A registered result in its source context

E8.GAUSSIAN.CODE.01

Original ledger classification: Review contract; first slice machine-closed [E] (v689); remaining: theorem writeup.

Original claim text

Review contract (external review, theorem candidate, registered 2026-08-03): E8(Z[i])/(1+i) is the information space of RM(1,3) -- the mu4 complex structure J makes E8 a rank-4 Z[i]-lattice; the (1+i)-quotient is F2^4; the 240 roots fall 15 x 16; sigma acts as the RM(1,3) family permutation. FIRST SLICE EXECUTED by v689 (26/26, GAUSSIAN-CODE-BRIDGE-EXACT): the full 6-step census verbatim, exact arithmetic, all must-fail controls firing. REMAINING: the paper-level theorem writeup (the census IS the proof skeleton; the residual gauge order 18 documented). NOTE (2026-08-04, v736/v737 -- marker UNCHANGED): the ORBIT PACKET lemma is machine-closed [E] (Burnside 7 = (15+3+3)/3, the canonical 5 x 48 split, the (1,1,2) anchor from the fixed-syndrome leader weights (0,1,1,2), the q = 16 normal form 240 = 16*15 / 248 = 240+8; P1/P2 typed as EXACT-INTERNAL-RECONSTRUCTION behind the circularity fence; companion Lean module OrbitPacket.lean, 34 theorems kernel-checked), and the seam-48 intertwiner sharpening is DEAD (v737: incidence distribution 0:96/1:64/2:64/3:16 instead of == 1, representative-independent over all 2304 order-5 elements) -- 240 = 48 x 5 remains a factorization WITHOUT coordinatization. NOTE (2026-08-05, v782/v783 -- marker UNCHANGED): the code bridge acquires its operational identification -- the 60 Gaussian lines ARE the 60 two-qubit stabilizer rays entry-exactly over Z[i] with U G31 U^-1 an index-2 subgroup of the Clifford matrix group (classes = the 15 Pauli contexts, spreads = the MUB pentads; the index bit is the sqrt2/Hadamard Galois bit, NOT J <-> -J; v783), and the 240 = 16 x 15 transition reading is settled at TORSOR level (each class fiber a canonical v_perp pair-torsor; the frozen predicate reproduces all 57600 inner products; NO deck-equivariant 16-state labeling exists -- proof-grade obstruction; v782).

Original classification detail

EXECUTED (first slice): v689 closes the census + semantics exactly (26/26); remaining: theorem writeup.

Dependencies as recorded

E8.GAUSSCODE.01; E8.CODESEM.01; E8.CODE.01