A registered result in its source context

NORMALFORM.CFIN.01

Original ledger classification: Exact identity-grade normal form [Identity] with the built-in checked NEGATIVE (v775 ROOTCLASS-MIXED re-anchored via the 128-spinor counting bound + the saturated 8 + 7 census) and the typed P2 bridge: C_fin does NOT derive A1-A3 / the linearity scope / the v776 uniqueness selection -- P2 NARROWED to the v799 residual R1' ([C]), NOT eliminated; SPEC v2 declared (v836 precedent, no numeric result changed); no marker move (Python-only per GATE.WOLFRAM.02)

Original claim text

v845 -- NORMALFORM.CFIN.01: the finite compiler normal form C_fin = (V, hbar, q*, sigma, iota) assembled as ONE machine-checked object from the Gaussian quotient, with the code-to-matter kill built in as a checked NEGATIVE and the remaining P2 bridge typed -- the round's central corpus compression, ONE module from one probe (28/28 checks, declared SPEC v2, verdict NORMAL-FORM-ASSEMBLED; discovery probe finite_compiler_normal_form_probe.py, 2026-08-07, re-run identically at promotion, promoted VERBATIM with no downscoping, ~4 s). THE OBJECT, read off the lattice and not postulated: V = L/(1+i)L rebuilt from the Gaussian Construction-A E8 (the unique mu4/sigma-invariant placement C*, 2 of 30; census 240 = 15 x 16, zero class EMPTY); hbar = the descended symplectic form with a FOUND family/anchor basis (F1, F2, F3, A) of Gram J - I, equal to the bit form on ALL 256 label pairs; sigma = the descended order-3 deck (sigma^3 = id, symplectic, EXACTLY 3 fixed nonzero classes {A, F_Sigma, F_Sigma + A}, the other 12 in exactly 4 free 3-orbits -- the family cycle); q* = the distinguished quadratic refinement (EXACTLY 16 refinements by brute force over 2^16, Arf census 6 + 10; the frozen selector sigma-invariant 4 -> q(A) = 1: 2 -> q(F_Sigma) = 0: 1 picks a UNIQUE q*, Arf type 1, sigma-preserved); iota = the parity lift onto the even five-slot code C_even(5) (bijective; beta = iota.iota == hbar on all 256 cells; q_wt = wt(iota)/2 mod 2 IS q*; sigma acts on the FIVE carrier slots as the 3+2 split -- message register and carrier register intertwined). DERIVED COUNTING from the one object: |Sp(4,2)| = 720 by full 65536-matrix census; |Stab(q*)| = 120 acting FAITHFULLY as S5 on the five, orbits [1, 5, 10]; 16 = 1 + 5 + 10 and 15 = 5 + 10; the PASCAL READING (iota-weight census (1, 10, 5) = (C(5,0), C(5,2), C(5,4))); the PROJECTIVE READING (PG(3,2): 15 points, 35 lines, 15 isotropic = the doily; the 5bar is an OVOID meeting every isotropic line exactly once); the BUDGET against the actual lattice objects: 240 = 16 x (5+10), 60 lines = 4 x 15, 30 = 2 x (5+10) = h(E8) (MESSAGE.LADDER.01 rung 1), rank 8 (HNF index 16), 248 = 16 x (5+10) + 8. THE MANDATORY NEGATIVE (built in, v775 re-anchored): the exact counting bound -- every D5(+)A3 c E8 has 128 spinor-side roots, so at most floor(128/16) = 8 all-spinor classes and >= 7 of the 15 classes ALWAYS contain adjoint-side roots (the 15 mailboxes canNOT be 15 pure matter multiplets); the concrete doubled-model census SATURATES both bounds (8 spinor-pure + 7 adjoint-side, ZERO both-type classes -- the J-quotient respects the D8 grading); the WEIGHT-level kill at the canonical split D = (0,2,4,6,7): each spinor-pure class restricts to 8 DISTINCT half-spinor weight pairs, never 1 -- v775 ROOTCLASS-MIXED [E] re-verified, NOT overturned. WHAT THE NORMAL FORM DOES NOT REMOVE (P2 typed, no upgrade): all 30 placements are Type II [8,4] doubly-even self-dual codes (enumerator 1 + 14 z^4 + z^8) -- the v799 TYPEII-FORCED echo; C_fin does NOT derive the three seam axioms A1-A3, the OPE-linearity scope note, or the v776 selection of ONE copy -- P2 (g_car = 5 = the iota slot count) is NARROWED to the v799 residual R1' ([C] class), not eliminated. Controls fire: the non-alternating dot form admits 0 refinements; the trivial deck leaves 4 selector candidates (q* NOT unique without the family 3-cycle); the wrong lift breaks C_even membership and beta == hbar. SPEC v2 declared (v836 precedent; the v1 wording of S7(b) mis-typed the v775 bound as 'mixed classes'; the factual census is the clean 8 + 7 split along the D8 grading; no numeric result changed). Exact integer/sympy; no floats, no RNG, no fit. Python-only per GATE.WOLFRAM.02.

Original classification detail

NORMAL-FORM-ASSEMBLED: C_fin = (V, hbar, q*, sigma, iota) read off the Gaussian quotient -- selector-unique q*, faithful S5 stabilizer (|Sp(4,2)| = 720, Stab = 120, orbits [1,5,10]), Pascal (1,10,5), ovoid projective reading, budget 240 = 16*15 / 248 = 16*15 + 8 against the actual census; the code-to-matter reading stays DEAD (bounds saturated 8 + 7, weight kill 8 pairs never 1); P2 narrowed to v799 R1' ([C]), not eliminated; all controls fire

Dependencies as recorded

AX.P2.01; v752; v774; v775; v799; v776; v833; MESSAGE.LADDER.01