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Original ledger classification: Universal synthesis [E]/[C] (every sector = a gapped operator with a unique attractor + spectral gap => parameter-free; extends v303 theory-wide; 3 gaps computed, the cross-sector identification [C])

Recorded statement: The UNIVERSAL spectral-gap / Perron-Frobenius principle (2026-06-23, bird's-eye synthesis): every TFPT sector is the SAME structural object -- a gapped operator with a UNIQUE leading attractor (the physics) and a spectral gap (the reason…

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Paper context: Origin Theory

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DYNAMICS.UNIVERSAL.01

Original ledger classification: Universal synthesis [E]/[C] (every sector = a gapped operator with a unique attractor + spectral gap => parameter-free; extends v303 theory-wide; 3 gaps computed, the cross-sector identification [C])

Original claim text

The UNIVERSAL spectral-gap / Perron-Frobenius principle (2026-06-23, bird's-eye synthesis): every TFPT sector is the SAME structural object -- a gapped operator with a UNIQUE leading attractor (the physics) and a spectral gap (the reason there is no free parameter). Extends v303 (which named this only for F_transfer) to the sectors made parameter-free AFTER it. [E] FLAVOR (computed): cusp transfer spectrum {1,(2/3)^6,(1/3)^6}, simple Perron leading 1, gap 6 ln(3/2)>0 (v56/v82/v240). [E] DISCRETE COMPILER (computed): affine-E8 adjacency Perron 2 (Kac marks, v312/v313), subleading 2cos(pi/5)=phi, gap 2-phi=1/phi^2>0. [E] DECOUPLING MARGIN (computed): Delta_eff=6 ln(3/2)-31/(4 pi^2)~1.648>0 (v76/v337). [E] TWO NUMBER-FIELD FACETS (v314): golden phi in Q(sqrt5) (carrier-5, static) and (2/3)^6 in Q (family-3, dynamic) are the prime-5 and prime-3 facets of the order-30 Coxeter clock 30=2*3*5=h(E8) -- a factorisation, NOT a forced equality. [C] OTHER SECTORS = SAME STRUCTURE: gravity=deltaS=0 equilibrium (v358/v359), QG=Gaussian saddle (v365), QFT=stable holomorphic c=8 RG fixed point (v157/v158), all-order S-matrix=adiabatic limit (v381), recovery=Petz fixed point (2/3)^6 (v221), F_transfer (v303), tau=i (v333). [C] META-THEOREM: gapped => unique attractor => parameter-free, theory-wide -- 'parameter-freeness is a theorem' (v56) is ONE spectral-gap statement wearing many hats. Anti-numerology: no new number.

Original classification detail

[E] the three computed gaps (flavor 6 ln(3/2); discrete 2-phi=1/phi^2; decoupling 1.648) + the two number-field facets (v314); [C] the cross-sector identification (gravity/QG/QFT/recovery/F_transfer) + the meta-theorem 'parameter-freeness = spectral gap, theory-wide'. A synthesis (like v303/v337/v353), reuses established gaps, introduces no new number.

Dependencies as recorded

v56; v82; v303; v312; v313; v314; v337; v358; v359; v365; v381; v221; v157; v158

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Registered verification modules

  • v383_dynamics_universal.pyRegistered verification module · frontier
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    DYNAMICS.UNIVERSAL.01: the UNIVERSAL spectral-gap / Perron-Frobenius principle -- every TFPT sector is the SAME object (a gapped operator with a UNIQUE leading attractor = the physics, a spectral gap = the reason there is no free parameter), extending v303 from F_transfer to the whole theory. [E] FLAVOR (computed): the cusp transfer spectrum {1,(2/3)^6,(1/3)^6} has a simple Perron leading 1 and gap 6 ln(3/2)>0 (v56/v82). [E] DISCRETE COMPILER (computed): the affine-E8 adjacency has Perron eigenvalue 2 (Kac marks, v312/v313) and subleading 2cos(pi/5)=phi, gap 2-phi=1/phi^2>0. [E] DECOUPLING MARGIN: Delta_eff=6 ln(3/2)-31/(4 pi^2)~1.648>0 (v76/v337). [E] TWO NUMBER-FIELD FACETS (v314): golden phi in Q(sqrt5) (carrier-5, static) and (2/3)^6 in Q (family-3, dynamic) are the prime-5 and prime-3 facets of the order-30 Coxeter clock 30=2*3*5=h(E8) -- a factorisation, not an equality. [C] the other sectors are the same structure: gravity (v358/v359), QG saddle (v365), RG fixed point (v157/v158), all-order S-matrix (v381), recovery (v221), F_transfer (v303), tau=i (v333). [C] META-THEOREM: gapped => unique attractor => parameter-free, theory-wide. A synthesis, no new number.

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