Skip to main content

A registered result in its source context

Original ledger classification: Identity [I] (exact arithmetic/matrix identities; audit typing for the 121 lemma)

Recorded statement: 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…

Statement, assumptions and sources

Paper context: TFPT — Introduction and reading guide

The exact identifier, original classification and full claim are available below.

The source wording and classification below are preserved as recorded. A paper link, shared script or authored topic relation does not upgrade the claim or report a new proof run. Read later reviewed findings separately.

Read the exact registered claim and its dependencies

ARCH.TRIAD.01

Original ledger classification: Identity [I] (exact arithmetic/matrix identities; audit typing for the 121 lemma)

Original claim text

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

Original classification detail

Identity: anchor ratio triad (2/3 4/3 5/3) = e/p0; 121 = anchor norm of R (audit); micro-identities exact

Dependencies as recorded

ARCH.QUAD.01; FLAV.KQ.01; FLAV.DIAMOND.01-02; FR.KOIDE.06; SYNTH.INVENTORY.01

Open the original ledger source, row 203

Location recorded in the ledger

These document locations are recorded directly on the ledger row. They are document level navigation, rather than a newly inferred section citation.

Navigation through a shared verification script

These sections cite a script associated with the claim. This is a source navigation join, rather than an explicit citation of the claim or a theorem equivalence.

All 11 linked sections

Registered verification modules

  • v119_review_validation_2.pyRegistered verification module · registry
    Read the description recorded in the module registry

    SECOND EXTERNAL-REVIEW VALIDATION (triad + 121 audit + micro-identities, all exact): ANCHOR RATIO TRIAD [I] — the three elementary symmetric values of the anchor normalised by the family count, (e₃,e₁,e₂)/p₀ = (2/3, 4/3, 5/3) = (Koide branch/sheet ratio, seed gain |μ₄|/N_fam, carrier branch); the canonical flow's critical points are EXACTLY (2,5) = (e₃,e₂) with inflection 7/2 = (e₃+e₂)/2 — the recurring fractions are the three normalised anchor coefficients, not scattered numbers; THE 121 AUDIT LEMMA [I, audit-typed]: (1+a)ᵀR(1+a) = 121 = 11² = ‖Pl(K)‖₁² = (p₃+1)² — the quark-ratio 11 appears a second independent time as the quadratic anchor norm of the residue operator R; sensitivity: orderings give {105,121,135}, only the canonical anchor ordering yields 121; bonus: 1ᵀR1 = 22 = 2·11, aᵀRa = 40 = p₁p₃ = 10b₁−1 (oriented Plücker stays the derivation); MICRO-IDENTITIES: Ω_adm = 2p₁p₂ = 48, 10b₁ = 1+p₁p₃ = 41, Δ_Y = e₂² = p₀²+2·rank = 25, h(E8) = e₃p₀e₂ = 30, rank = p₀+e₂; flavor surface M(s,t) claim = established v94/v95 (presentational); μ₄ projection/triptych/interior-free already closed (v115/v116, v104/v105, v113)

A registered module is a source reference. Its presence does not assert that the module was executed in this snapshot.

Search later reviewed research for this identifierRead the coverage boundaries