A registered result in its source context
Original ledger classification: Reconciliation [E]/[N]/[P]/[X] (A_s predicted+dimensionless; tension = reheating channel; archive comparison)
Recorded statement: A_s is predicted (not missing), is DIMENSIONLESS (so it does NOT define an absolute mass), and the apparent -11 sigma tension is a reheating-channel question -- reconciled with the archived old derivation (TFPT v4.5/v4.6, 2026-06-22). [E]…
Statement, assumptions and sources
Paper context: Origin Theory
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AS.RECONCILE.01
Original ledger classification: Reconciliation [E]/[N]/[P]/[X] (A_s predicted+dimensionless; tension = reheating channel; archive comparison)
Original claim text
A_s is predicted (not missing), is DIMENSIONLESS (so it does NOT define an absolute mass), and the apparent -11 sigma tension is a reheating-channel question -- reconciled with the archived old derivation (TFPT v4.5/v4.6, 2026-06-22). [E] A_s = N_star^2 (M_scal/Mbar)^2/(24 pi^2) = N_star^2 c3^7/(24 pi^2) (v86); M_scal/Mbar = c3^{7/2} = 1.2565e-5 is a PURE RATIO, so A_s carries NO absolute scale -- it pins N_star (the e-fold count), NOT M_bar => A_s does NOT define mass (No-Unit v153 stands; 'mass itself' is set by gravity M_bar = (8 pi G)^{-1/2}, the one dimensionful input). [N] the -11.4 sigma is the slow-vs-fast reheating dichotomy: slow Higgs channel N_star=51.44 -> A_s=1.764e-9 (-11.4 sigma vs Planck 2.105(30)e-9); the A_s-preferred N_star=56.2 (~ the instantaneous bound 55.6). [P] ARCHIVE COMPARISON: the old v4.5/v4.6 (07_cmb_operational_closure) used the ALGEBRAIC N_star=3/phi0-1=55.42 (+ alpha_R=(Omega_adm/4pi)e^{1/phi0}) and reported A_s=2.124e-9; at that N_star the current normalisation gives A_s=2.047e-9 (-1.9 sigma) -- consistent (~4% offset = alpha_R vs c3^7); the old clean A_s = N_star~55.4 (near-instantaneous), NOT the slow channel. [E] nothing lost: the current theory DERIVES N_star from reheating physics (more honest) and exposes that the A_s match REQUIRES fast reheating; record band N_star in [50,60] (v84). [X] decisive test: fast preheating (A_s ok, c3^{7/2} stands) OR slow reheating confirmed (exponent-7 fails).
Original classification detail
[E] the dimensionless A_s formula + the no-mass-definition consequence; [N] the reheating-channel quantification; [P] the archive comparison (the old N_star=3/phi0-1 is a posited algebraic count, NOT re-promoted to [E]); [X] the test. Does NOT change the frozen band.
Dependencies as recorded
v86; v153; v84; SCALE.OVERDET.01
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- Origin Theory
Sections that explicitly cite this claim
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- 2026-06-22 ( [formula in source] reconciled with the archived derivation: predicted \& dimensionless (so it does not define a mass), the tension is the reheating channel: v340)Research changelog; TFPT — Introduction and reading guide
Navigation through a shared verification script
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- A closure program (next phase)input 4 origin theory
- A closure program (next phase)origin theory
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
- A closure program (next phase)Origin Theory
- A closure program (next phase)input 4 origin theory
Registered verification modules
- v340_As_reconcile.pyRegistered verification module · frontier
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A_s is predicted (not missing), is DIMENSIONLESS (so it does NOT define an absolute mass), and the apparent -11 sigma tension is a reheating-channel question -- reconciled with the archived old derivation (TFPT v4.5/v4.6). [E] A_s = N_star^2 (M_scal/Mbar)^2/(24 pi^2) = N_star^2 c3^7/(24 pi^2) (v86); M_scal/Mbar = c3^{7/2} = 1.2565e-5 is a PURE RATIO, so A_s carries NO absolute scale -- it pins N_star, NOT M_bar => A_s does NOT define mass (No-Unit v153 stands). [N] the -11 sigma is the slow-vs-fast reheating dichotomy (slow Higgs N_star=51.44 -> A_s=1.764e-9; A_s-preferred N_star=56.2). [P] ARCHIVE: old v4.5/v4.6 used the algebraic N_star=3/phi0-1=55.42 and reported A_s=2.124e-9; at that N_star the current normalisation gives 2.047e-9 (-1.9 sigma). [E] nothing lost: the current theory DERIVES N_star (record band [50,60], v84). [X] decisive test: fast preheating or slow reheating confirmed.
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