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Original ledger classification: Honest promotion of an exact integer theorem [typed evidence line: 11/11 checks, zero fails, verdict WINDING-DECODER-EXACT; frozen spec SHA 6a54768d...]

Recorded statement: THE WINDING DECODER OF THE CLOCK ALPHABET (2026-08-08 round 36, v874; discovery probe g31_winding_decoder_probe.py 11/11, verdict WINDING-DECODER-EXACT; exact arithmetic). THEOREM: the v857 winding quadratic q_wind(t) = t^2 - g_car t +…

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E8.WINDING.DECODER.01

Original ledger classification: Honest promotion of an exact integer theorem [typed evidence line: 11/11 checks, zero fails, verdict WINDING-DECODER-EXACT; frozen spec SHA 6a54768d...]

Original claim text

THE WINDING DECODER OF THE CLOCK ALPHABET (2026-08-08 round 36, v874; discovery probe g31_winding_decoder_probe.py 11/11, verdict WINDING-DECODER-EXACT; exact arithmetic). THEOREM: the v857 winding quadratic q_wind(t) = t^2 - g_car t + |Z2| maps the G31 clock alphabet {2, 3, 5, 6} = {|Z2|, N_fam, g_car, |R+(A3)|} (v858) to the atom quadruple (-|mu4|, -|mu4|, |Z2|, h(D5)) = (-4, -4, 2, 8) -- with q(2) = q(3) FORCED by the palindrome q(5-t) = q(t) (axis g_car/2) and 2 + 3 = 5 = g_car; the decoder polynomial D(y) = prod(y - q(a)) = (y+4)^2 (y-2)(y-8) = y^4 - 2y^3 - 48y^2 - 32y + 256 carries the signed budget coefficients (|Z2|, Omega_adm = N_fam dim S+ = 48, 2^g_car = 32, 2^rank(E8) = 256) with the double root -|mu4| forced by the palindrome pair; and THE FOURIER BRIDGE: |mu4| q(|Z2|)/|R(E8)| = 4 x (-4)/240 = -1/15 is EXACTLY the nonzero-character Walsh eigenvalue of the Gaussian shell census (E8.SIMPLEX.FOURIER.01; now global by E8.SHELL.GLOBAL.01), and -16 = |mu4| q(|Z2|) = rhat(u != 0). CONTROLS (all fire): sibling directions collapse the bridge (q2 -> 1/15, q3 -> 1/15, q_row -> -1/12); alternative alphabets change the decoder ({2,3,5,7}: constant 512 = 2^9 NOT 2^rank(E8); {1,2,3,5} different). HONEST LINES (typed): the -32 y coefficient survives in both alternatives -- per-coefficient selectivity is weak, the selective object is the full vector (-2,-48,-32,+256); the 6-vs-7 tension typed (replacing 6 by 7 loses the y^3/y^2/constant identifications). TYPE: exact AUDIT theorem, NOT a physical functor -- an explicit intertwiner would be needed to make it causal. NO physics claim beyond the audit statement.

Original classification detail

WINDING-DECODER-EXACT: q({2,3,5,6}) = (-4,-4,2,8); D(y) = (y+4)^2(y-2)(y-8) with budget coefficients (2,48,32,256); |mu4| q(|Z2|)/|R(E8)| = -1/15 == the Walsh message eigenvalue; typed audit-not-functor.

Dependencies as recorded

E8.G31.CLOCK_ALPHABET.01; E8.SIMPLEX.FOURIER.01; E8.SHELL.GLOBAL.01; FLAVOR.FEEDBACK.NORMALFORM.01; 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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