A registered result in its source context
Original ledger classification: Numerical (spectral action) [E]/[C]/[O]
Recorded statement: SPECTRAL-ACTION HEAT-KERNEL EXPANSION (a0,a2,a4) + EXPLICIT kappa(f2/f0) (2026-06-17): closes the open obligation v252 #11 (spectral-action expansion) and makes the kappa-dependence on the cutoff moments explicit (v253 #5). The bosonic…
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Paper context: Research contracts
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PS.SPECACT.01
Original ledger classification: Numerical (spectral action) [E]/[C]/[O]
Original claim text
SPECTRAL-ACTION HEAT-KERNEL EXPANSION (a0,a2,a4) + EXPLICIT kappa(f2/f0) (2026-06-17): closes the open obligation v252 #11 (spectral-action expansion) and makes the kappa-dependence on the cutoff moments explicit (v253 #5). The bosonic spectral action S = Tr f(D/Lambda) has the Seeley-DeWitt expansion S ~ 2 f4 Lambda^4 a0 + 2 f2 Lambda^2 a2 + f0 a4 (f4,f2 moments, f0=f(0)). (1) [E] expansion structure: a0=cosmological (N int sqrt g), a2=Einstein-Hilbert + Higgs mass, a4=Yang-Mills + Weyl^2 + R^2 + Higgs quartic + R|H|^2, with N=dim H_F=96 (Gilkey/Chamseddine-Connes). (2) [E] trace inputs a=Tr(Y+Y)=2.96, b=Tr((Y+Y)^2)=2.92, b/a^2=0.333=1/3 (top-Yukawa dominated, the Chamseddine-Connes value). (3) [E] gauge normalisation: the a4 Yang-Mills term fixes g3=g2=sqrt(5/3)g1, sin^2 thetaW=(sum T3^2)/(sum Q^2)=3/8 (cross-check v245). (4) [C] Higgs quartic: lambda(Lambda) ~ g^2 b/a^2 = g^2/3; with the sigma ingredient present (v254) this is the famous ~125 GeV (vs ~170 GeV without sigma) Higgs-mass prediction after RG running (m_H vs 125.25 GeV); exact coefficient + running cited. (5) [E] scalaron from R^2: the gravitational a4 carries a Weyl^2 + R^2 term with coefficient ~ f0 N; the R^2 spin-0 mode IS the Starobinsky scalaron, M_s its mass (R+R^2 gravity emerges from the spectral action). (6) [C] kappa made explicit: a2 carries f2 (Einstein-Hilbert), a4 carries f0 (R^2/scalaron + gauge), so kappa=M_PS/M_s=sqrt((f2/f0) c_PS/c_grav) is an explicit ratio of the two moments x traces over H_F; the RG value kappa~1.3 (v253) fixes f2/f0 to O(1). (7) [O] the exact kappa decimal and exact lambda(Lambda) need the cutoff function f fixed -- the last genuinely open input.
Original classification detail
[E] Seeley-DeWitt expansion structure + trace inputs (b/a^2=1/3) + sin^2 thetaW=3/8 + scalaron from R^2; [C] Higgs quartic ~125 GeV + explicit kappa(f2/f0); [O] cutoff moments; closes v252 spectral-action obligation
Dependencies as recorded
PS.DIRAC.02; PS.KAPPA.01; CONTRACT.QFT4D.01
Open the original ledger source, row 341Location recorded in the ledger
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- Research contracts
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- 2026-06-17 (Remaining NCG obligations discharged or honestly typed: inner fluctuations, spectral action, orientability/Poincar\'e, v254– v256)Research changelog; TFPT — Introduction and reading guide
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
Navigation through a shared verification script
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- The ambient closure: one spectral-action measure, IR-complete by decouplingtfpt 2 standard model
- Research Contract 1 — [formula in source]tfpt research contracts
- 2026-06-18 (Paper consistency pass: the closure ledger and the status/QFT sections updated for the Modular Spectral Closure, with an explicit ``what is not closed'' line)Research changelog; TFPT — Introduction and reading guide
- The ambient closure: one spectral-action measure, IR-complete by decouplingStandard Model and flavor structure
- 2026-06-17 (The Modular Spectral Closure: Dirac as covariance induction, the modular cutoff, the Kummer/K3 unification, and the assembly certificate, v258– v261)Research changelog; TFPT — Introduction and reading guide
- Research Contract 1 — [formula in source]tfpt research contracts
- Full quantum gravity — induced from the boundary kernelFrontier and open physical interfaces
- Front matter / supportResearch contracts
Registered verification modules
- v255_spectral_action_expansion.pyRegistered verification module · registry
Read the description recorded in the module registry
PS.SPECACT.01 — the spectral-action heat-kernel (Seeley-DeWitt) expansion S = 2f₄Λ⁴a₀ + 2f₂Λ²a₂ + f₀a₄ over the finite triple; closes v252 #11 (spectral-action expansion) and makes κ(f₂/f₀) explicit. [E] expansion structure (a₀ cosmological, a₂ Einstein-Hilbert+Higgs-mass, a₄ Yang-Mills+Weyl²+R²+Higgs-quartic, N=96); [E] trace inputs b/a²=1/3 (top-dominated, Chamseddine-Connes); [E] sin²θ_W=3/8 (cross-check v245); [C] Higgs quartic λ(Λ)~g²b/a² → ~125 GeV with σ; [E] scalaron = R² spin-0 mode (gravitational a₄~f₀N); [C] κ=√((f₂/f₀)c_PS/c_grav) explicit; [O] exact decimal needs the cutoff moments fixed.
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