The spectral running of the inflation branch
Original ledger classification: Identity [E] (LO relations + exact slow roll) + Physical [C] (data confrontation; N_star input)
Recorded statement: Spectral-index running of the Starobinsky branch, PROMOTED from the 2026-07-20 scorecard prediction-of-record row (same N_star_reheating group as n_s/r/A_s; never an independent hit). [E] LO identities (sympy exact): alpha_s = dn_s/dln k =…
Statement, assumptions and sources
Paper context: Architecture, E8 and the electromagnetic fixed point
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COSMO.RUNNING.01
Original ledger classification: Identity [E] (LO relations + exact slow roll) + Physical [C] (data confrontation; N_star input)
Original claim text
Spectral-index running of the Starobinsky branch, PROMOTED from the 2026-07-20 scorecard prediction-of-record row (same N_star_reheating group as n_s/r/A_s; never an independent hit). [E] LO identities (sympy exact): alpha_s = dn_s/dln k = -2/N_star^2 = -r/6, beta_s = -4/N_star^3 (NOT -8/N^3); LO band N_star in [50,60]: [-8.0e-4, -5.6e-4]. [E] exact slow roll on the Einstein-frame Starobinsky potential (third-order Lyth-Riotto + finite-difference cross-check <1%): alpha_s(51.4) = -7.09e-4, beta_s(51.4) = -2.70e-5; exact band edges -7.48e-4 / -5.23e-4. [C] data confrontation: Planck 2018 TTTEEE+lowE+lensing (-0.0045+/-0.0067) -> +0.57 sigma; record leg P-ACT-LB (+0.0062+/-0.0052) -> -1.33 sigma (watch channel: the central value is POSITIVE); beta_s (Planck run+runrun, 0.010+/-0.013) -> -0.77 sigma. Forecast: LiteBIRD+CMB-S4 sigma(alpha_s) ~ 4.9e-3 (0.14 sigma); CMB-S4+DESI+Euclid statistical ~3.3e-4 (2.2 sigma, systematics-limited). KILL: robust alpha_s < -5e-3 or > +3e-3 at >=5 sigma; any robust POSITIVE running kills the plateau branch. FENCE: N_star stays an external reheating input (GATE.NSTAR.01); the frozen band [50,60] stays the surface of record; no gate closes, no marker moves
Original classification detail
[E] LO identities + exact-SR values; [C] pulls +0.57 sigma (Planck) / -1.33 sigma (P-ACT-LB record leg); kill = robust positive running; band [50,60] stays the record
Dependencies as recorded
COSMO.INF.01; COSMO.NSTAR.01; GATE.NSTAR.01
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- Architecture, E8 and the electromagnetic fixed point
Sections that explicitly cite this claim
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- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
- 2026-07-21 (the two 2026-07-20 prediction-of-record rows promoted to the suite: v494 — [formula in source] running [formula in source] [formula in source] -distortion branch discriminator machine-checked, ledger rows COSMO.RUNNING.01/ COSMO.MUDIST.01, prediction surfaces synced; no gate closes, no marker moves)Research changelog; TFPT — Introduction and reading guide
Navigation through a shared verification script
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- Inflation interfacetfpt 1 architecture e8
- Inflation interfacetfpt 1 architecture e8
- Inflation interfaceArchitecture, E8 and the electromagnetic fixed point
- The [formula in source] truncation is [formula in source] -boundedtfpt 2 standard model
- The [formula in source] truncation is [formula in source] -boundedStandard Model and flavor structure
Registered verification modules
- v494_cosmo_running_mu_record.pyRegistered verification module · gravity
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α_s/β_s running + μ-distortion promoted to the suite: [E] LO identities α_s=−2/N★²=−r/6, β_s=−4/N★³ (sympy exact) + exact slow roll α_s(51.4)=−7.09×10⁻⁴, β_s=−2.70×10⁻⁵ (band −8.0…−5.6×10⁻⁴ LO); [C] Planck 2018 +0.57σ, record leg P-ACT-LB −1.33σ (kill: robust POSITIVE running ≥5σ); [C] μ-distortion branch discriminator (Chluba window, +21% LCDM-anchored): sharp 1.6×10⁻⁸ / profiled 1.94×10⁻⁸, band 1.5–2.3×10⁻⁸, split 3.0×10⁻⁹ = 3σ at Voyage-2050 σ(μ)=10⁻⁹ (PIXIE baseline does not reach); [E] the frozen log-comb is structurally blind in the μ window (|F|=0.033, δμ=7.4×10⁻¹² = 0.007σ). N★ stays an external input (GATE.NSTAR.01); band [50,60] stays the record.
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