Chiral lattice matter and the mirror sector

CHIRAL4D.NOMIRROR.01

Original ledger classification: Open (research contract; 1+1D chiral Gauss census executed; SMG mechanism toy-proved [E]; Nielsen-Ninomiya as Gauss statement; 4D Spin(10) theorem stays [O]; no 3+1D closure) | Round-3 v1023 adds an exact finite block lemma [E]/conditional GW reading [C]; NOMIRROR remains Open [O].

Original claim text

THE CHIRAL 4D LATTICE MATTER CONTRACT [O] (registered 2026-08-27; step (4) of the firewall route ordering). The seam's c_- = 8 and Chern/inflow structure are a boundary-ANOMALY signal, not yet 4D matter. DEMAND: an explicit chiral lattice operator (Ginsparg-Wilson/overlap type) for the TFPT representation content with proofs of (C1) a local gauge-invariant fermion measure; (C2) perturbative AND global anomaly freedom; (C3) no Witten SU(2) anomaly; (C4) no mirror generation in the physical spectrum (mirror decoupling surviving the continuum limit); (C5) correct index and charges (TFPT charge lattice, N_fam generations); (C6) a stable continuum limit compatible with QFT4D.OS.RECON.01. CALIBRATION (state of the art): Mastropietro arXiv:2303.02790 -- weakly coupled 4D U(1) with a MASSIVE gauge field; the TFPT target (chiral SU(3)xSU(2)xU(1), three generations, massless nonabelian fields, EWSB and confinement downstream) is far stronger. KILL TESTS: mirror fails to decouple (WOIT kill test 3 at lattice level); Witten anomaly obstructs the carrier SU(2); every gauge-invariant measure is provably nonlocal. CONSISTENCY (ledger wins): the celestial-branch scope fence honestly lists interacting RP, mirror decoupling, internal SU(2), both helicities, local matter fields, EWSB, confinement as NOT closed; the contradictory 'zero open internal mechanisms' phrase in docs/OPEN_PROBLEMS.md is corrected in the same change. EXECUTED UPDATE (2026-08-28, v989): chiral Gauss census on a two-species Z4 Hamiltonian (factorized 16 x 256, 4096 never materialised) -- single-exponent Gauss iff q_L = q_R; two-exponent Gauss always (lattice Dirac doubling); V^4 = I; mutant (g_L,g_R)=(1,0) on vectorlike fails. NOT the TFPT representation content and not 3+1D. Contract stays [O]. Python-only / Wolfram mirror deferred. EXECUTED UPDATE (2026-08-28, completeness wave, v997): FK SMG toy theorem -- N=8 unique Spin(7)-singlet ground state, Schmidt rank 1, volume-independent gap 14 at L=1,2,3; N=4 contrast 2^L-degenerate; physical chiral edge keeps its pi/L spectrum exactly. SMG mechanism toy-proved [E]; 4D Spin(10) theorem stays [O]. Contract stays [O]. Python-only / Wolfram mirror deferred. WAVE-5 KILL (2026-08-29, v1002): number-preserving Casimir projector route excluded -- singlet census one 16 = {N=0:1, N=16:1} (none at N=8); k=2 half-filling multiplicity 27; k=3: 1463 (exact Weyl alternation, |W(D5)|=1920); uniqueness fails at every cluster size. The DET16 number-violating projector is a SEPARATE candidate (CHIRAL4D.MIRROR.DET16.01 [C]). EXECUTED UPDATE (2026-09-05, v1023): child CHIRAL4D.MIRROR.DFILTER.BLOCK.01 proves the finite derivative-filtered 2x2 singular-value block, exact ker(D_GW) preservation and the adiabatically mirror-continuated high branch. The bare mirror variable is not invariant, the low branch is quadratic (z=2), and no bare-mirror response gap, Weyl cone, DET16/DET32 realization, interacting parent, local measure/anomaly/index control or 3+1D continuum theorem follows. Parent status stays Open [O]. ROUND-4 CURRENT: v1027 repairs canonical DET excitations under the singlet premise and preserves signed z=1 dispersion for fixed c-number gauge fields. It changes flatDeltaQ to additiveDeltaNa. No hard bare-mirror gap, quantum-link CAR diagonalization, chiral SM or continuum closure; [O] unchanged.

Original classification detail

Open: explicit GW/overlap chiral lattice operator for the TFPT content. EXECUTED (v989): 1+1D Gauss census (single-exponent iff vectorlike; two-exponent always). No 3+1D closure. EXECUTED (v997): SMG mechanism toy-proved [E] (N=8 unique Spin(7) singlet, gap 14 volume-independent; N=4 2^L contrast; physical edge pi/L exact). 4D Spin(10) theorem stays [O]. No 3+1D closure. WAVE-5 (2026-08-29, v1002): number-preserving Casimir projector route excluded (census N=8:0, k=2:27, k=3:1463, |W(D5)|=1920). Display unmoved Open. | ROUND3 2026-09-05: finite derivative-filtered block only; no invariant mirror-response gap, Weyl cone, many-body realization or 4D closure. Display stays [O]. | ROUND-4 CURRENT: v1027 repairs canonical DET excitations under the singlet premise and preserves signed z=1 dispersion for fixed c-number gauge fields. It changes flatDeltaQ to additiveDeltaNa. No hard bare-mirror gap, quantum-link CAR diagonalization, chiral SM or continuum closure; [O] unchanged.

Dependencies as recorded

DIMENSION.UPLIFT.FIREWALL.01; QFT4D.OS.RECON.01; WOIT.OS.TWISTOR.01 (kill test 3)