A registered result in its source context

ARF.BOUNDARY.CODE.01

Original ledger classification: Exact [E] finite selection chain (census / Construction A / Arf selector, all exact arithmetic) + OPEN research contract [O]: derive the doubly-even self-dual universe premise from the seam axioms; NO P2-removal claim (Python-only per GATE.WOLFRAM.02).

Original claim text

Boundary code uniqueness -- the non-circular selection chain boundary -> code -> E8 -> F2^4 -> 5 slots EXISTS with g_car = 5 as OUTPUT, and the residual premise is named (one module, 31 checks, ~2 s; discovery probe boundary_hamming_uniqueness_probe.py 31/31, verdict BOUNDARY-CODE-UNIQUE; frozen design SHA-256 c1893641...). THE CHAIN, REBUILT WITHOUT HAMMING/E8 INPUT: direct enumeration gives 135 self-dual binary codes of length 8 (mass formula), 30 doubly even; J-compatibility leaves 14; sigma-equivariance (deck 3-cycle pair-coherence) leaves 2, swapped by the anchor transposition (67) -- which IS boundary gauge (centralizer order 12) until the flag datum; the flag/side-orientation datum selects EXACTLY ONE code, identically under all three predeclared formalizations (FF1/FF2/FF3), and the decisive content is ONE deck-invariant Z2 = the product of the four side orientations (all 16 assignments decide by sum(s) mod 2 alone). DERIVED CHAIN EXACT: Construction A of the selected code IS E8 (240/2160 theta, Cartan det 1, arms 1-2-4; weight-4 supports == the deployed v638 C* list verbatim, post-selection cross-check); L/(1+i)L = F2^4 with the canonical symplectic bbar; the Arf selector with the BOUNDARY-canonical anchor naming (A = class of the flag-transversal root) picks a unique q*; sigma-orbit packets output g_car = 1 + 4 = 5 (240 = 5 x 48, 60 = 5 x 12). Controls fire (drop-J / drop-flag / twisted deck / illegal deck / all 105 non-doubly-even codes fail Construction-A evenness). HONEST RESIDUALS (typed): R1 the UNIVERSE premise -- 'the boundary realizes a doubly-even self-dual binary code on its 8 sides' is the new named premise (the circularity is RELOCATED and SHRUNK, not removed); R2 deck-placement blindness -- WHICH pair is the anchor is invisible to the selection (Aut(C*) contains every straight pair 3-cycle); the placement is SEMANTIC, not selective (the wrong-deck control does not fire, typed as an honest deviation); R3 anchor naming -- bbar(F_Sigma, A) = 1, so A vs A + F_Sigma changes q*; the flag-transversal naming is boundary-canonical but part of the frozen selector, not a theorem. NO P2-REMOVAL CLAIM. OPEN CONTRACT FORM (registered here [O]): derive evenness/self-duality of the mark bookkeeping from the seam axioms (R1), plus the R2/R3 residuals; kills: a second boundary-legal code surviving the flagged selection, or a seam-axiom derivation forcing a non-doubly-even universe. No marker move, NO RH claim. NOTE (2026-08-06, v798/v799 -- marker UNCHANGED): all three honest residuals move -- R1 is REPLACED by R1' (v799 TYPEII-FORCED: exhaustively at length 8, mutual locality <=> self-orthogonal, integer conformal spin <=> doubly even, holomorphy/index one <=> self-dual; the universe premise reduces to the three physical axioms A1-A3, each a standard physical demand, not a coding-theory premise); R2 is SOLVED semantically (v798: the deck J = iI IS the metaplectic anomaly (T3 K3)^3 of the total symplectic Fourier at tau = i, and zeta8 = (1+J)/sqrt2 the real half-deck swapping the seam pair); R3 is NAMED, not fixed (v798: the strict census over the 46080 coset elements is EMPTY -- no Theta-real metaplectic involution fixes q* -- but the sigma-orbit of lifts has Arf defects exactly {A + F_Sigma + F_i} whose XOR is the anchor A itself). NO P2 marker move anywhere. NOTE (2026-08-06, v803 -- marker UNCHANGED): the attack surface is SHARPENED by the affine NS/R reconstruction -- the [8,4,4] Hamming code re-emerges as the evaluation code of affine functions on the 8-point NS/R torsor A = chi_NSR^{-1}(1), with Stab(chi_NSR) = AGL(3,2) = Aut(H8) carrying the same natural 8-point action (1344 equivalences, exact census); HONEST TYPING: the route to V still passes through Gaussian E8, so this is an exact INTERNAL reconstruction, not a P2 removal and not an independent boundary-code derivation -- residual R1' (the three physical axioms, v799) unchanged.

Original classification detail

BOUNDARY-CODE-UNIQUE: census 135 -> 30 -> 14 -> 2 -> 1 without Hamming/E8 input; flag datum = one deck-invariant Z2; Construction A -> E8 exact; q* unique; g_car = 1 + 4 = 5 as OUTPUT; residuals R1 (universe premise, the relocated+shrunk circularity), R2 (deck placement semantic), R3 (anchor naming) typed; open contract: derive evenness/self-duality from the seam axioms; NO P2-removal claim; no RH statement.

Dependencies as recorded

ARF.SPINORCOMPILER.01; AX.P2.01; E8.GAUSSCODE.01; E8.PROJHAMMING.01; v689; v736; v638; v752