": {
      "type": "string",
      "description": "decimal string. e.g. 0"
    },
    "w": {
      "type": "string",
      "description": "decimal string. e.g. 128"
    },
    "kind": {
      "type": "string",
      "description": "the language-game context kind: atc, proteins or materials, e.g. atc"
    },
    "seed": {
      "type": "string",
      "description": "decimal string; JSON numbers still admitted. e.g. 7"
    },
    "span_scale_q16": {
      "type": "string",
      "description": "decimal string, framing to grade; 65536 = unity. e.g. 65536"
    }
  }
}

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 field posted as a JSON value that is not a string is REFUSED_NOT_A_STRING.

Argument	Type	Description
config	string	computational bits s0,s1,... each 0 or 1, one per site, e.g. 0,1
constraints	string	ZZ terms i,j,jnum,jden;... e.g. 0,1,1,1 (sites 0 and 1, coupling 1/1)
jordanBondExclusions	string	alias of constraints. e.g. 0,1,1,1

Input schema (JSON)

{
  "type": "object",
  "required": [],
  "properties": {
    "config": {
      "type": "string",
      "description": "computational bits s0,s1,... each 0 or 1, one per site, e.g. 0,1"
    },
    "constraints": {
      "type": "string",
      "description": "ZZ terms i,j,jnum,jden;... e.g. 0,1,1,1 (sites 0 and 1, coupling 1/1)"
    },
    "jordanBondExclusions": {
      "type": "string",
      "description": "alias of constraints. e.g. 0,1,1,1"
    }
  }
}

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 the served template send exactly 'Rust no_std wasm32' or omit the field ('wasm32' alone is refused). Verdicts are a ladder of rungs 0-7, not a coin: 7 CALORIE_AFFINE_ARTIFACT_DELIVERED, 6 ARTIFACT_ASSEMBLED_NOT_DELIVERED, 5 ARTIFACT_WIN_UNVERIFIABLE, 4 ARTIFACT_PROTOCOL_CONTRADICTED, 3 ARTIFACT_TARGET_ABSENT, 2 ARTIFACT_LAW_BROKEN, 1 NOT_KNOWN, 0 REFUSED_NO_BRIEF, with qmt_verdict WIN only at rung 7 and MISS below it. THE CEILING: a cell with no toolchain still judges - it reads the brief, enforces Affine law and checks the WASM target and protocol - but caps SOURCE at rung 6 ARTIFACT_ASSEMBLED_NOT_DELIVERED with qmt_verdict MISS, because certifying DELIVERED would claim a build that never happened; REFUSED_NO_CRUCIBLE_HOST is NOT reachable through this tool: its arguments are brief, artifact and target_architecture, and none of them asks for a build - measured 2026-09-29, a brief whose Target Architecture line reads 'Swift 6.4 ~Copyable' (the toolchain no cell has) answers with a rung and qmt_verdict, not that status. To reach rung 7 on any cell, post a COMPILED module: the artifact field as base64 of the wasm bytes (magic 00 61 73 6d 01 00 00 00) with the brief verbatim; the court verifies the magic, version word and section table, seals the bytes and returns them as an MCP resource blob with their sha256 (law_checked=false for a posted module; submit the source in a second call to have Constraints 3/4/5 decided over it).

Argument	Type

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.

Argument	Type	Description
matrix	string	rows \| cells , integer entries. e.g. 1,1,1\|1,1,1\|1,1,1

Input schema (JSON)

{
  "type": "object",
  "required": [],
  "properties": {
    "matrix": {
      "type": "string",
      "description": "rows | cells , integer entries. e.g. 1,1,1|1,1,1|1,1,1"
    }
  }
}

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.

Argument	Type	Description
intent*	string	the transition verb, one of the enum values, e.g. INGEST
economics	object	Optional I_PF economics object: executor hash + impact matrix (Rational weights), keys executor_btc_address_hash and context_class, e.g. {"executor_btc_address_hash":"0123456789abcdef0123456789abcdef","context_class":"default"}
entity_id*	string	wallet_geo entityID hex. e.g. 0123456789abcdef0123456789abcdef
bond_status	string	the bond state the caller reports for itself, recorded with the turn; e.g. BONDED. Omitted -> UNKNOWN
c4_constraints	array	Rational lanes as num/den strings. e.g. ["1/1","0/1","2/3","1/4"]
s4_coordinates	array	Rational lanes as num/den strings. e.g. ["1/2","3/4","0/1","5/1"]
user_vqbit_hash	string

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.

Argument	Type	Description
A	string	first lattice for kind=jordan or lattice: x0,x1,x2,x3,x4,x5,x6,x7\|z as decimal strings, e.g. 1,2,3,4,5,6,7,8\|0
B	string	second lattice, same shape as A, e.g. 1,1,1,1,1,1,1,1\|0
K	string	the lock (kernel) lattice for a Jordan shear, same shape as A. e.g. 3,-2,5,1,7,1,4,2\|1
op	string	lattice operation for kind=lattice, e.g. add; lattice_op with an empty op lists them
kind	string	affine_key\|jordan\|lattice\|qc_\|qma_\|math_court domain. e.g. qc_shor
q_hex	string	alias of object for affine_key. e.g. 0479be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8
object	string	puzzle object; Affine key hex for affine_key. e.g. 0479be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8

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.

No arguments.

Input schema (JSON)

{
  "type": "object",
  "properties": {}
}

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.

Argument	Type	Description
h	string	decimal string. e.g. 128
n	string	decimal string, population. e.g. 16
t	string	decimal string, step index. e.g. 0
w	string	decimal string. e.g. 128
kind	string	the language-game context kind: atc, proteins or materials, e.g. proteins
seed	string	decimal string; JSON numbers still admitted. e.g. 7
at_seq	string	decimal string, pinned corpus epoch. e.g. 1
target	string	decimal string, refine until score >= this (0-1000, default 950). e.g. 950
max_iter	string	decimal string, iteration cap, default 10. e.g. 10

Input schema (JSON)

ide_rebuild_mesh

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

No arguments.

Input schema (JSON)

{
  "type": "object",
  "properties": {}
}

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.

Argument	Type	Description
A	string	first lattice: x0,x1,x2,x3,x4,x5,x6,x7\|z, decimal strings, negatives allowed. e.g. 1,1,1,1,1,1,1,1\|1
B	string	second lattice for shear, add, sub, mul, distance, locking_distance; same shape as A. e.g. 1,1,1,1,1,1,1,1\|1
K	string	the distance (kernel) lattice for shear; same shape as A. e.g. 3,-2,5,1,7,1,4,2\|1
op	string	the operation; empty lists the ops
mask	string	park only: decimal 0-255 homology mask. e.g. 255

Input schema (JSON)

{
  "type": "object",
  "required": [],
  "properties": {
    "A": {
      "type": "string",
      "description": "first lattice: x0,x1,x2,x3,x4,x5,x6,x7|z, decimal strings, negatives allowed. e.g. 1,1,1,1,1,1,1,1|1"
    },
    "B": {
      "type": "string",
      "description": "second lattice for shear, add, sub, mul, distance, locking_distance; same shape as A. e.g. 1,1,1,1,1,1,1,1|1"
    },
    "K": {
      "type": "string",
      "description": "the distance (kernel) lattice for shear; same shape as A. e.g. 3,-2,5,1,7,1,4,2|1"
    },
    "op": {
      "enum": [
        "verify",
        "shear",
        "add",
        "sub",
        "mul",
        "distance",
        "locking_distance",
        "lane_mask",
        "park",
        "permute_p1",
        "permute_p2",
        "is_zero"
      ],
      "type": "string",
      "description": "the operation; empty lists the ops"
    },
    "mask": {
      "type": "string",
      "description": "park only: decimal 0-255 homology mask. e.g. 255"
    }
  }
}

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 catalog: domain_count is the number of courts and domains names each with its roles and may_ingest fields - take the count from the catalog, not from any text. Decimal strings on the wire. Floats refused.

Argument	Type	Description
A	string	the presented private face as decimal or 64-hex, e.g. 1. Read by qc_affine_key/researcher; post it only for those domains - a court names the fields it grades on in its REFUSED_NO_INSTANCE detail.
M	string	the number of marked entries out of N, e.g. 1. Read by qc_ampest/researcher; post it only for those domains - a court names the fields it grades on in its REFUSED_NO_INSTANCE detail.
N	string	the modulus N of the period or Shor witness (qc_period, qc_shor: 15) or the search size (qc_ampest: 4), e.g. 15. Read by qc_ampest/researcher, qc_period/researcher, qc_shor/researcher, qc_shor_twin/researcher; post it only for those domains - a court names the fields it grades on in its REFUSED_NO_INSTANCE detail.

membrane_health

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

No arguments.

Input schema (JSON)

{
  "type": "object",
  "properties": {}
}

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.

Argument	Type	Description
lane	string	weather \| space (maps to gaiaftcl.radar.*)
wallet_hash	string	optional caller fiber (sha256 of the wallet, lowercase hex); carried into the invocation receipt, not read by the weather lanes. e.g. 5df6e0e2761359d30a8275058e299fcc0381534545f55cf43e41983f5d4c9456
c4_invariant_scf	string	optional C4 invariant SCF hex of the caller session; carried into the invocation receipt, not read by the weather lanes. e.g. 0123456789abcdef0123456789abcdef

Input schema (JSON)

{
  "type": "object",
  "required": [],
  "properties": {
    "lane": {
      "enum": [
        "weather",
        "space"
      ],
      "type": "string",
      "description": "weather | space (maps to gaiaftcl.radar.*)"
    },
    "wallet_hash": {
      "type": "string",
      "description": "optional caller fiber (sha256 of the wallet, lowercase hex); carried into the invocation receipt, not read by the weather lanes. e.g. 5df6e0e2761359d30a8275058e299fcc0381534545f55cf43e41983f5d4c9456"
    },
    "c4_invariant_scf": {
      "type": "string",
      "description": "optional C4 invariant SCF hex of the caller session; carried into the invocation receipt, not read by the weather lanes. e.g. 0123456789abcdef0123456789abcdef"
    }
  }
}

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.

Argument	Type	Description
A	string	the private face: a secp256k1 scalar as decimal or 64-hex, e.g. 2; the court projects Q = A*G
Q	string	same face as q_hex, old label. e.g. 0479be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8
k	string	same face as A, old label. e.g. 1
q_hex	string	the public face: uncompressed 04-prefixed secp256k1 point, 130 hex characters; the court projects its shear and period, never a scalar. e.g. 0479be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8

Input schema (JSON)

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.

Argument	Type	Description
N*	string	the modulus, decimal, e.g. 15 - carried in every shape; without it there is no question
factor	string	post factor together with cofactor (e.g. 3 and 5) and the court projects halfPow by CRT
halfPow	string	post this half (a with a^2 == 1 mod N, a != 1, N-1), e.g. 4, and the court projects factor and cofactor
cofactor	string	N / factor, decimal, e.g. 5; posted together with factor

Input schema (JSON)

{
  "type": "object",
  "anyOf": [
    {
      "required": [
        "N"
      ]
    },
    {
      "required": [
        "N",
        "halfPow"
      ]
    },
    {
      "required": [
        "N",
        "cofactor",
        "factor"
      ]
    }
  ],
  "required": [
    "N"
  ],
  "properties": {
    "N": {
      "type": "string",
      "description": "the modulus, decimal, e.g. 15 - carried in every shape; without it there is no question"
    },
    "factor": {
      "type": "string",
      "description": "post factor together with cofactor (e.g. 3 and 5) and the court projects halfPow by CRT"
    },
    "halfPow": {
      "type": "string",
      "description": "post this half (a with a^2 == 1 mod N, a != 1, N-1), e.g. 4, and the court projects factor and cofactor"
    },
    "cofactor": {
      "type": "string",
      "description": "N / factor, decimal, e.g. 5; posted together with factor"
    }
  }
}

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, digest (sha256 over the canonical bytes), arms_total, arms_ok, failing, missing, franklin (the narration lines), sealed_by and status. The court opens no app and runs no prover: the arms are the caller's measurements. It WRITES NOTHING on the cell and reads no clock; nine cells return the same bytes for the same record.

Argument	Type	Description
date	string	optional: the caller's clock, echoed as graded_at on the receipt; the court reads no clock of its own. e.g. 2026-10-06T21:10:00Z
record	string	the canonical regression record: UTF-8 lines, tab-separated, LF endings, first line affine_ide_regression<TAB>1, then version, build, date, host, optional dmg_sha256, app_sha256, studies, one arm line per arm (arm<TAB>surface<TAB>name<TAB>ok\|BAD<TAB>detail) and one shot line per screenshot (shot<TAB>name<TAB>bytes<TAB>sha256). e.g. affine_ide_regression 1 version 0.2.6.4 build 3282 date 2026-10-06T21:10:00Z host macOS 27.2 app_sha256 <64 lowercase hex> studies 1 arm stage study-47 ok route domain · showing DomainViewer ...

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.

Argument	Type	Description
edges	string	couplings i,j,J;... integer J, e.g. 0,1,1;1,2,1;2,0,1
spins	string	discrete spins +1,-1,... one per site, e.g. 1,-1,1

Input schema (JSON)

{
  "type": "object",
  "required": [],
  "properties": {
    "edges": {
      "type": "string",
      "description": "couplings i,j,J;... integer J, e.g. 0,1,1;1,2,1;2,0,1"
    },
    "spins": {
      "type": "string",
      "description": "discrete spins +1,-1,... one per site, e.g. 1,-1,1"
    }
  }
}

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 writes the usda.

Argument	Type	Description
sea*	object	the sea plane, every value a decimal string of micrometres. e.g. {"half_width_um":"60000000","half_depth_um":"40000000","z_um":"0"}
study*	string	the study the stage belongs to; the default prim is Scene_<study>. e.g. iliad
assets	array	optional: the scene_ingest INGESTED answers to place, in placement order; each needs usda, seal_row and digest exactly as returned. e.g. [{"usda":"<usda>","seal_row":"<seal_row>","digest":"<digest>"}]
camera	object	optional: the hero camera, four x,y,z micrometre triples; absent keys keep the Iliad stage's defaults. e.g. {"eye":"6000000,19000000,86000000","forward":"0,0,-1000000"}

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 at weld_cell_um and doubles the cell up to 12 times until faces fit face_budget (REFUSED_BUDGET), and SceneProvenanceLaw seals the canonical row. INGESTED returns usda (one def Mesh with int2[] px pairs, the welded mesh as sealed; the pose in the row is applied by scene_compose), seal_row, digest (sha256 of the row), source_sha256, triangles_in, faces_out, points_out, weld_cell_um, mesh_fnv1a, placement (HELD when a second rights field such as a Smithsonian copyright is recorded) and sealed_by. It fetches nothing, reads no clock and writes nothing on the cell; nine cells return the same bytes for the same call.

Argument	Type	Description
kind*	string	what the bytes are: stl (binary or ASCII). obj, ply, glb, geojson_coast, elevation_rows and star_rows are later steps and answer REFUSED_FORMAT. e.g. stl
name*	string	the asset's name, recorded in the seal row; the stage names the mesh Scan/<name>. e.g. 3d_model_of_Sphere
text

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.

Argument	Type	Description
study*	string	the study that owns the document, e.g. study-51 or franklin-avatar
prompt*	string	the person's words. Iliad selects the Iliad cut. Franklin avatar composes the next avatar stage.
example_usda	string	optional: the text of iliad-01-scene-01-imax.usda, for an Iliad scene 01 prompt that wants the native companion baked. Without it the court answers NAMED with the shipped companion's name.

Input schema (JSON)

{
  "type": "object",
  "required": [
    "study",
    "prompt"
  ],
  "properties": {
    "study": {
      "enum": [
        "study-51",
        "study-52",
        "study-53",
        "study-54",
        "franklin-avatar"
      ],
      "type": "string",
      "description": "the study that owns the document, e.g. study-51 or franklin-avatar"
    },
    "prompt": {
      "type": "string",
      "description": "the person's words. Iliad selects the Iliad cut. Franklin avatar composes the next avatar stage."
    },
    "example_usda": {
      "type": "string",
      "description": "optional: the text of iliad-01-scene-01-imax.usda, for an Iliad scene 01 prompt that wants the native companion baked. Without it the court answers NAMED with the shipped companion's name."
    }
  }
}

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 exact closed form exists and refuses by name otherwise; a later release builds it).

Argument	Type	Description
pieces	array	declared PieceFrame rows as decimal strings. e.g. [{"piece_id":"3","rotation_milli_deg":"15000"}]
piece_id*	string	decimal string, the piece to solve for. e.g. 3
relative_to_head	boolean	state the pose relative to the head (camera-free) rather than the anchor. e.g. true

Input schema (JSON)

{
  "type": "object",
  "required": [
    "piece_id"
  ],
  "properties": {
    "pieces": {
      "type": "array",
      "items": {
        "type": "object",
        "properties": {
          "piece_id": {
            "type": "string",
            "description": "decimal string, one of the seven declared ids 0..6 (0 head, 1 eye_globe_l, 2 eye_globe_r, 3 lid_upper_l, 4 lid_lower_l, 5 lid_upper_r, 6 lid_lower_r), e.g. 3"
          },
          "parent_id": {
            "type": "string",
            "description": "decimal string, the id of the parent piece, e.g. 0 (the head)"
          },
          "extent_milli": {
            "type": "string",
            "description": "decimal string, extent in millimetres, e.g. 12"
          },
          "origin_x_milli": {
            "type": "string",
            "description": "decimal string, origin X in millimetres, e.g. 0"
          },
          "origin_y_milli": {
            "type": "string",
            "description": "decimal string, origin Y in millimetres, e.g. 0"
          },
          "origin_z_milli": {
            "type": "string",
            "description": "decimal string, origin Z in millimetres, e.g. 0"
          },
          "rotation_milli_deg": {
            "type": "string",
            "description": "decimal string, rotation in milli-degrees, e.g. 15000 for 15 degrees"
          }
        }
      },
      "description": "declared PieceFrame rows as decimal strings. e.g. [{\"piece_id\":\"3\",\"rotation_milli_deg\":\"15000\"}]"
    },
    "piece_id": {
      "type": "string",
      "description": "decimal string, the piece to solve for. e.g. 3"
    },
    "relative_to_head": {
      "type": "boolean",
      "description": "state the pose relative to the head (camera-free) rather than the anchor. e.g. true"
    }
  }
}

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

Argument	Type	Description
title	string	human label for the session, <= 80 characters, informational only. e.g. first long play
domain	string	which Long Play law governs the session
node_id	string	the session node: any stable string naming the client or tab that plays this session, e.g. ide-tab-1. This is NOT the caller identity; identity is user_vqbit_hash, entity_id or wallet_hash
entity_id	string	caller identity, alternative to user_vqbit_hash: the wallet_geo entity id hex, e.g. 00112233445566778899aabbccddeeff
max_turns	string

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.

Argument	Type	Description
direct	boolean	true: after resuming, advance one turn (equivalent to one umc_direct call). e.g. true
domain*	string	the domain the session was started under
node_id*	string	the session node: any stable string naming the client or tab that plays this session, e.g. ide-tab-1. This is NOT the caller identity; identity is user_vqbit_hash, entity_id or wallet_hash
entity_id	string	caller identity, alternative to user_vqbit_hash: the wallet_geo entity id hex, e.g. 00112233445566778899aabbccddeeff
session_id*	string	the session id given to umc_direct. e.g. r5-session-1
wallet_hash	string

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.

No arguments.

Input schema (JSON)

{
  "type": "object",
  "properties": {}
}

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.

Argument	Type	Description
marked*	string	0-based index of the 1 (the marked entry), decimal. e.g. 3
oracle*	string	0/1 string, length 2..8, exactly one 1, e.g. 0001
iterations*	string	presented iterate count, decimal; 1 at N=4. e.g. 1

Input schema (JSON)

{
  "type": "object",
  "required": [
    "iterations",
    "marked",
    "oracle"
  ],
  "properties": {
    "marked": {
      "type": "string",
      "description": "0-based index of the 1 (the marked entry), decimal. e.g. 3"
    },
    "oracle": {
      "type": "string",
      "description": "0/1 string, length 2..8, exactly one 1, e.g. 0001"
    },
    "iterations": {
      "type": "string",
      "description": "presented iterate count, decimal; 1 at N=4. e.g. 1"
    }
  }
}

verify_amplitude_estimation

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

Argument	Type	Description
M*	string	number of marked entries, 0..N, decimal, e.g. 1
N*	string	size of the sample space, 1..64, decimal, e.g. 4
fraction*	string	the presented amplitude fraction as an exact rational, must equal M/N, e.g. 1/4

Input schema (JSON)

{
  "type": "object",
  "required": [
    "M",
    "N",
    "fraction"
  ],
  "properties": {
    "M": {
      "type": "string",
      "description": "number of marked entries, 0..N, decimal, e.g. 1"
    },
    "N": {
      "type": "string",
      "description": "size of the sample space, 1..64, decimal, e.g. 4"
    },
    "fraction": {
      "type": "string",
      "description": "the presented amplitude fraction as an exact rational, must equal M/N, e.g. 1/4"
    }
  }
}

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.

Argument	Type	Description
ab*	string	two measured bits, e.g. 00 or 11
class*	string	the two Bell-class bits claimed for the pair, e.g. 00

Input schema (JSON)

{
  "type": "object",
  "required": [
    "ab",
    "class"
  ],
  "properties": {
    "ab": {
      "type": "string",
      "description": "two measured bits, e.g. 00 or 11"
    },
    "class": {
      "type": "string",
      "description": "the two Bell-class bits claimed for the pair, e.g. 00"
    }
  }
}

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.

Argument	Type	Description
hidden*	string	the hidden bit string s, length 1..8, e.g. 101
answers*	string	one bit per query, concatenated in query order, e.g. 101 = popcount(s AND q_i) mod 2 for each query
queries*	string	query bit strings of the same length as hidden, separated by ';' (a comma-separated list is REFUSED_SHAPE), e.g. 100;010;001

Input schema (JSON)

{
  "type": "object",
  "required": [
    "answers",
    "hidden",
    "queries"
  ],
  "properties": {
    "hidden": {
      "type": "string",
      "description": "the hidden bit string s, length 1..8, e.g. 101"
    },
    "answers": {
      "type": "string",
      "description": "one bit per query, concatenated in query order, e.g. 101 = popcount(s AND q_i) mod 2 for each query"
    },
    "queries": {
      "type": "string",
      "description": "query bit strings of the same length as hidden, separated by ';' (a comma-separated list is REFUSED_SHAPE), e.g. 100;010;001"
    }
  }
}

verify_deutsch_jozsa

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

Argument	Type	Description
class*	string	constant or balanced, e.g. balanced for table 0110
table*	string	the oracle's truth table as a 0/1 string of length 2 or 4, e.g. 0110

Input schema (JSON)

{
  "type": "object",
  "required": [
    "class",
    "table"
  ],
  "properties": {
    "class": {
      "type": "string",
      "description": "constant or balanced, e.g. balanced for table 0110"
    },
    "table": {
      "type": "string",
      "description": "the oracle's truth table as a 0/1 string of length 2 or 4, e.g. 0110"
    }
  }
}

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.

Argument	Type	Description
marked*	string	0-based index of that single 1, decimal, e.g. 2 for oracle 0010
oracle*	string	0/1 string of length 2..8 with exactly one 1, e.g. 0010

Input schema (JSON)

{
  "type": "object",
  "required": [
    "marked",
    "oracle"
  ],
  "properties": {
    "marked": {
      "type": "string",
      "description": "0-based index of that single 1, decimal, e.g. 2 for oracle 0010"
    },
    "oracle": {
      "type": "string",
      "description": "0/1 string of length 2..8 with exactly one 1, e.g. 0010"
    }
  }
}

verify_hhl

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

Argument	Type	Description
b*	string	right-hand side b as comma-separated rationals, one per row, e.g. 2,4
x*	string	the presented solution x as comma-separated rationals, e.g. 1,2; the court checks A x = b exactly and never inverts
matrix*	string	integer matrix A, 1x1 or 2x2: rows separated by '\|', entries by ',', e.g. 2,0\|0,2

Input schema (JSON)

{
  "type": "object",
  "required": [
    "b",
    "matrix",
    "x"
  ],
  "properties": {
    "b": {
      "type": "string",
      "description": "right-hand side b as comma-separated rationals, one per row, e.g. 2,4"
    },
    "x": {
      "type": "string",
      "description": "the presented solution x as comma-separated rationals, e.g. 1,2; the court checks A x = b exactly and never inverts"
    },
    "matrix": {
      "type": "string",
      "description": "integer matrix A, 1x1 or 2x2: rows separated by '|', entries by ',', e.g. 2,0|0,2"
    }
  }
}

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.

Argument	Type	Description
A	string	x0,x1,x2,x3,x4,x5,x6,x7\|z decimal lattice (the source). e.g. 1,1,1,1,1,1,1,1\|1
B	string	x0,x1,x2,x3,x4,x5,x6,x7\|z decimal lattice (the target). e.g. 1,1,1,1,1,1,1,1\|1
K	string	x0,x1,x2,x3,x4,x5,x6,x7\|z distance lattice (the kernel the shear runs through). e.g. 3,-2,5,1,7,1,4,2\|1
q_hex	string	optional: a secp256k1 point (130-hex 04... or 66-hex compressed) for the Q-only Affine expose instead of lattices. e.g. 0279be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798
object	string	alias of q_hex. e.g. 0279be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798
source_creator_hash

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.

Argument	Type	Description
n	string	particle count as decimal string. e.g. 2
rho2	string	a11,a12\|a21,a22 as num/den rationals. e.g. 1/2,0/1\|0/1,1/2

Input schema (JSON)

{
  "type": "object",
  "required": [],
  "properties": {
    "n": {
      "type": "string",
      "description": "particle count as decimal string. e.g. 2"
    },
    "rho2": {
      "type": "string",
      "description": "a11,a12|a21,a22 as num/den rationals. e.g. 1/2,0/1|0/1,1/2"
    }
  }
}

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.

Argument	Type	Description
N*	string	modulus, decimal, e.g. 15
a*	string	base, coprime with N, decimal, e.g. 2
r*	string	the presented period: a^r == 1 (mod N), decimal, e.g. 4
proper_divisors*	string	REQUIRED on the wire: comma-separated proper divisors of r that must NOT be periods (that is the order claim), e.g. 1,2 for r=4. Absent -> REFUSED_NO_INSTANCE 'missing proper_divisors'

Input schema (JSON)

{
  "type": "object",
  "required": [
    "N",
    "a",
    "proper_divisors",
    "r"
  ],
  "properties": {
    "N": {
      "type": "string",
      "description": "modulus, decimal, e.g. 15"
    },
    "a": {
      "type": "string",
      "description": "base, coprime with N, decimal, e.g. 2"
    },
    "r": {
      "type": "string",
      "description": "the presented period: a^r == 1 (mod N), decimal, e.g. 4"
    },
    "proper_divisors": {
      "type": "string",
      "description": "REQUIRED on the wire: comma-separated proper divisors of r that must NOT be periods (that is the order claim), e.g. 1,2 for r=4. Absent -> REFUSED_NO_INSTANCE 'missing proper_divisors'"
    }
  }
}

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.

Argument	Type	Description
k*	string	eigenphase index, decimal, 0 <= k < 2^m. e.g. 1
m*	string	register width, decimal, >= 1. e.g. 1
phase*	string	claimed phase as an exact rational num/den, e.g. 1/2

Input schema (JSON)

{
  "type": "object",
  "required": [
    "k",
    "m",
    "phase"
  ],
  "properties": {
    "k": {
      "type": "string",
      "description": "eigenphase index, decimal, 0 <= k < 2^m. e.g. 1"
    },
    "m": {
      "type": "string",
      "description": "register width, decimal, >= 1. e.g. 1"
    },
    "phase": {
      "type": "string",
      "description": "claimed phase as an exact rational num/den, e.g. 1/2"
    }
  }
}

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.

Argument	Type	Description
A	string	private face, 64-hex or decimal scalar, e.g. 1 (its public face is G itself)
Q	string	public face: uncompressed 04-prefixed secp256k1 point, 130 hex characters, e.g. 0479BE667E...B8 for A=1
k	string	same face as A, old label. e.g. 1
q_hex	string	same face as Q, old label. e.g. 0279be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798
lock_q	string	a lock face: the public point the pair must be verified against, same shape as Q. e.g. 0279be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798
object	string	alias of q_hex. e.g. 0279be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798

Input schema (JSON)

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.

Argument	Type	Description
edges*	string	couplings i,j,J;... e.g. 0,1,1;1,2,1;2,0,1 (integer J)
spins*	string	discrete spins +1,-1,... one per site, e.g. 1,-1,1

Input schema (JSON)

{
  "type": "object",
  "required": [
    "edges",
    "spins"
  ],
  "properties": {
    "edges": {
      "type": "string",
      "description": "couplings i,j,J;... e.g. 0,1,1;1,2,1;2,0,1 (integer J)"
    },
    "spins": {
      "type": "string",
      "description": "discrete spins +1,-1,... one per site, e.g. 1,-1,1"
    }
  }
}

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.

Argument	Type	Description
k*	string	input index, 0 <= k < n, decimal, e.g. 1
n*	string	register size: 2, 4 or 8, e.g. 4
phases*	string	the n phases j*k/n as exact rationals, comma-separated in j order, e.g. 0/4,1/4,2/4,3/4 for n=4, k=1

Input schema (JSON)

{
  "type": "object",
  "required": [
    "k",
    "n",
    "phases"
  ],
  "properties": {
    "k": {
      "type": "string",
      "description": "input index, 0 <= k < n, decimal, e.g. 1"
    },
    "n": {
      "type": "string",
      "description": "register size: 2, 4 or 8, e.g. 4"
    },
    "phases": {
      "type": "string",
      "description": "the n phases j*k/n as exact rationals, comma-separated in j order, e.g. 0/4,1/4,2/4,3/4 for n=4, k=1"
    }
  }
}

verify_qpe_phase

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

Argument	Type	Description
k*	string	eigenphase index, 0 <= k < 2^m, decimal, e.g. 1
m*	string	precision bits, 1..8, e.g. 2
phase*	string	the presented phase as an exact rational num/den, must equal k/2^m, e.g. 1/4 for m=2, k=1

Input schema (JSON)

{
  "type": "object",
  "required": [
    "k",
    "m",
    "phase"
  ],
  "properties": {
    "k": {
      "type": "string",
      "description": "eigenphase index, 0 <= k < 2^m, decimal, e.g. 1"
    },
    "m": {
      "type": "string",
      "description": "precision bits, 1..8, e.g. 2"
    },
    "phase": {
      "type": "string",
      "description": "the presented phase as an exact rational num/den, must equal k/2^m, e.g. 1/4 for m=2, k=1"
    }
  }
}

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.

Argument	Type	Description
count*	string	claimed number of 1s, decimal. e.g. 1
oracle*	string	0/1 string, length 2..8, e.g. 0001

Input schema (JSON)

{
  "type": "object",
  "required": [
    "count",
    "oracle"
  ],
  "properties": {
    "count": {
      "type": "string",
      "description": "claimed number of 1s, decimal. e.g. 1"
    },
    "oracle": {
      "type": "string",
      "description": "0/1 string, length 2..8, e.g. 0001"
    }
  }
}

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.

Argument	Type	Description
end*	string	claimed ending vertex, 0 or 1. e.g. 0
start*	string	starting vertex, 0 or 1. e.g. 0
steps*	string	number of steps, decimal, >= 0. e.g. 2

Input schema (JSON)

{
  "type": "object",
  "required": [
    "end",
    "start",
    "steps"
  ],
  "properties": {
    "end": {
      "type": "string",
      "description": "claimed ending vertex, 0 or 1. e.g. 0"
    },
    "start": {
      "type": "string",
      "description": "starting vertex, 0 or 1. e.g. 0"
    },
    "steps": {
      "type": "string",
      "description": "number of steps, decimal, >= 0. e.g. 2"
    }
  }
}

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.

Argument	Type	Description
N	string	the modulus, decimal, e.g. 15
q_hex	string	optional Affine Q hex; Q-only expose envelope; no k. e.g. 0279be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798
factor	string	gcd(halfPow-1, N), decimal, e.g. 3
object	string	alias of q_hex. e.g. 0279be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798
halfPow	string	the witness a with a^2 == 1 (mod N) and a != 1, N-1, decimal, e.g. 4 for N=15
cofactor	string	N / factor, decimal, e.g. 5

Input schema (JSON)

{
  "type": "object",
  "anyOf": [
    {
      "required": [
        "N",
        "cofactor",
        "factor",
        "halfPow"
      ]
    },
    {
      "required": [
        "q_hex"
      ]
    },
    {
      "required": [
        "object"
      ]
    }
  ],
  "required": [],
  "properties": {
    "N": {
      "type": "string",
      "description": "the modulus, decimal, e.g. 15"
    },
    "q_hex": {
      "type": "string",
      "description": "optional Affine Q hex; Q-only expose envelope; no k. e.g. 0279be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798"
    },
    "factor": {
      "type": "string",
      "description": "gcd(halfPow-1, N), decimal, e.g. 3"
    },
    "object": {
      "type": "string",
      "description": "alias of q_hex. e.g. 0279be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798"
    },
    "halfPow": {
      "type": "string",
      "description": "the witness a with a^2 == 1 (mod N) and a != 1, N-1, decimal, e.g. 4 for N=15"
    },
    "cofactor": {
      "type": "string",
      "description": "N / factor, decimal, e.g. 5"
    }
  }
}

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.

Argument	Type	Description
x*	string	first input bit string, same length as mask. e.g. 00
y*	string	second input bit string; x XOR y must equal mask. e.g. 11
fx*	string	presented f(x), decimal or bit string. e.g. 0
fy*	string	presented f(y); must equal fx. e.g. 0
mask*	string	hidden mask as a bit string, e.g. 11

Input schema (JSON)

{
  "type": "object",
  "required": [
    "fx",
    "fy",
    "mask",
    "x",
    "y"
  ],
  "properties": {
    "x": {
      "type": "string",
      "description": "first input bit string, same length as mask. e.g. 00"
    },
    "y": {
      "type": "string",
      "description": "second input bit string; x XOR y must equal mask. e.g. 11"
    },
    "fx": {
      "type": "string",
      "description": "presented f(x), decimal or bit string. e.g. 0"
    },
    "fy": {
      "type": "string",
      "description": "presented f(y); must equal fx. e.g. 0"
    },
    "mask": {
      "type": "string",
      "description": "hidden mask as a bit string, e.g. 11"
    }
  }
}

verify_superdense

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

Argument	Type	Description
bits*	string	the two bits sent, e.g. 10
decoded*	string	the two bits decoded at the receiver, must equal bits, e.g. 10

Input schema (JSON)

{
  "type": "object",
  "required": [
    "bits",
    "decoded"
  ],
  "properties": {
    "bits": {
      "type": "string",
      "description": "the two bits sent, e.g. 10"
    },
    "decoded": {
      "type": "string",
      "description": "the two bits decoded at the receiver, must equal bits, e.g. 10"
    }
  }
}

verify_teleport

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

Argument	Type	Description
bob*	string	Bob's reconstructed two bits, must equal alice XOR corrections, e.g. 01
alice*	string	Alice's two measurement bits, e.g. 10
corrections*	string	the two Pauli-correction bits Bob applies, e.g. 11

Input schema (JSON)

{
  "type": "object",
  "required": [
    "alice",
    "bob",
    "corrections"
  ],
  "properties": {
    "bob": {
      "type": "string",
      "description": "Bob's reconstructed two bits, must equal alice XOR corrections, e.g. 01"
    },
    "alice": {
      "type": "string",
      "description": "Alice's two measurement bits, e.g. 10"
    },
    "corrections": {
      "type": "string",
      "description": "the two Pauli-correction bits Bob applies, e.g. 11"
    }
  }
}

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.

Argument	Type	Description
q*	string	claimed Eisenstein q, decimal. e.g. 0
r*	string	claimed Eisenstein r, decimal. e.g. 1
word*	string	the cited word

Input schema (JSON)

{
  "type": "object",
  "required": [
    "q",
    "r",
    "word"
  ],
  "properties": {
    "q": {
      "type": "string",
      "description": "claimed Eisenstein q, decimal. e.g. 0"
    },
    "r": {
      "type": "string",
      "description": "claimed Eisenstein r, decimal. e.g. 1"
    },
    "word": {
      "enum": [
        "Z2_a2b",
        "Z2_abAB"
      ],
      "type": "string",
      "description": "the cited word"
    }
  }
}

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.

Argument	Type	Description
config*	string	computational bits s0,s1,... each 0 or 1, one per site, comma-separated, e.g. 0,1
constraints*	string	ZZ terms i,j,jnum,jden separated by ;, e.g. 0,1,1,1 (sites 0 and 1, coupling 1/1) - the same law as execute_2local_hamiltonian

Input schema (JSON)

{
  "type": "object",
  "required": [
    "config",
    "constraints"
  ],
  "properties": {
    "config": {
      "type": "string",
      "description": "computational bits s0,s1,... each 0 or 1, one per site, comma-separated, e.g. 0,1"
    },
    "constraints": {
      "type": "string",
      "description": "ZZ terms i,j,jnum,jden separated by ;, e.g. 0,1,1,1 (sites 0 and 1, coupling 1/1) - the same law as execute_2local_hamiltonian"
    }
  }
}

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.

Argument	Type	Description
cells*	array	declared convective cells: id, vertices, and layer as decimal strings. Declaring none returns NOT_MEASURED_NO_CONVECTIVE_CELLS_DECLARED, never CONTAINED. e.g. [{"id":"SQUARE","base_feet":"0","top_feet":"40000","vertices":[{"lat_micro_deg":"0","lon_micro_deg":"0"},{"lat_micro_deg":"0","lon_micro_deg":"30000"},{"lat_micro_deg":"30000","lon_micro_deg":"30000"},{"lat_micro_deg":"30000","lon_micro_deg":"0"}]}]
track_micro_deg*	array	lat_micro_deg,lon_micro_deg,alt_feet points as decimal strings; two or more, since this names a breaching SEGMENT. e.g. [{"lat_micro_deg":"50000","lon_micro_deg":"50000","alt_feet":"30000"},{"lat_micro_deg":"50000","lon_micro_deg":"80000","alt_feet":"30000"}]
margin_micro_deg	string	optional standoff as decimal string in the same declared units; strict, so exactly this far away is contained. e.g. 1000

Input schema (JSON)

{
  "type": "object",
  "required": [
    "track_micro_deg",
    "cells"
  ],
  "properties": {
    "cells": {
      "type": "array",
      "items": {
        "type": "object",
        "properties": {
          "id": {
            "type": "string",
            "description": "the cell id, e.g. SQUARE"
          },
          "top_feet": {
            "type": "string",
            "description": "decimal string, cell top altitude in feet, e.g. 40000"
          },
          "vertices": {
            "type": "array",
            "items": {
              "type": "object",
              "properties": {
                "lat_micro_deg": {
                  "type": "string",
                  "description": "decimal string, vertex latitude in micro-degrees, e.g. 30000"
                },
                "lon_micro_deg": {
                  "type": "string",
                  "description": "decimal string, vertex longitude in micro-degrees, e.g. 30000"
                }
              }
            },
            "description": "three or more polygon vertices in micro-degrees, e.g. [{\"lat_micro_deg\":\"0\",\"lon_micro_deg\":\"0\"},{\"lat_micro_deg\":\"0\",\"lon_micro_deg\":\"30000\"},{\"lat_micro_deg\":\"30000\",\"lon_micro_deg\":\"30000\"},{\"lat_micro_deg\":\"30000\",\"lon_micro_deg\":\"0\"}]"
          },
          "base_feet": {
            "type": "string",
            "description": "decimal string, cell base altitude in feet, e.g. 0"
          }
        }
      },
      "description": "declared convective cells: id, vertices, and layer as decimal strings. Declaring none returns NOT_MEASURED_NO_CONVECTIVE_CELLS_DECLARED, never CONTAINED. e.g. [{\"id\":\"SQUARE\",\"base_feet\":\"0\",\"top_feet\":\"40000\",\"vertices\":[{\"lat_micro_deg\":\"0\",\"lon_micro_deg\":\"0\"},{\"lat_micro_deg\":\"0\",\"lon_micro_deg\":\"30000\"},{\"lat_micro_deg\":\"30000\",\"lon_micro_deg\":\"30000\"},{\"lat_micro_deg\":\"30000\",\"lon_micro_deg\":\"0\"}]}]"
    },
    "track_micro_deg": {
      "type": "array",
      "items": {
        "type": "object",
        "properties": {
          "alt_feet": {
            "type": "string",
            "description": "decimal string, altitude in feet, e.g. 30000"
          },
          "lat_micro_deg": {
            "type": "string",
            "description": "decimal string, latitude in micro-degrees, e.g. 50000"
          },
          "lon_micro_deg": {
            "type": "string",
            "description": "decimal string, longitude in micro-degrees, e.g. 50000"
          }
        }
      },
      "description": "lat_micro_deg,lon_micro_deg,alt_feet points as decimal strings; two or more, since this names a breaching SEGMENT. e.g. [{\"lat_micro_deg\":\"50000\",\"lon_micro_deg\":\"50000\",\"alt_feet\":\"30000\"},{\"lat_micro_deg\":\"50000\",\"lon_micro_deg\":\"80000\",\"alt_feet\":\"30000\"}]"
    },
    "margin_micro_deg": {
      "type": "string",
      "description": "optional standoff as decimal string in the same declared units; strict, so exactly this far away is contained. e.g. 1000"
    }
  }
}

brief*	string	The complete ARTIFACT INGESTION BRIEF: four sections ([LANGUAGE GAME DEFINITION], [STRUCTURAL GOAL], [PAYLOAD SHAPE], [WASM MEMBRANE INTEGRATION]) with every field filled. The blank template is refused as REFUSED_UNFILLED_PLACEHOLDER. e.g. the served template https://affine.earth/language-game/court-client.brief.txt with every field filled
artifact*	string	The source the agent generated to satisfy the brief. Generation is the caller's half; the crucible compiles, evaluates and seals. e.g. the source text of one file, or the base64 of a compiled wasm module such as AGFzbQEAAAABBQFgAAF/ (which reaches rung 7)
target_architecture	string	OPTIONAL and redundant: the brief's [PAYLOAD SHAPE] is the single home for this value. Supplied only for callers using the original schema; a value that contradicts the brief is REFUSED_ARCHITECTURE_CONFLICT rather than silently overriding it. e.g. Rust no_std wasm32 - the enum member that equals the served template's 'Target Architecture:' line verbatim; 'wasm32' alone is REFUSED_ARCHITECTURE_CONFLICT. Omit the field to let the brief carry it

Affine.Earth Math Court

Try it

affine_translate_text

Affine.Earth Math Court

Try it

affine_translate_text

Tools (55)