Name: Affine.Earth Math Court
Author: affine

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 Universa

Parameter	Type	Required	Notes
source_lang	string	yes	ISO 639-1 source language; required, 'auto' refused. e.g. en
target_lang	string	no	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). I
target_langs	array	no	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
text	string	no	one source text to render. e.g. Book
texts	array	no	up to 64 source texts; rendered in order, one line each. e.g. ["Book","Water"]

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

Parameter	Type	Required	Notes
horizontal_minima_micro_deg	string	yes	REQUIRED decimal string, no default -- a defaulted separation standard is a verdict about a rule the caller never stated. e.g. 5000
lon_scale_den	string	no	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 deno
lon_scale_num	string	no	OPTIONAL exact rational longitude scale, numerator as decimal string. Stands for cos(latitude), which is not rational -- so the caller states the approximation it chose and everything after that choic
look_ahead_seconds	string	no	optional horizon clipped forward from the earliest declared time, decimal string. e.g. 600
obs_seq	string	no	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 fabr
reference_lat_micro_deg	string	no	OPTIONAL decimal string, the latitude the scale was computed for. REQUIRED whenever a scale is declared: all three fields travel together and a partial declaration is refused with REFUSED_INCOMPLETE_L
trajectories	array	yes	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"},{
vertical_minima_feet	string	yes	REQUIRED decimal string, no default. e.g. 1000

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 der

Parameter	Type	Required	Notes
A	string	no	presented private face, 64-hex or decimal. e.g. 1
k	string	no	same face as A, old label. e.g. 1
Q	string	no	same face as q_hex, old label. e.g. 0479be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8
q_hex	string	no	open key, uncompressed 04-prefixed pubkey hex (required). e.g. 0479be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8

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 sc

Parameter	Type	Required	Notes
files	array	no	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
left_file	object	no	Whole source file of the first implementation. The payload IS the file. e.g. {"path":"left.ll","content":"define i32 @f() { ret i32 143 }"}
left_ir	string	no	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_file	object	no	Whole source file of the second implementation. The payload IS the file. e.g. {"path":"right.ll","content":"define i32 @f() { ret i32 143 }"}
right_ir	string	no	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 }

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.

Parameter	Type	Required	Notes
at_seq	string	no	decimal string, caller-pinned stream position; same value = same bytes. e.g. 1
limit	string	no	decimal string, rows up to 8192; JSON numbers still admitted. e.g. 64
sector	string	no	hex sector prefix: the four hex digits of the top 16 bits of a bond's Morton key, e.g. 0a3f

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.

Parameter	Type	Required	Notes
at_seq	string	no	decimal string, caller-pinned stream position; same value = same bytes. e.g. 1
limit	string	no	decimal string, window size up to 8192. e.g. 256
source	string	no	optional lane filter: LLM_WEIGHTS, LLVM_IR, LLVM_IR_I64, AUDIO_SPEECH. e.g. LLVM_IR

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.

Parameter	Type	Required	Notes
cursor_sample	string	no	decimal string, cursors to decode, up to 1024; the bound is stated in the reply. e.g. 256

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.

Parameter	Type	Required	Notes
h	string	no	decimal string. e.g. 128
kind	string	no	the language-game context kind: atc, proteins or materials, e.g. atc
n	string	no	decimal string. e.g. 16
seed	string	no	decimal string; JSON numbers still admitted. e.g. 7
span_scale_q16	string	no	decimal string, framing to grade; 65536 = unity. e.g. 65536
t	string	no	decimal string. e.g. 0
w	string	no	decimal string. e.g. 128

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 again

Parameter	Type	Required	Notes
config	string	no	computational bits s0,s1,... each 0 or 1, one per site, e.g. 0,1
constraints	string	no	ZZ terms i,j,jnum,jden;... e.g. 0,1,1,1 (sites 0 and 1, coupling 1/1)
jordanBondExclusions	string	no	alias of constraints. e.g. 0,1,1,1

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 Ta

Parameter	Type	Required	Notes
artifact	string	yes	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 mod
brief	string	yes	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 refuse
target_architecture	string	no	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_C

#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 d

Parameter	Type	Required	Notes
matrix	string	no	rows \| cells , integer entries. e.g. 1,1,1\|1,1,1\|1,1,1

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.

Parameter	Type	Required	Notes
bond_status	string	no	the bond state the caller reports for itself, recorded with the turn; e.g. BONDED. Omitted -> UNKNOWN
c4_constraints	array	no	Rational lanes as num/den strings. e.g. ["1/1","0/1","2/3","1/4"]
client_signature	string	yes	sha256(INTENT\|scf_hex\|user_vqbit_hash\|genesis_epoch) first 16 bytes as 32 lowercase hex; or the game seal sha256(INTENT\|scf_hex\|user_vqbit_hash); or an ML-DSA-87 IDENTITY_BIND package. scf_hex is NOT
economics	object	no	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"
entity_id	string	yes	wallet_geo entityID hex. e.g. 0123456789abcdef0123456789abcdef
intent	string	yes	the transition verb, one of the enum values, e.g. INGEST
s4_coordinates	array	no	Rational lanes as num/den strings. e.g. ["1/2","3/4","0/1","5/1"]
user_vqbit_hash	string	no	Exactly 32 lowercase hex, or OMIT it and the cell derives sha256(entity_id\|scf_hex)[0:16]. A stated value that is not 32 hex is REFUSED rather than replaced - the cell will not verify your signature a

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 sea

Parameter	Type	Required	Notes
A	string	no	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	no	second lattice, same shape as A, e.g. 1,1,1,1,1,1,1,1\|0
K	string	no	the lock (kernel) lattice for a Jordan shear, same shape as A. e.g. 3,-2,5,1,7,1,4,2\|1
kind	string	no	affine_key\|jordan\|lattice\|qc_\|qma_\|math_court domain. e.g. qc_shor
object	string	no	puzzle object; Affine key hex for affine_key. e.g. 0479be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8
op	string	no	lattice operation for kind=lattice, e.g. add; lattice_op with an empty op lists them
q_hex	string	no	alias of object for affine_key. e.g. 0479be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8
source	string	no	attribution for a math_court domain kind (who or what posted it), e.g. steward; absence is refused there

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 parameter schema on file.

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.

Parameter	Type	Required	Notes
at_seq	string	no	decimal string, pinned corpus epoch. e.g. 1
h	string	no	decimal string. e.g. 128
kind	string	no	the language-game context kind: atc, proteins or materials, e.g. proteins
max_iter	string	no	decimal string, iteration cap, default 10. e.g. 10
n	string	no	decimal string, population. e.g. 16
seed	string	no	decimal string; JSON numbers still admitted. e.g. 7
t	string	no	decimal string, step index. e.g. 0
target	string	no	decimal string, refine until score >= this (0-1000, default 950). e.g. 950
w	string	no	decimal string. e.g. 128

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

No parameter schema on file.

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), p

Parameter	Type	Required	Notes
A	string	no	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	no	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	no	the distance (kernel) lattice for shear; same shape as A. e.g. 3,-2,5,1,7,1,4,2\|1
mask	string	no	park only: decimal 0-255 homology mask. e.g. 255
op	string	no	the operation; empty lists the ops

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 wit

Parameter	Type	Required	Notes
a	string	no	the base a of the period claim, coprime to N, e.g. 7. Read by qc_period/researcher; post it only for those domains - a court names the fields it grades on in its REFUSED_NO_INSTANCE detail.
A	string	no	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.
ab	string	no	the two measured Bell bits, e.g. 00. Read by qc_bell/researcher; post it only for those domains - a court names the fields it grades on in its REFUSED_NO_INSTANCE detail.
alice	string	no	Alice's two measurement bits, e.g. 01. Read by qc_teleport/researcher; post it only for those domains - a court names the fields it grades on in its REFUSED_NO_INSTANCE detail.
answers	string	no	the oracle's answer to each query, in query order (bits, ';'-separated like queries), e.g. 101. Read by qc_bv/researcher; post it only for those domains - a court names the fields it grades on in its
arc_order_ppt	string	no	arc-order statistic in parts per thousand, e.g. 800. Read by eht/experimentalist, eht/theorist; post it only for those domains - a court names the fields it grades on in its REFUSED_NO_INSTANCE detail
arm_counts	array	no	health/trialist,regulator and the health grader: per-arm assay counts as an array of decimal strings, e.g. ["30","30"]
arrival_min	string	no	declared by fluids/operator in the catalog; carried with the ingest and not read by the fluids verdict today (measured 2026-09-29: fluids grades phi_in and phi_out), e.g. 42. Read by fluids/operator;
b	string	no	the right-hand side of the linear system as num/den rationals, comma-separated, e.g. 3/1,5/1. Read by qc_hhl/researcher; post it only for those domains - a court names the fields it grades on in its R
bits	string	no	the two classical bits sent over one entangled qubit, e.g. 11. Read by qc_superdense/researcher; post it only for those domains - a court names the fields it grades on in its REFUSED_NO_INSTANCE detai
bob	string	no	Bob's two bits after the corrections, e.g. 01. Read by qc_teleport/researcher; post it only for those domains - a court names the fields it grades on in its REFUSED_NO_INSTANCE detail.
cid	string	no	PubChem CID of the compound, e.g. 2244. Read by chemistry/chemist, chemistry/steward, complex/chemist, complex/researcher, complex/steward; post it only for those domains - a court names the fields it
cited_id	string	no	the citation id the court matches against its authored fixture: meyer-2023-5d60 (gofirst), iso16-a440 (rife), z2-a2b-half-step (dynamo), e.g. iso16-a440. Read by dynamo/researcher, dynamo/steward, dyn
cited_url	string	no	the source URL of the citation, echoed with the verdict, e.g. https://en.wikipedia.org/wiki/A440_(pitch_standard). Read by dynamo/researcher, rife/researcher; post it only for those domains - a court
class	string	no	the claimed class: constant or balanced for qc_dj, the Bell class bits for qc_bell, e.g. constant. Read by qc_bell/researcher, qc_dj/researcher; post it only for those domains - a court names the fiel
clock	string	no	the clock tick the table row is read at, e.g. 1. Declared by health/regulator, health/trialist and the three physics roles; no verdict reads it: the health verdict is computed from other fields, and t
closure_conc_ppt	string	no	closure-phase concentration in parts per thousand, e.g. 900. Read by eht/experimentalist, eht/theorist; post it only for those domains - a court names the fields it grades on in its REFUSED_NO_INSTANC
cod	string	no	Crystallography Open Database id, e.g. 1011097. Read by material/crystallographer, material/steward; post it only for those domains - a court names the fields it grades on in its REFUSED_NO_INSTANCE d
cofactor	string	no	the cofactor N/factor of the witness, e.g. 5. Read by 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 det
color_isolated	string	no	1 if a colour row is isolated (illegal), 0 otherwise, e.g. 0. Read by qcd/jet_analyst; post it only for those domains - a court names the fields it grades on in its REFUSED_NO_INSTANCE detail.

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

No parameter schema on file.

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.

Parameter	Type	Required	Notes
c4_invariant_scf	string	no	optional C4 invariant SCF hex of the caller session; carried into the invocation receipt, not read by the weather lanes. e.g. 0123456789abcdef0123456789abcdef
lane	string	no	weather \| space (maps to gaiaftcl.radar.*)
wallet_hash	string	no	optional caller fiber (sha256 of the wallet, lowercase hex); carried into the invocation receipt, not read by the weather lanes. e.g. 5df6e0e2761359d30a8275058e299fcc0381534545f55cf43e41983f5d4c9456

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

Parameter	Type	Required	Notes
A	string	no	the private face: a secp256k1 scalar as decimal or 64-hex, e.g. 2; the court projects Q = A*G
k	string	no	same face as A, old label. e.g. 1
Q	string	no	same face as q_hex, old label. e.g. 0479be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8
q_hex	string	no	the public face: uncompressed 04-prefixed secp256k1 point, 130 hex characters; the court projects its shear and period, never a scalar. e.g. 0479be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b1

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

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

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

Parameter	Type	Required	Notes
date	string	no	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	no	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
self_test	string	no	optional: 1 asks the court to run its own self-test over the law instead of grading a record - every arm first shown a planted defect; answers RELEASE_REGRESSION_COURT_SELFTEST_OK with arms_total, arm

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 e

Parameter	Type	Required	Notes
edges	string	no	couplings i,j,J;... integer J, e.g. 0,1,1;1,2,1;2,0,1
spins	string	no	discrete spins +1,-1,... one per site, e.g. 1,-1,1

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,

Parameter	Type	Required	Notes
example_usda	string	no	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.
prompt	string	yes	the person's words. Iliad selects the Iliad cut. Franklin avatar composes the next avatar stage.
study	string	yes	the study that owns the document, e.g. study-51 or franklin-avatar

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_*_m

Parameter	Type	Required	Notes
piece_id	string	yes	decimal string, the piece to solve for. e.g. 3
pieces	array	no	declared PieceFrame rows as decimal strings. e.g. [{"piece_id":"3","rotation_milli_deg":"15000"}]
relative_to_head	boolean	no	state the pose relative to the head (camera-free) rather than the anchor. e.g. true

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 car

Parameter	Type	Required	Notes
checkpoint	boolean	no	true seals the tip to the KV bucket at the end of the call so umc_resume can pick it up. e.g. true
domain	string	no	which Long Play law governs the session
entity_id	string	no	caller identity, alternative to user_vqbit_hash: the wallet_geo entity id hex, e.g. 00112233445566778899aabbccddeeff
max_turns	string	no	decimal string: hard cap on turns advanced by this call. e.g. 4
node_id	string	no	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
session_id	string	no	caller-chosen stable id; the same id on a later call resumes rather than restarts. e.g. r5-session-1
tau_height	string	no	decimal string: how far along tau to run this call (turns are integer steps of tau); omit for the domain default. e.g. 8
title	string	no	human label for the session, <= 80 characters, informational only. e.g. first long play
user_vqbit_hash	string	no	caller identity, one of the three this MESH-class tool accepts: exactly 32 lowercase hex, e.g. 0123456789abcdef0123456789abcdef. Send user_vqbit_hash, entity_id or wallet_hash or the call is REFUSED_G
wallet_hash	string	no	caller identity, alternative to user_vqbit_hash: sha256 of the caller wallet, lowercase hex, e.g. 9f86d081884c7d659a2feaa0c55ad015a3bf4f1b2b0b822cd15d6c15b0f00a08

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-

Parameter	Type	Required	Notes
direct	boolean	no	true: after resuming, advance one turn (equivalent to one umc_direct call). e.g. true
domain	string	yes	the domain the session was started under
entity_id	string	no	caller identity, alternative to user_vqbit_hash: the wallet_geo entity id hex, e.g. 00112233445566778899aabbccddeeff
node_id	string	yes	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
session_id	string	yes	the session id given to umc_direct. e.g. r5-session-1
user_vqbit_hash	string	no	caller identity, one of the three this MESH-class tool accepts: exactly 32 lowercase hex, e.g. 0123456789abcdef0123456789abcdef. Send user_vqbit_hash, entity_id or wallet_hash or the call is REFUSED_G
wallet_hash	string	no	caller identity, alternative to user_vqbit_hash: sha256 of the caller wallet, lowercase hex, e.g. 9f86d081884c7d659a2feaa0c55ad015a3bf4f1b2b0b822cd15d6c15b0f00a08

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 parameter schema on file.

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 REFUSE

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

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

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

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.

Parameter	Type	Required	Notes
ab	string	yes	two measured bits, e.g. 00 or 11
class	string	yes	the two Bell-class bits claimed for the pair, e.g. 00

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.

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

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

Parameter	Type	Required	Notes
class	string	yes	constant or balanced, e.g. balanced for table 0110
table	string	yes	the oracle's truth table as a 0/1 string of length 2 or 4, e.g. 0110

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.

Parameter	Type	Required	Notes
marked	string	yes	0-based index of that single 1, decimal, e.g. 2 for oracle 0010
oracle	string	yes	0/1 string of length 2..8 with exactly one 1, e.g. 0010

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

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

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 matche

Parameter	Type	Required	Notes
A	string	no	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	no	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	no	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
object	string	no	alias of q_hex. e.g. 0279be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798
q_hex	string	no	optional: a secp256k1 point (130-hex 04... or 66-hex compressed) for the Q-only Affine expose instead of lattices. e.g. 0279be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798
source_creator_hash	string	no	legacy table limb, 32 hex; only for callers that do not present lattices. e.g. 0123456789abcdef0123456789abcdef
target_creator_hash	string	no	legacy table limb, 32 hex; only for callers that do not present lattices. e.g. 0123456789abcdef0123456789abcdef

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.

Parameter	Type	Required	Notes
n	string	no	particle count as decimal string. e.g. 2
rho2	string	no	a11,a12\|a21,a22 as num/den rationals. e.g. 1/2,0/1\|0/1,1/2

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.

Parameter	Type	Required	Notes
a	string	yes	base, coprime with N, decimal, e.g. 2
N	string	yes	modulus, decimal, e.g. 15
proper_divisors	string	yes	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'
r	string	yes	the presented period: a^r == 1 (mod N), decimal, e.g. 4

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.

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

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

Parameter	Type	Required	Notes
A	string	no	private face, 64-hex or decimal scalar, e.g. 1 (its public face is G itself)
k	string	no	same face as A, old label. e.g. 1
lock_q	string	no	a lock face: the public point the pair must be verified against, same shape as Q. e.g. 0279be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798
object	string	no	alias of q_hex. e.g. 0279be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798
Q	string	no	public face: uncompressed 04-prefixed secp256k1 point, 130 hex characters, e.g. 0479BE667E...B8 for A=1
q_hex	string	no	same face as Q, old label. e.g. 0279be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798

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 grad

Parameter	Type	Required	Notes
edges	string	yes	couplings i,j,J;... e.g. 0,1,1;1,2,1;2,0,1 (integer J)
spins	string	yes	discrete spins +1,-1,... one per site, e.g. 1,-1,1

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.

Parameter	Type	Required	Notes
k	string	yes	input index, 0 <= k < n, decimal, e.g. 1
n	string	yes	register size: 2, 4 or 8, e.g. 4
phases	string	yes	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

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

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

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.

Parameter	Type	Required	Notes
count	string	yes	claimed number of 1s, decimal. e.g. 1
oracle	string	yes	0/1 string, length 2..8, e.g. 0001

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.

Parameter	Type	Required	Notes
end	string	yes	claimed ending vertex, 0 or 1. e.g. 0
start	string	yes	starting vertex, 0 or 1. e.g. 0
steps	string	yes	number of steps, decimal, >= 0. e.g. 2

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'

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

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.

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

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

Parameter	Type	Required	Notes
bits	string	yes	the two bits sent, e.g. 10
decoded	string	yes	the two bits decoded at the receiver, must equal bits, e.g. 10

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

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

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.

Parameter	Type	Required	Notes
q	string	yes	claimed Eisenstein q, decimal. e.g. 0
r	string	yes	claimed Eisenstein r, decimal. e.g. 1
word	string	yes	the cited word

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 nam

Parameter	Type	Required	Notes
config	string	yes	computational bits s0,s1,... each 0 or 1, one per site, comma-separated, e.g. 0,1
constraints	string	yes	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

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 th

Parameter	Type	Required	Notes
cells	array	yes	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
margin_micro_deg	string	no	optional standoff as decimal string in the same declared units; strict, so exactly this far away is contained. e.g. 1000
track_micro_deg	array	yes	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_micr

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Affine.Earth Math Court MCP

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