A registered result in its source context
Original ledger classification: Exact [E] dictionary/uniqueness identities + 40-digit certificates + Gamma-monomial closed forms + [C] the fork-basis residue (sympy + mpmath)
Recorded statement: The canonical period normalization -- the analytic bridge closes (one module, 19 checks, ~6 s; discovery probe canonical_periods_probe.py 19/19, verdict PERIOD-NORMALIZED; executes v612's named step B5). DECK-FREE ROTATION [E, 40-digit…
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Paper context: TFPT — Introduction and reading guide
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QGEO.PERNORM.01
Original ledger classification: Exact [E] dictionary/uniqueness identities + 40-digit certificates + Gamma-monomial closed forms + [C] the fork-basis residue (sympy + mpmath)
Original claim text
The canonical period normalization -- the analytic bridge closes (one module, 19 checks, ~6 s; discovery probe canonical_periods_probe.py 19/19, verdict PERIOD-NORMALIZED; executes v612's named step B5). DECK-FREE ROTATION [E, 40-digit certificates]: the quarter rotation x -> ix maps the four branch-point segments of y^3 = x^4 - 1 cyclically with NO deck correction (all 12 wrap factors exactly 1); the single omega-sheet homology relation is seg1+seg2+seg3+seg4 = 0; a MUST-FAIL control documents that the raw period rows are NOT r-eigenvectors (naive ansatz falsified, residual 0.42). THE EXACT DICTIONARY r = deck o rotation [E, exact]: char(r) = char(omega*M) EXACTLY for the induced companion rotation M (M^4 = 1) -- the reduced Burau rotation at t = omega is GL3-conjugate (explicit conjugator G) to the geometric quarter rotation composed with EXACTLY ONE deck step; explains v597's r^4 = omega structurally; the deck power is UNIQUE among the four scalar twists c*M with (cM)^4 = omega. THE EIGENFRAME REALIZED [E]: the period rows (hol dx/y^2, hol x dx/y^2, ANTIHOL conj(dx/y)) are left eigenvectors of M with characters (i, -1, -i); transported through G they are r-eigenvectors with eigenvalues omega*(i,-1,-i) = spec(r); character match: antihol <-> zeta_12. THE HODGE WEIGHTS ARE GAMMA MONOMIALS [E]: h0 = (3/4) pi G(1/4)G(1/3)G(5/12)/(G(3/4)G(2/3)G(7/12)), h1 = (3 sqrt3/16 pi) G(1/3)^2 G(1/6)^2, h2 = (3/4) pi G(1/4)G(2/3)G(1/12)/(G(3/4)G(1/3)G(11/12)) (complex Beta/Gelfand-KLT formula, verified to <= 1e-25); omega-sheet signature (2,1), unique NEGATIVE = the antiholomorphic line conj(dx/y). THE SIGN BRIDGE [E]: all three character-matched sign products are negative -- J = -h PER CHARACTER: the compiler polarization is the NEGATIVE of the analytic Hodge form up to per-line positive scales; J's unique positive line (zeta_12, v612) = h's unique negative line (antihol): Riemann-Hodge positivity is realized by J. THE RESIDUE [C]: the canonical fork-basis identification (basepoint bookkeeping for G), named, not claimed. GATE.QGEO does not move; no marker changes. [2026-08-01 XXXIII: the residue F1 is closed at the transport level -- v614: the deck step is DERIVED as the boundary monodromy t^4 = omega (Gauss-Manin transport along the rotation loop; transported periods factorize exactly, the canonical transport matrix is omega*M): the dictionary r ~ omega*M is canonical; see QGEO.TRANSPORT.01.]
Original classification detail
PERIOD-NORMALIZED: rotation deck-free on segments (12 wrap factors = 1); r = deck o rotation exactly (char(r) = char(omega*M), deck power unique); period rows realize the eigenframe (antihol <-> zeta_12); Hodge weights = explicit Gamma monomials, signature (2,1); J = -h per character (Riemann-Hodge positivity realized); 19/19 checks
Dependencies as recorded
QGEO.POLFRAME.01; QGEO.PERIODS.01; QGEO.LANDSCAPE.01; QGEO.REAL.01; v597; v599; v610; v611; v612
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- Architecture, E8 and the electromagnetic fixed point
- Standard Model and flavor structure
- E8 audit and bootstrap
Sections that explicitly cite this claim
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- =150 2026-08-01 (XXX) (the canonical period normalization lands ( v613 promoted) — THE ANALYTIC BRIDGE CLOSES: the quarter rotation acts DECK-FREE on the four branch segments (all [formula in source] wrap factors exactly [formula in source] ), and the exact dictionary is [formula in source] — [formula in source] EXACTLY, explaining [formula in source] structurally, with the deck power unique; the period rows (hol [formula in source] , hol [formula in source] , antihol [formula in source] ) realize the rotation eigenframe; the Hodge weights are explicit Gamma monomials ( [formula in source] , complex Beta formula); and [formula in source] PER CHARACTER: the compiler polarization is MINUS the analytic Hodge form — Riemann–Hodge positivity realized, v612's named step B5 executed)Research changelog; TFPT — Introduction and reading guide
- Front matter / supportE8 audit and bootstrap
- =150 2026-08-01 (XXXI) (the Gauss–Manin transport round lands ( v614 promoted) — THE DECK STEP IS THE BOUNDARY MONODROMY: transporting the segment cycles along the rigid quarter-rotation loop, the discriminant [formula in source] winds ONCE around [formula in source] and the transported periods factorize EXACTLY, [formula in source] ; at [formula in source] the deck factor is [formula in source] on EVERY sheet (the exponent [formula in source] forced by the puncture count); the canonical transport matrix in the segment basis is EXACTLY [formula in source] — the v613 dictionary [formula in source] is CANONICAL, no conjugator freedom left, and [formula in source] re-derives [formula in source] ; v613's residue F1 closed at the transport level)Research changelog; TFPT — Introduction and reading guide
- Group-theoretic audits (optional)input 5 tfpt 3 e8 audit bootstrap
- Group-theoretic audits (optional)input 5 tfpt 3 e8 audit bootstrap
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.
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
Registered verification modules
- v613_canonical_periods.pyRegistered verification module · core
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QGEO.PERNORM.01: die kanonische Perioden-Normierung — DIE ANALYTISCHE BRÜCKE SCHLIESST: die Viertel-Rotation x→ix wirkt DECK-FREI auf den vier Verzweigungs-Segmenten (alle 12 Wrap-Faktoren exakt 1; Homologie-Relation seg₁+seg₂+seg₃+seg₄ = 0; Must-fail-Kontrolle: rohe Periodenzeilen sind KEINE r-Eigenvektoren); **DAS EXAKTE WÖRTERBUCH r = Deck ∘ Rotation**: char(r) = char(ω·M) exakt — die reduzierte Burau-Rotation bei t = ω ist GL₃-konjugiert zur geometrischen Rotation mal GENAU EINEM Deck-Schritt (erklärt v597s r⁴ = ω strukturell; Deck-Potenz eindeutig unter den vier Skalar-Twists); die Periodenzeilen (hol dx/y², hol x·dx/y², ANTIHOL conj(dx/y)) realisieren den Rotations-Eigenrahmen mit Charakteren (i,−1,−i) und transportiert spec(r); DIE HODGE-GEWICHTE SIND Γ-MONOME: h₀, h₁ = (3√3/16π)Γ(1/3)²Γ(1/6)², h₂ via komplexer Beta-Formel (≤1e−25 verifiziert), Signatur (2,1); **DIE VORZEICHEN-BRÜCKE J = −h PRO CHARAKTER**: Js einzige positive Linie (ζ₁₂) = hs einzige negative Linie (antiholomorph) — Riemann–Hodge-Positivität durch die Kompiler-Polarisierung realisiert (19 checks, ~6 s)
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