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Original ledger classification: Honest promotion of an exact integer theorem [typed evidence line: 14/14 checks, zero fails, verdict FEEDBACK-NORMALFORM-EXACT; all decisions exact sympy; frozen spec SHA f5f40996...]

Recorded statement: THE FEEDBACK NORMAL FORM OF THE WINDING LINE (2026-08-08 round 36, v874; discovery probe flavor_feedback_probe.py 14/14, verdict FEEDBACK-NORMALFORM-EXACT; exact sympy/integer arithmetic in every decision). THEOREM: with the integral basis…

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FLAVOR.FEEDBACK.NORMALFORM.01

Original ledger classification: Honest promotion of an exact integer theorem [typed evidence line: 14/14 checks, zero fails, verdict FEEDBACK-NORMALFORM-EXACT; all decisions exact sympy; frozen spec SHA f5f40996...]

Original claim text

THE FEEDBACK NORMAL FORM OF THE WINDING LINE (2026-08-08 round 36, v874; discovery probe flavor_feedback_probe.py 14/14, verdict FEEDBACK-NORMALFORM-EXACT; exact sympy/integer arithmetic in every decision). THEOREM: with the integral basis P = [2*1 | e3 | R e3] (det P = -4, SNF diag(1,2,2)) the WHOLE winding line R_s = R + s 1 e1^T conjugates EXACTLY (symbolic in s) to M(s) = [[s+4,0,3],[0,0,-2],[4,1,5]]: a gain channel s + |mu4|, the companion block of the v857 winding quadratic q_wind = t^2 - g_car t + |Z2|, and the coupling pair (3,4) with loop product N_fam x |mu4| = 12 = dim g_SM; the conjugated deformation P^{-1}(1 e1^T)P = E11 is a PURE GAIN; hence chi_{R_s}(t) = (t - s - |mu4|) q_wind(t) - 12t identically (equivalently the remainder identity chi_R - (t-4) q_wind = -12t, a pure t-tap at gain offset 4 = |mu4|), and at the locked point s = 6 the coefficients (15, 40, 20) of chi_L are the three gain-10 readouts 10+5, 50+2-12, 10x2. CONTROLS (all fire): directions 1 e2^T (s leaks into the coupling; constant graft +8, offset 8 != 4), 1 e3^T (not integral; mixed remainder), and the sibling row matrix e1 1^T (smeared over all rows; offset 4 coincides -- typed honestly -- but the remainder -11t - 4 has a nonzero constant). THE HONEST TYPING (load-bearing, kernel-checked in FORM.FLAVOR.FEEDBACK.01): the quotient Z^3/PZ^3 = Z2 x Z2 has CARDINALITY 4 = |mu4| but EXPONENT 2 -- the same cardinality as mu4 = Z4, NOT the same group; any mu4 reading would need an extra order-4 witness (none claimed). NO physics claim beyond the audit statement.

Original classification detail

FEEDBACK-NORMALFORM-EXACT: P^{-1} R_s P = [[s+4,0,3],[0,0,-2],[4,1,5]] exact symbolic in s; chi_{R_s} = (t-s-|mu4|) q_wind - 12t; quotient Z2^2 typed NOT mu4; all sibling controls fire.

Dependencies as recorded

E8.SIMPLEX.FOURIER.01; E8.G31.CLOCK_ALPHABET.01; v4; v857; v858

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Registered verification modules

  • v874_feedback_decoder_lean.pyRegistered verification module · core
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    FLAVOR.FEEDBACK.NORMALFORM.01 + E8.WINDING.DECODER.01: **FEEDBACK-NORMALFORM-EXACT + WINDING-DECODER-EXACT (14/14 + 11/11, + Lean-Spiegel)** — zwei exakte Compiler-Theoreme: EINE ganzzahlige Basis P = [2·𝟙 | e₃ | R e₃] (det −4, SNF diag(1,2,2)) konjugiert die GESAMTE Windungslinie R_s = R + s 𝟙 e₁ᵀ exakt (symbolisch in s) in die Gain-plus-Companion-Normalform [[s+4,0,3],[0,0,−2],[4,1,5]]: Gain-Kanal s+|μ₄|, Companion-Block des Windungsquadrats q_wind = t²−g_car t+|Z₂|, Kopplungspaar (3,4) mit Schleifenprodukt N_fam·|μ₄| = 12 = dim g_SM — also χ_{R_s} = (t−s−|μ₄|)·q_wind − 12t, und bei s = 6 sind (15,40,20) die drei Gain-10-Ablesungen; die ehrliche Typisierung ist tragend: der Quotient ℤ³/Pℤ³ = ℤ₂² hat KARDINALITÄT 4 = |μ₄|, aber EXPONENT 2 — NICHT μ₄, keine Identifikation behauptet. Der Decoder: q_wind bildet das G31-Uhr-Alphabet {2,3,5,6} auf (−|μ₄|,−|μ₄|,|Z₂|,h(D5)) ab (q(2)=q(3) von der Palindrom-Achse g_car/2 erzwungen); D(y) = (y+4)²(y−2)(y−8) trägt die Budget-Koeffizienten (|Z₂|, Ω_adm=48, 2^g_car=32, 2^rk(E8)=256); und |μ₄|·q(|Z₂|)/|R(E8)| = −1/15 ist EXAKT der Walsh-Eigenwert des Gauß-Zensus — typisiert als AUDIT-Theorem, kein physikalischer Funktor. Lean-Spiegel: TfptCarrier/FlavorFeedback.lean (11 Theoreme, Standard-Axiome, kein sorry).

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