A registered result in its source context

EXTREV.LATTICE.01

Original ledger classification: Exact [E] closure/bytecode/congruence identities + [X] the ill-posed retype + [C] conditional typing (sympy; citations web-verified)

Original claim text

The external-review lattice audit (one module, 14 checks, <1 s; discovery probe external_lattice_audit_probe.py 14/14, verdict LATTICE-AUDIT-PASSED; external review 2026-08-02, three claimed derivations machine-checked, one follow-up retyped honestly). THE FOUR-MARK CLOSURE [E, conditional]: generalizing the glue to D_{d+1} + A_{d-1}, THREE independent selectors each force d = 4 -- the disc-group census (Z_d = Z_4 with cyclic D-side; negative controls d = 3, 5, 8), the even-glue norm equation (d+1)/4 + (d-1)/d = 2 (unique positive solution; no other even target admits an integer d), and the Pythagorean selector (d-1)^2 + d^2 = (d+1)^2 (the (3,4,5) = (cycles, marks, carrier) triple); (1,1,2) is the unique 3-part partition of 4 and c_3 = 1/(2 e_1 pi) = 1/(8 pi): under the named architecture the two-input presentation reduces to ONE boundary degree d = 4 plus pi; honest: conditional on the glue architecture, the residue moves to why the boundary realizes the minimal cyclically-glueable genus-0 divisor. THE ANCHOR BYTECODE [E]: chi_a = (t-1)^2(t-2) carries (4, 5, 2); p_n = 2 + 2^n with p_{n+2} = 3p_{n+1} - 2p_n; Newton recovers the e_k; p_1 p_2 p_3 = 240, p_4 - p_3 = 8, 240 + 8 = 248 (H-realization v602). THE LORENTZ CONGRUENCE [E + X]: P^T J_det P = J_fix EXACTLY with det P = -6 -- the prime-front determinant form and the v604 cover polarization lattice are the SAME rational quadratic form, the cover an index-6 sublattice (36 = 6^2, 6 = p_2(a)); the review's follow-up (integer R to B = M^dagger J) is ILL-POSED as stated (B COMPLEX symmetric, det 8 verified); partial positive: the third symmetric-Gauss ratio is an exact Q(omega) square; P-canonicity and the Hodge-chamber question are the named opens. CITATIONS VERIFIED: Suzuki arXiv 2606.09096 (screw-function Weil framework, Yoshida odd-criterion) and arXiv 2607.24830 (numerical realization) -- the basis of the PRIME.WEIL.OPERATOR contract. No marker moves; AX.P2.01 keeps its typing; no RH statement. [2026-08-02 XL: the prime-shadow audit lands -- v625: the 'primes appear AFTER E8' reading is exact at the theta level (Theta_E8 = E_4, shell counts 240 sigma_3(n) multiplicative, commuting Hecke channels with the theta as simultaneous eigenvector, L(E_4,s) = zeta(s) zeta(s-3)); the direction of explanation (geometry first, primes as readout) is fixed within the narrative; see PRIME.SHADOW.01.] [2026-08-02 XLI: the Lorentz congruence P^T J_det P = J_fix is additionally machine-proved in Lean (experiments/lean4-carrier-rigidity/TfptCarrier/LorentzCongruence.lean, kernel decide on the explicit integer matrices, lake build green, no sorry); P-canonicity and the operator construction of P executed by v635/v636 (see PRIME.PCANON.01 / PRIME.PCONSTRUCT.01).] [2026-08-02 XLV: look-elsewhere quantification -- v664: the observation 6 = Lorentz-congruence index = p_2(a) carries p_max = 0.169 under the most conservative null model: retyped as an observation WITHOUT statistical weight (the exact congruence P^T J_det P = J_fix itself is [E] and untouched).] [2026-08-28 CXL: v993 lifts the architecture conditionality at the census level -- full rank-8 ADE with cyclic Z4 both sides selects (D5, A3) uniquely; the D+A split is an OUTPUT. EXTREV.LATTICE.01's own v624 checks and typing UNCHANGED (they remain the architecture-conditional selectors).]

Original classification detail

LATTICE-AUDIT-PASSED: four-mark closure forces d = 4 three ways (conditional); bytecode exact (240 + 8 = 248); Lorentz congruence P^T J_det P = J_fix exact (index 6); B-test retyped ill-posed; Suzuki citations verified; 14/14 checks | 2026-08-28 v993: architecture conditionality lifted at census level (this row's v624 checks unchanged)

Dependencies as recorded

AX.P2.01; QGEO.EQORDER.01; QGEO.DUALFORMS.01; PRIME.UNIFC.01; v47; v602; v604; v618