A registered result in its source context
Original ledger classification: Numerical (finite-block) [E]/[O]
Recorded statement: KMS / THERMAL TIME (2026-06-17): the modular flow of v238 makes the seam state a KMS (thermal) state at the canonical inverse temperature beta = 1, and the geometric (Unruh/Bisognano-Wichmann) normalisation fixes the physical seam…
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DYN.KMS.01
Original ledger classification: Numerical (finite-block) [E]/[O]
Original claim text
KMS / THERMAL TIME (2026-06-17): the modular flow of v238 makes the seam state a KMS (thermal) state at the canonical inverse temperature beta = 1, and the geometric (Unruh/Bisognano-Wichmann) normalisation fixes the physical seam temperature via the seam unit 2 pi = 1/(4 c3). Tomita-Takesaki: a cyclic-separating state is automatically KMS at beta = 1 for its own modular flow. (1) [E] KMS at beta=1: omega(A sigma_i(B)) = omega(B A) for random Hermitian A,B (omega(X)=Tr(rho X), rho=e^{-Lambda_Sigma}/Z), so modular time (v238) is a thermal time (Connes-Rovelli) and the seam state is the Gibbs state of the modular Hamiltonian. (2) [E] NEG: the same identity at beta=1/2 fails -- Tomita-Takesaki pins beta=1, no tunable knob. (3) [E] the seam unit: beta_phys = 2 pi = 1/(4 c3) exactly (v58; 1/4=1/|mu4|), so the modular KMS temperature is the horizon temperature T_H = kappa/(2 pi) = c3/M (v57/v208) -- thermal time = horizon time. (4) [E] one object with v238: the same Lambda_Sigma generates sigma_t and rho=e^{-Lambda_Sigma}/Z; the recovery generator L's stationary state is the beta->0 democratic point. (5) [O] residual: that this beta=1 flow is the geometric boost (T_H physical) is the QGEO.SYM.01/BW premise (HOR.BHTHERMO.01 [P]) -- a target, not a closure
Original classification detail
[E] KMS at beta=1 (modular flow is thermal); seam unit 2 pi = 1/(4 c3) = horizon temperature T_H = c3/M; one object with v238. [O] the geometric-boost identification = QGEO.SYM.01 -- a target, not a closure
Dependencies as recorded
DYN.SEMIGROUP.01; HOR.BHTHERMO.01
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- Research contracts
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- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
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- The whole integer skeleton from one pair [formula in source]input 4 origin theory
- The EM closure: [formula in source] as an explicit fixed point (made explicit here)tfpt 1 architecture e8
- 2026-07-14 (III) ( v484 — the two open analytic targets MERGE: the shared `` [formula in source] per boundary insertion'' rule of ALPHA.QUILLEN.EXACT.01 and HYP.PHI0.PUNCTURE.01 is the KMS seam unit [formula in source] with [formula in source] , derived on the seam circle for the finite cycle sector — no gate closes, no marker moves)Research changelog; TFPT — Introduction and reading guide
- The unique attractor: a gapped transport selects ONE fixed pointorigin theory
- The unique attractor: a gapped transport selects ONE fixed pointinput 4 origin theory
- The whole integer skeleton from one pair [formula in source]input 4 origin theory
- The EM closure: [formula in source] as an explicit fixed point (made explicit here)tfpt 1 architecture e8
- 2026-06-22 (the four black-hole-birth completion routes investigated: none closes all or is 100\% provable alone; all four converge on SEAM.EQUIV.01 [formula in source] the decoupled QG contour: v343)Research changelog; TFPT — Introduction and reading guide
All 18 linked sections
- The whole integer skeleton from one pair [formula in source]
- The EM closure: [formula in source] as an explicit fixed point (made explicit here)
- Research Contract 1 — [formula in source]
- The unique attractor: a gapped transport selects ONE fixed point
- 2026-06-17 (The Modular Spectral Closure: Dirac as covariance induction, the modular cutoff, the Kummer/K3 unification, and the assembly certificate, v258– v261)
- 2026-07-14 (IV) ( v485 — the merged analytic target's computable side COMPLETED: the diagonal self-energy is renormalised to ZERO exactly at the KMS seam scale, the mark contact calculus resums in closed form (BFK route), and the [formula in source] / [formula in source] multiplicities are ONE state set under two response weights — the residual collapses onto the SEAM.EQUIV.01 face alone; no gate closes, no marker moves)
- Research Contract 1 — [formula in source]
- The whole integer skeleton from one pair [formula in source]
- Front matter / support
- The unique attractor: a gapped transport selects ONE fixed point
Registered verification modules
- v239_kms_thermal_time.pyRegistered verification module · registry
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DYN.KMS.01 — KMS / thermal time: the modular flow of v238 makes the seam state a KMS (thermal) state at β=1, and the geometric normalisation fixes the seam temperature via 2π = 1/(4c3). [E] KMS at β=1: ω(A σ_i(B)) = ω(BA) (ω(X)=Tr(ρX), ρ=e^{−Λ_Σ}/Z), so modular time (v238) is a thermal time (Connes–Rovelli); NEG β≠1 fails (Tomita–Takesaki pins β=1). [E] the seam unit β_phys = 2π = 1/(4c3) (v58) makes the KMS temperature the horizon temperature T_H = c3/M (v57/v208) — thermal time = horizon time. [E] one object with v238 (same Λ_Σ generates σ_t and the Gibbs state). [O] the geometric-boost identification = QGEO.SYM.01 (HOR.BHTHERMO.01 [P]) — a target, not a closure.
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