Original ledger status
FLAV.KQ.01
Q-Sigma algebra: K=R+Q*Sigma; L=R+Q*(I+Sigma); chi_Q=(t-1)(t^2-5t+3); chi_K=(t-1)(t^2-8t+4); det ladder (3;4;8;20) product 1920=|W(D5)|; a^T K a=41
Recorded status: Lattice
Dependencies, status detail and source
Canonical status: Lattice
Dependencies: FLAV.R.01; Sigma=diag(1;-1;-1)
Scripts: v10_projection_involution.py, v11_unique_KQ.py, v12_mass_generation_polynomials.py
Location: tfpt_2
Original CSV, line 14Original ledger status
ARCH.TRIAD.01
SECOND EXTERNAL-REVIEW VALIDATION (2026-06-11b): the anchor ratio triad, the 121 audit lemma and the normal-form micro-identities, all exact: (1) MICRO-IDENTITIES [I]: Omega_adm = 2 p1 p2 = 48; 10 b1 = 1 + p1 p3 = 41; Delta_Y = e2^2 = p0^2 + 2 rank E8 = 25; h(E8) = e3 p0 e2 = 30; rank E8 = p0 + e2 = 8; |R(E8)| = p1 p2 p3 = 240; dim E8 = 240 + (p4 - p3) = 248. (2) ANCHOR RATIO TRIAD [I] (named lemma): the three elementary symmetric values of the anchor normalised by the family count - e3/p0 = 2/3 (the Koide branch / sheet ratio, cf SYNTH.INVENTORY.01 seven appearances), e1/p0 = 4/3 (the seed gain |mu_4|/N_fam, ARCH.QUAD.01), e2/p0 = 5/3 (the carrier branch: the canonical flow's critical points are EXACTLY (2,5) = (e3,e2), FR.KOIDE.06, inflection 7/2 = (e3+e2)/2) - the recurring fractions 2/3, 4/3, 5/3 are the three normalised anchor coefficients, not scattered numbers. (3) THE 121 AUDIT LEMMA [I, typed AUDIT not load-bearing]: (1+a)^T R (1+a) = 121 = 11^2 = ||Pl(K)||_1^2 = (p3+1)^2 with the established residue operator R (det 8, SNF (1,1,8)) - the quark-ratio 11 (c_u/c_d = 5x11/(9x13)) appears a SECOND independent time as the quadratic anchor norm of R; sensitivity control: the 3 orderings of h = (2,2,3) give {105, 121, 135}, only the canonical anchor ordering yields 121; bonus checksums 1^T R 1 = 22 = 2x11 (entry sum) and a^T R a = 40 = p1 p3 = 10b1 - 1; the oriented Plucker mechanism (FLAV.KQ.01/v42/v49) remains the derivation. (4) FLAVOR SURFACE claim = established FLAV.DIAMOND.01/02 (re-verified, presentational). (5) BOOKKEEPING: mu4 projection = GATE.UWALL.07/08, triptych = HOR.CLOCK.01/SYNTH.INVENTORY.01, interior-free = CAR.QFREE.01 (all closed); anchor-first presentation recorded as editorial item
Recorded status: Identity [I] (exact arithmetic/matrix identities; audit typing for the 121 lemma)
Dependencies, status detail and source
Canonical status: Identity: anchor ratio triad (2/3 4/3 5/3) = e/p0; 121 = anchor norm of R (audit); micro-identities exact
Dependencies: ARCH.QUAD.01; FLAV.KQ.01; FLAV.DIAMOND.01-02; FR.KOIDE.06; SYNTH.INVENTORY.01
Scripts: v119_review_validation_2.py
Location: introduction; tfpt_research_contracts
Original CSV, line 203