What the code interpretation preserves and loses

E8.CODESEM.01

Original ledger classification: Exact [E] code/dictionary identities + [E, kill] the 30-census control (exact arithmetic; Python-only per GATE.WOLFRAM.02).

Original claim text

The code-semantics rounds, kill + stage 2 (one module, 27 checks, ~3 s; discovery probes code_semantics_kill_probe.py 13/13 CODE-SEMANTICS-RELABELLED and code_semantics_stage2_probe.py 27/27 DICTIONARY-SHARP). Stage 1 (kill): the naive v626 placement is DEAD for the family 3-cycle pisig; exactly 2/30 S8-placements of the extended Hamming code carry BOTH compiler symmetries mod 2 (piJ = mu4 in-pair swap, pisig = family pair 3-cycle), exchanged by the anchor transposition (67) -- ONE placement C* up to anchor orientation. Stage 2 (the dictionary, DICTIONARY-SHARP): under binary position labels C* IS Reed-Muller RM(1,3) on AG(3,2) (piJ = translation by 001, pisig affine, the 14 weight-4 supports = the 14 planes; 30 = |S8|/|AGL(3,2)|); NO equivariant 4+4 block split exists (all 6 pair-unions are codeword supports), the UNIQUE minimal Z6-orbit of information sets is the transversal pair 'one bit per mu4 pair, anchor-flipped' (3 family bits + 1 anchor bit); the 12 sigma-fixed roots reduce mod 2 to exactly {0, t_even, t_odd} (4 each); the clock-orbit fibration reproduces 60 = 7 x 4 + 4 x 8 and the sigma census 3 + 19 (the v629 tower 240 -> 60 -> 3+19); SYNDROME SEMANTICS: all 3840 single-coordinate errors sit at squared distance EXACTLY 1 with the tie pair collapsing mod 2; the syndrome space factors as the flag 0 < <q> < F2^4 (q = the universal in-pair bit) with sigma acting on the pair directions as the 3-CYCLE + fixed anchor (P3 = P0+P1+P2) and piJ trivial on the quotient; DECODE = PROJECTION verbatim on the single-error class (3840/3840, exact Fraction arithmetic; boundary regime honest: mismatches need >= 2 rounding errors). KILL CONTROL: {universal in-pair syndrome} = {zero fragmented Z6 orbits} = {both-invariant} = the two C* relabellings -- the equivariance is load-bearing; the whole dictionary dies for every non-equivariant placement. [2026-08-02 XLIII: the reverse reading executed -- v646: the sigma-fixed syndromes carry the anchor decomposition exactly (leader weights (0,1,1,2), norm 6, anchor = family sum; the SELECTION is equivariance-specific, the raw (1,1,2)/norm-6 weights are generic for any [8,4,4] placement), while the bytecode p-sequence p_n = 2 + 2^n has NO code reading (0/11 families; 18/27/81 without any hit -- the bingo is buried); the kill control fires selectively; see E8.RM13REV.01.] [2026-08-02 XLV: look-elsewhere quantification -- v664: the CODESEM number battery (anchor norm 6 et al.) carries p_max = 0.593 under the conservative null model -- the v646 finding quantified: the numeric coincidences of this row are observations without statistical weight; the [E] structure theorems (RM(1,3) dictionary, decode = projection) are untouched.] [2026-08-03 L: the message space is IDENTIFIED as a lattice congruence -- v689: E8(Z[i])/(1+i) = F2^4 carries this module's RM(1,3) info-bit semantics exactly (240 = 15 x 16 census, zero class provably empty; sigma = c^4 = the family 3-cycle + fixed anchor on the quotient; residual gauge order 18; coordinate block = F1+F2+F3), presentation-independent and with all must-fail controls firing; see E8.GAUSSCODE.01.]

Original classification detail

DICTIONARY-SHARP: the equivariant placement is RM(1,3) on AG(3,2) with an exact dictionary (information bits one per mu4 pair, syndrome flag with the sigma 3-cycle, decode = projection); only 2/30 placements carry it; residual: the anchor-pair orientation; no physics claim, no marker moves.

Dependencies as recorded

E8.CODE.01; E8.INCIDENCE.01; v626; v629