A registered result in its source context

E8.TRANSITIONBUS.01

Original ledger classification: Exact [E] finite structure theorem (torsor + predicate + obstruction census) behind the interpretation fence ('transition bus / instruction set' language stays interpretation); no marker move (Python-only per GATE.WOLFRAM.02).

Original claim text

The transition-bus structure theorem (35/35 checks, ~2 s; discovery probe e8_transition_bus_probe.py TRANSITION-BUS-TORSOR, 2026-08-05). The 240 roots of the unimodular hermitian Gaussian E8 lattice are 15 disjoint coordinate 8-frames (cross-polytopes) over the class map V = L/(1+i)L; on L/2L the quadratic form q(y) = <y,y>/4 mod 2 is well defined and the 120 root PAIRS are exactly the 120 q = 1 points of the plus-type quadratic space; the 8 pair-images of class v form a coset of (1+i) v_perp inside the 16-element fiber of L/2L -> V -- a canonical TORSOR under v_perp (an affine F2^3 with no distinguished origin); the deck J acts on each pair fiber as translation by v and -1 = J^2 acts trivially on L/2L. THE OBSTRUCTION CENSUS IS PROOF-GRADE: -1 acts freely on the 240 roots but trivially on V x (V minus 0), and J acts on each 16-root fiber with cycle type 4+4+4+4 while any torsor translation has order <= 2 -- hence NO bijection R(E8) -> V x (V minus 0) can be equivariant under the deployed deck symmetries; the honest structured object is the pair-level torsor plus an unoriented sign (the strict 16-state labeling, if written down, is pure bookkeeping). THE FROZEN PREDICATE (trained on a frozen 3-class-pair set, hashed, then verified): with the basepoint rule rho_v = lex-min pair image and C(v,v') = q(rho_v + rho_v'), the symplectic dictionary reproduces ALL 57600 ordered inner products, with the SIGN LAW part of the claim (the central -1 is invisible at every mod-(1+i)^2 level; every realized key carries the sign-symmetric value set) and the h-refinement ((q-bit, hbar) -> h value classes). SPREAD LAYER: 240 = 5 x 3 x 16 (context x family direction x state) via the certified isotropic spreads with the arf-certified q* selector. A15 COMPARISON QUANTIFIED: A15's 240 roots are LITERALLY the transitions of 16 states (a strict bus with a canonical start state); E8 preserves the count, the fibration, the frame and the translation involution but DOUBLES the cross-class non-orthogonality (26880 vs 13440 ordered pairs) and provably has NO start state. Controls C1-C3 fire (the C3 control-design correction disclosed: the original label transposition was vacuous, corrected to a class-assignment scramble; frozen spec untouched). ROOTCLASS-MIXED (v775) unaffected: no matter assignment. No marker move, NO RH claim. NOTE (2026-08-06, v800 -- marker UNCHANGED): the torsor structure acquires its canonical CHARACTER reading -- the 120 projective Fourier rays of the origin-free fibers are canonical (an origin shift is a global sign), orthogonal (Gram = 16 I), deck/Pauli-diagonal and G31-monomial through Sp(4,2); the 8 R-fibers' 64 rays factorize as (1+5+10) x (1+3) under W(D5) x W(A3) -- the carrier Pascal at character level, with the weight basis exactly mutually unbiased (ROOTCLASS-MIXED intact). See E8.TORSOR.FOURIER.01.

Original classification detail

TRANSITION-BUS-TORSOR: 15 coordinate 8-frames; pair fibers = canonical v_perp-torsors; NO deck-equivariant V x (V-0) labeling exists (proof-grade obstruction); the frozen symplectic predicate reproduces all 57600 inner products incl. the sign law; 240 = 5 x 3 x 16 spread layer; A15 comparison quantified; controls fire; no RH statement.

Dependencies as recorded

v752; v689; ARF.SPINORCOMPILER.01; ARF.ROOTCLASS.01