A registered result in its source context

E8.SYNDROME.ALGEBRA.01

Original ledger classification: DEAD as frozen [E kill, preregistered adjudication fired]: the twisted V-graded basis reading of E8 killed at rank level; the surviving structures typed exactly; successor criterion named

Original claim text

E8.SYNDROME.ALGEBRA.01: the honest kill -- E8 is NOT an error-correction hull in the sharpest sense, one probe (13/13 checks incl. the 3 must-fire controls, ~6 s; discovery probe e8_syndrome_algebra_probe.py, 2026-08-06, verdict SYNDROME-DEAD, the kill fired exactly as preregistered). THE QUESTION: do the 240 root operators U_r |x> = i^{c(r).x} |x XOR v> plus the 16 neutral kernels form a 256-dimensional mu4-twisted V-graded basis of End(S+)? THE KILL FIRES: the frozen mu4-linear-lift realization family reaches max rank 222/256 over ALL FOUR frozen phase conventions (Im/Re 222, Re+-Im 160; sympy-exact over Q(i)) -- with a STRUCTURAL obstruction: any phase rule Z-linear in the root gives c(-r) = -c(r), so +-r pairs with c in {0,2}^4 produce PROPORTIONAL operators (collision witness printed; 240 - 228 = 12 c-vector collisions), unreachable for the ENTIRE diagonal-phase x translation family; TWO post-hoc diagnostics score WORSE (nonlinear BFS transversal 215, zeta8-linear float 160) -- the death is robust, not a convention artifact; a successor would need root-individual (non-linear-in-r) operator data. WHAT SURVIVES: the syndrome-table counting 16 + 240 = 256 = 1x16 + 15x16, the neutral sector (the 16 v112 kernels ARE the diagonal maximal abelian subalgebra; same-class products land in A_0 with mu4 coefficients EXACTLY), the fine (class, d, k) groupoid composition law (associative on all 3375 section triples), and the W(3,2) commutation skeleton (scalar commutators 15.1%, matching (-1)^hbar on only 51.5% -- the class-level symplectic reduction fails in this realization). NO scalar V-cocycle exists (section closure 0/210). Controls fire (scrambled classes, wrong cocycle i^hbar fails the 2-cocycle identity on 960/4096 triples, random c-assignments). The sharpest E8-is-a-hull form (twisted V-graded basis) is DEAD as frozen; successor criterion named. No matter semantics (v775 ROOTCLASS-MIXED stands). No marker move, NO RH claim. Python-only per GATE.WOLFRAM.02.

Original classification detail

SYNDROME-DEAD: max rank 222/256 over all four frozen phase conventions (two post-hoc diagnostics score worse: 215/160); the +-r proportionality obstruction structural for the whole diagonal-phase family; SURVIVES: 16 + 240 = 256 counting, the 16 v112 neutral kernels ARE the diagonal MASA, same-class products A_0-valued with mu4 coefficients exactly, the fine groupoid law associative 0/3375; successor needs root-individual (non-linear-in-r) operator data; no matter semantics.

Dependencies as recorded

E8.PROJHAMMING.01; ARF.ROOTCLASS.01; v752; v111; v112; v775