A registered result in its source context

E8.RAMIFIED.JETCODE.01

Original ledger classification: Exact [E] ring/module/extension structure theorems (integer/F2/Z[i] arithmetic, exhaustive censuses) behind the interpretation fence; the reconstruction-chain reading typed [H neu]; carries E8.AFFINE.NSR.01

Original claim text

E8.RAMIFIED.JETCODE.01 (+ E8.AFFINE.NSR.01): the jet-code normal form of the Gaussian E8 compiler + the NS/R bit as an affine 8-point geometry, ONE module from two probes (18/18 + 15/15 checks, ~3 s; discovery probes e8_ramified_jetcode_probe.py JETCODE-EXACT and e8_affine_nsr_probe.py AFFINE-NSR-EXACT, both 2026-08-06, FROZEN_SPEC SHA-hashed before any root data). PART 1, THE JET CODE (all [E neu], machine-certified): Z[i]/(2) = F2[eps]/(eps^2) with eps = 1 + i and 2 = -i(1+i)^2 (2 RAMIFIES; the ring iso is UNIQUE -- the only nonzero nilpotent is 1+i -- and the wrong split ring F2 x F2 is NOT isomorphic: all 24 bijections fail, control C1); W = L/2L is FREE of rank 4 over the dual numbers (explicit Z[i]-basis by Hermite reduction over the Euclidean domain Z[i], covolume-certified index 1; the 4^4 = 256 dual-number combinations enumerate W bijectively); 0 -> eps W -> W -> V -> 0 is an exact SELF-extension with V = eps W canonically and ker(eps) = im(eps) -- the self-dual differential code; the deck IS the jet unit J = 1 + eps, whence the certified v782 transition-bus torsor translation rho(Jr) = rho(r) + iota(v) on ALL 240 roots (the full 15-row fiber-translation table re-derived from ring algebra); the extension admits ZERO mu4-equivariant splittings among all 65536 = 16^4 linear sections (-1 = +1 mod 2 makes mu4-equivariance = J-equivariance) -- the no-canonical-origin obstruction IS non-splitness; the 120 root pairs are EXACTLY the q = 1 unit shell of the plus-type quadratic form (census 120/136, Arf 0, polarization b = <x,y>/2 mod 2 with trivial radical), so every root is canonically the triple (address v, admissible error jet in the affine v_perp coset, orientation +-): 240 = 15 x 8 x 2. PART 2, THE AFFINE NS/R GEOMETRY (A1-A6 [E neu], chain reading [H neu]): V \ {0} = (7 NS classes = ker chi_NSR \ 0) u (8 R classes = the affine F2^3-torsor A = chi^{-1}(1)); the 7 NS classes carry EXACTLY the 112 D8 roots and the 8 R classes the 128 Ramond spinor roots -- 248 = (112 + 8) + 128 anchored in v148/v227/v301; Stab_GL(4,2)(chi_NSR) has order 1344 = 20160/15 and EQUALS -- as a permutation group with its natural 8-point action -- AGL(3,2) = Aut(H8) (brute force over all 40320 coordinate permutations; the chart composition is the explicit iso of actions); the evaluation code of affine functions on the 8 points of A is the [8,4,4] code RM(1,3) = H8 with EXACTLY 1344 equivalence permutations; the deployed Sp(4,2) stabilizes chi in an order-48 subgroup acting INSIDE AGL(3,2) (the kill does not fire). HONEST TYPING: the reconstruction chain NS/R bit -> affine 8-point space -> H8 SHARPENS the ARF.BOUNDARY.CODE.01 attack surface but the route to V still passes through Gaussian E8 -- an exact internal reconstruction, NOT a P2 removal. Controls fire in both parts (wrong ring, seeded scrambles, unique parity functional 14/14, flipped code bit). No matter semantics (v775 ROOTCLASS-MIXED cited). No marker move, NO RH claim. Python-only per GATE.WOLFRAM.02.

Original classification detail

JETCODE-EXACT + AFFINE-NSR-EXACT: Z[i]/(2) = F2[eps]/(eps^2) unique iso; W = L/2L free rank 4 (Hermite-certified); exact self-extension with ker eps = im eps; J = 1 + eps reproduces the v782 torsor on all 240 roots; 0/65536 mu4-equivariant splittings -- non-splitness IS the no-origin obstruction; 240 roots = oriented q = 1 unit jets (15 x 8 x 2); Stab(chi_NSR) = AGL(3,2) order 1344 = Aut(H8), same natural 8-point action; affine functions = RM(1,3) = H8 (1344 equivalences); typed internal reconstruction, no P2 removal; no matter semantics.

Dependencies as recorded

E8.TRANSITIONBUS.01; ARF.BOUNDARY.CODE.01; v752; v689; v782; v776; v646; v148; v227; v301