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Original ledger classification: Exact identity-grade compression [Identity]: both parts exact sympy/integer arithmetic; the compression is a normal form of existing corpus surfaces (tfpt_1 anchor power compiler + budget lines, tfpt_2 flavor spectral selector + bilinear table); no marker move (Python-only per GATE.WOLFRAM.02)

Recorded statement: ANCHOR.AFFINE.01 + FLAVOR.BIDIR.01: the anchor affine normal form and the flavor bidirectional checksum -- two exact corpus compressions, ONE module from two probes (18/18 + 15/15 checks, verdicts ANCHOR-AFFINE-EXACT and…

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Paper context: input 5 tfpt 3 e8 audit bootstrap

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ANCHOR.AFFINE.01

Original ledger classification: Exact identity-grade compression [Identity]: both parts exact sympy/integer arithmetic; the compression is a normal form of existing corpus surfaces (tfpt_1 anchor power compiler + budget lines, tfpt_2 flavor spectral selector + bilinear table); no marker move (Python-only per GATE.WOLFRAM.02)

Original claim text

ANCHOR.AFFINE.01 + FLAVOR.BIDIR.01: the anchor affine normal form and the flavor bidirectional checksum -- two exact corpus compressions, ONE module from two probes (18/18 + 15/15 checks, verdicts ANCHOR-AFFINE-EXACT and FLAVOR-BIDIR-CHECKSUM (selective); discovery probes anchor_affine_probe.py and flavor_bidir_probe.py, 2026-08-07, re-run identically at promotion, promoted VERBATIM). PART A: the anchor a = (1,1,2) has power sums p_n = 2 + 2^n satisfying the affine recursion p_{n+1} = 2 p_n - 2 identically in n (sympy); T(x) = 2x - 2 has the UNIQUE fixed point 2 = |Z_2| (the sheet), and the T-orbit of 4 is exactly the compiler quintet (4, 6, 10, 18, 34) = (|mu4|, |R+(A3)|, A_L, N_fam |R+(A3)|, Z6-lift) with p_0 = 3 = N_fam prepended. THE BUDGET FROM ONE RECURSION: |R(E8)| = p1 p2 p3 = 240, dim E8 = 240 + q3 = 248 (ladder identity p4 - p3 = p3 - 2 = 8 = h(D5) = rank E8), h(E8) = p2 p3/2 = 30, |R(D5)| = p1 p3 = 40, Omega_adm = 2 p1 p2 = 48, chi_a(t) = (t-1)^2(t-2) with (e1,e2,e3) = (4,5,2) = (|mu4|, g_car, |Z_2|), 10 b1 = e1^2 + e2^2 = 41 -- every number a word in the T-orbit and the fixed point. PART B: R = [[1,3,0],[1,5,2],[2,5,3]] decodes the SAME anchor on both sides -- R a = (4, 10, 13) = (p_1, p_3, N(3+2i)) and R^T a = (6, 18, 8) = (p_2, p_4, p_3 - 2); tr R = 9 = p_0^2, det R = 8, principal 2-minors {2,3,5}, chi_R = t^3 - p_0^2 t^2 + p_3 t - (p_3 - 2), ||R||_F^2 = 78, SNF diag(1,1,8). THE SIBLING ABLATION: of the 12 down-row candidates (all orderings of {1,2,5} and the sibling {1,3,4}) EXACTLY ONE -- the accepted (1,5,2) -- satisfies the full identity set; the anchor contraction (R a)_2 = 10 = p_3 kills both siblings (11 and 12). Controls fire (wrong map, wrong anchor, sibling (1,4,3) reproducing tfpt_2's failure numbers verbatim, scrambled ordering). A normal form / compression, NOT a new claim: no marker moves. Exact sympy/integer; no floats, no RNG, no fit. Python-only per GATE.WOLFRAM.02.

Original classification detail

ANCHOR-AFFINE-EXACT + FLAVOR-BIDIR-CHECKSUM (selective): the whole compiler budget from ONE affine recursion T(x) = 2x - 2 (orbit 4, 6, 10, 18, 34; fixed point 2); the flavor matrix R decodes the same anchor bidirectionally (rows p_1, p_3, 13; columns p_2, p_4, 8) and the accepted down-row (1,5,2) is the UNIQUE candidate of 12 passing the full identity set -- the kill test is the anchor contraction (R a)_2 = 10 = p_3

Dependencies as recorded

v1; v2; v6; v222; v230; v415

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Registered verification modules

  • v832_anchor_flavor_checksum.pyRegistered verification module · core
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    ANCHOR.AFFINE.01 + FLAVOR.BIDIR.01: die affine Anker-Normalform und die bidirektionale Flavor-Prüfsumme — zwei exakte Korpus-Kompressionen — **ANCHOR-AFFINE-EXACT + FLAVOR-BIDIR-CHECKSUM (selektiv) (18/18 + 15/15): der Anker a = (1,1,2) hat Potenzsummen p_n = 2 + 2^n mit der affinen Rekursion p_{n+1} = 2p_n − 2 identisch in n (sympy); T(x) = 2x − 2 hat den EINDEUTIGEN Fixpunkt 2 = |Z₂| (das Blatt), und der T-Orbit von 4 ist exakt das Compiler-Quintett (4, 6, 10, 18, 34) = (|μ₄|, |R⁺(A₃)|, A_L, N_fam·|R⁺(A₃)|, Z₆-Lift), mit p₀ = 3 = N_fam vorangestellt; das GESAMTE Budget aus EINER Rekursion: |R(E8)| = p₁p₂p₃ = 240, dim E8 = 240 + q₃ = 248 (Leiter-Identität p₄ − p₃ = p₃ − 2 = 8 = h(D5) = rank E8), h(E8) = p₂p₃/2 = 30, |R(D5)| = p₁p₃ = 40, Ω_adm = 2p₁p₂ = 48, (e₁,e₂,e₃) = (4,5,2), 10b₁ = 41. Teil B: R = [[1,3,0],[1,5,2],[2,5,3]] dekodiert DENSELBEN Anker beidseitig — Ra = (4, 10, 13) = (p₁, p₃, N(3+2i)), Rᵀa = (6, 18, 8) = (p₂, p₄, p₃−2); der Geschwister-Kill: von 12 Kandidaten besteht GENAU EINER — die akzeptierte (1,5,2) — den vollen Identitätssatz, und die Anker-Kontraktion (Ra)₂ = 10 = p₃ tötet beide Geschwister (11 und 12). Kontrollen feuern (falsche Karte, falscher Anker, Geschwister (1,4,3) reproduziert tfpt_2s Fehlerzahlen WÖRTLICH). Exakt sympy/Integer; keine Floats, kein RNG, kein Fit.**

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