A registered result in its source context

ARF.ROOTCLASS.01

Original ledger classification: Exact [E] finite census kill -- the fired preregistered physical kill; the fence is binding on all main claims (Python-only per GATE.WOLFRAM.02).

Original claim text

THE FIRED PHYSICAL KILL of the Arf compiler programme -- gaussian_class_d5_weight_purity, Priority 2, preregistered (one module, 18 checks, ~2 s; discovery probe gaussian_class_d5_purity_probe.py 18/18, verdict ROOTCLASS-MIXED, all 3 must-fail controls fire; FROZEN_SPEC SHA-256 58d9be9b935d92bbc3ddb838092d0cb7f8c1e5dad09e06ec28e850116ee3ef25, hashed BEFORE any root data). THE QUESTION: does each nonzero Gaussian class of V = L/(1+i)L carry exactly ONE SU(5) weight state of the D5 half-spinor 16, per the frozen F2-linear prediction table (F_i -> {c_i, w1}, A -> {w1, w2}, X = (-2,-2,-2,3,3))? THE ANSWER IS NO, FOR EVERY DEFENSIBLE CONVENTION: the embedding-INDEPENDENT counting bound kills the strict gate for EVERY D5(+)A3 c E8 (coordinate or not) -- every embedding has exactly 128 spinor-side roots, 15 x 16 = 240 > 128, so at most 8 of 15 classes can be all-spinor and >= 7 classes ALWAYS contain adjoint-side roots; the exhaustive scan (56 coordinate splits x 240 slot assignments x 2 chiralities) finds ZERO conventions with even one pure set of 15; under the canonical sigma-stable split all 8 spinor classes mix 8 distinct 16-weight pairs each; best-case match of the frozen dictionary over ALL assignments: 8/128 spinor roots; X-only weakened purity (secondary, not the gate): 0/15. CONTROLS: wrong charge vectors break the frozen X column and the root identity (C1); the LCG-scrambled class map destroys NS/R purity and +-pair symmetry (C2); of the 28 nondegenerate alternating forms every wrong form breaks the canonical pairing package (C3). CONSEQUENCE (binding fence): the code->matter reading must NOT enter any main claim -- including the 'empty mailbox = right-handed neutrino' reading; the Arf structure of v774 keeps its mathematics (census, symplectic form, polarity, NS/R point untouched). No marker move, NO RH claim. NOTE (2026-08-05, v781/v782/v783/v784/v786/v787/v790 -- marker UNCHANGED): the fence HELD through the strategic and prime-channel promotion round -- all new census/identification modules cite ROOTCLASS-MIXED as binding and none makes a code -> matter assignment; the fired kill stays the boundary of every main claim.

Original classification detail

ROOTCLASS-MIXED: no D5(+)A3/SU(5) convention makes even one full set of 15 classes pure -- counting bound (128 spinor roots, >= 7 adjoint-side classes for EVERY embedding), 0/56 splits pass, all 8 spinor classes mix 8 weight pairs; the code->matter table must not enter any main claim (fence incl. the right-handed-neutrino mailbox reading); no RH statement.

Dependencies as recorded

ARF.SPINORCOMPILER.01; E8.PROJHAMMING.01; PRIME.HECKEPOLARITY.01; v752; v1; v47; v310