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Original ledger classification: Numerical (spectral action) [E]/[C]

Recorded statement: MODULAR/KMS SPECTRAL-ACTION CUTOFF (2026-06-17): the spectral-action cutoff f is the seam's own modular/KMS weight (beta=1 by Tomita-Takesaki/BW, v239; 2pi=1/(4c3), v58), so the heat-kernel cutoff f(u)=e^{-u} is derived not chosen and the…

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PS.SPECACT.02

Original ledger classification: Numerical (spectral action) [E]/[C]

Original claim text

MODULAR/KMS SPECTRAL-ACTION CUTOFF (2026-06-17): the spectral-action cutoff f is the seam's own modular/KMS weight (beta=1 by Tomita-Takesaki/BW, v239; 2pi=1/(4c3), v58), so the heat-kernel cutoff f(u)=e^{-u} is derived not chosen and the moment ratio f_2/f_0=1 exactly -- reducing the last open scheme freedom of PS.KAPPA.01/PS.SPECACT.01 from a free function to a finite-triple trace ratio kappa=sqrt(c_PS/c_grav) (proposal Q4: the cutoff is modular, not chosen).

Original classification detail

[E] KMS cutoff moments f_0=f_2=f_4=1 so f_2/f_0=f_4/f_2=1 (sympy) + seam-fixed beta=1 + non-vacuous neg control (Gaussian cutoff gives sqrt(pi)/2 != 1) + kappa=sqrt(c_PS/c_grav) (no cutoff function left); [C] RG kappa~1.3 pins c_PS/c_grav~1.7 (O(1) band [0.3,3]) and lambda(Lambda) likewise a finite-triple number -- the [O] free scheme becomes a finite computation over the built triple.

Dependencies as recorded

PS.SPECACT.01; PS.KAPPA.01; DYN.KMS.01

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Registered verification modules

  • v259_modular_cutoff_kappa.pyRegistered verification module · registry
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    PS.SPECACT.02 — the spectral-action CUTOFF is the seam KMS weight, fixing f_2/f_0=1 EXACTLY and reducing the last open scheme freedom (v253 #5, v255 #7) from a free function to a finite-triple trace ratio (Q4: the cutoff is modular not chosen). By Tomita-Takesaki/BW the seam state is KMS at beta=1 (v239) and 2pi=1/(4c3) (v58) fixes beta, so the heat-kernel cutoff f(u)=e^{-u} is DERIVED. [E] KMS cutoff moments f_0=f(0)=1, f_2=int f=1, f_4=int u f=1, so f_2/f_0=f_4/f_2=1; [E] seam-fixed beta=1 (no new parameter beyond c3); [E] non-vacuous neg control: a Gaussian cutoff e^{-u^2} gives f_2/f_0=sqrt(pi)/2 != 1; [E] kappa=sqrt((f_2/f_0)c_PS/c_grav)=sqrt(c_PS/c_grav), no cutoff function left; [C] RG kappa~1.3 pins c_PS/c_grav~1.7 (O(1)); the [O] free scheme becomes a [C] finite computation over the built triple; [C] same logic fixes lambda(Lambda).

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