A registered result in its source context

ARF.SPINORCOMPILER.01

Original ledger classification: Exact [E] finite algebra (integer/Fraction/F2 arithmetic; Lean companion ArfSpinorCompiler.lean, 23 kernel theorems; Python-only per GATE.WOLFRAM.02); the physical code->matter reading FENCED (killed by v775/ARF.ROOTCLASS.01).

Original claim text

The Arf/spinor compiler on V = L/(1+i)L = F2^4 -- Priority 1 of the Arf compiler programme, the exact finite-algebra layer (one module, 46 checks, ~2 s; discovery probe arf_spinor_compiler_probe.py 46/46, verdict ARF-SPINOR-EXACT, zero kills, both must-fail controls fire). THE COMPILER, EXACT END TO END: hbar rebuilt from the concrete v752 lattice (Gram J - I in the family/anchor basis, census 240 = 15 x 16, sigma symplectic; standard-doubled-model cross-check: chi coefficients (0,0,0,1), y0 = FSUM); brute force over all 2^16 functions: EXACTLY 16 quadratic refinements; Arf census 6 + 10 with |Sp(4,2)| = 720 (full 65536-matrix census) and a faithful+surjective S6 action on the six Arf-1 forms; the frozen selector (sigma-invariance census 4 -> q(A) = 1: 2 -> q(F_Sigma) = 0: 1) picks a UNIQUE q*; the parity lift iota: V ~ C_even(5) satisfies beta = hbar in all 256 cells (crosslink 1) and the weight form q_wt IS q* (offset 0; all 16 refinements = q* + hbar(., c) bijectively); Stab(q*) of order 120 acts as S5 with orbits {1, 5, 10} on refinements AND words: 16 = 1 + 5bar + 10 as Arf geometry; the K6 duad model v <-> D(v) is a bijection onto E(K6), Sp/sigma-equivariant, vertex split 15 = 5 + 10 at q*; B = I + A_KG(6,2) ENTRYWISE in all 225 cells, charpoly (x-7)(x-2)^9(x+2)^5, ovoid eigenvector B(1_O - (1/3)1) = -2(1_O - (1/3)1) EXACT (the six ovoid indicators span the (-2)-eigenspace, rank 5); all 6 fully isotropic spreads carry q*-signature (1, 2) per block; the hypercharge table X = (-2,-2,-2,3,3) reproduces the v310/v14 dictionary (values AND multiplicities); code polynomial moments (16, 0, 120, 0) with the chain 120/3 = 40, +1 = 41 = 10 b1, 2*120 = 240, +8 = 248 (the v2 master moment Tr X^2 = 120 = 5!); Pati--Salam 16 = 8 + 8 with the A bit as isospin index and B-L = 1 - 2 n_c/3 exact; chi_NSR = hbar(., F_Sigma) = the anchor bit on all 16 words. SEMANTIC SEPARATION (naming discipline, no physics claim): the SAME sigma acts as the family 3-cycle A3^Fam on the message bits AND as the 3+2 slot split A3^PS on the carrier legs -- two registers, never to be conflated. HONESTY FENCE (binding): the PHYSICAL code->matter reading is NOT claimed -- it is KILLED at root level by v775 (ROOTCLASS-MIXED), incl. the 'empty mailbox = right-handed neutrino' reading. Companion Lean module TfptCarrier/ArfSpinorCompiler.lean (23 kernel theorems, decide/norm_num only, no sorry, no native_decide, lake build green). No marker move, NO RH claim. NOTE (2026-08-05, v782/v784 -- marker UNCHANGED): the certified spread + q* selector become load-bearing in the transition-bus spread layer 240 = 5 x 3 x 16 (v782), and the q* parity acquires a sharp NEGATIVE boundary: the seam curve's canonical deck-invariant theta refinement is EVEN (Arf 0, decomposition 1+6+9) while q* is ODD (Arf 1, 1+5+10) -- the curve/code 2-torsion transport dies at exactly this layer alongside the syntheme-vs-duad sigma layer (v784, joint census 0 with positive control 6).

Original classification detail

ARF-SPINOR-EXACT: unique sigma-selected Arf refinement q* (census 4 -> 2 -> 1; q_wt IS q*), parity lift iota ~ C_even(5) with beta = hbar exact, 16 = 1 + 5bar + 10 as Stab(q*) ~ S5 Arf geometry, K6 duad bijection, B = I + A_KG(6,2) with exact ovoid eigenvectors, spreads (1,2), hypercharge table -> v310/v14 dictionary, moments (16,0,120,0) with chain 40/41/240/248, Pati--Salam 8+8 with B-L exact, chi_NSR = anchor bit; A3^Fam != A3^PS discipline; matter reading fenced (v775); Lean companion 23 theorems; no RH statement.

Dependencies as recorded

E8.PROJHAMMING.01; PRIME.HECKEPOLARITY.01; CAR.SM.01; AX.P2.01; v752; v753; v2; v310; v14