IndisputableMonolith.Physics.Pion_Mass_RS
Module defining the RS-native pion mass certificate via a domain cost on the phi-ladder and a canonical positive threshold. Physicists deriving light meson masses from the Recognition Composition Law and the mass formula cite it. Structure is definitional: nonnegativity lemmas, an equality at the evaluation point, and an inhabited certificate record.
claimThe module introduces a domain cost $C$ (nonnegative), its value at a distinguished point, a canonical threshold $\theta>0$, and a pion-mass certificate record asserting that the RS mass prediction for the pion lies in the certified band relative to $\theta$ and the $\phi$-ladder yardstick.
background
Recognition Science places particle masses on a discrete $\phi$-ladder: mass equals a fixed yardstick times $\phi$ raised to (rung $-8+$ gap$(Z)$). The pion, as the lightest quark-antiquark bound state, sits at a low rung fixed by the same J-cost that appears in the forcing chain (T5: $J(x)=(x+x^{-1})/2-1$).
This module imports the RS constants (including the native tick $\tau_0$) and the Cost library. It specializes the general cost machinery to a domain cost whose nonnegativity and evaluation identity are recorded, together with a strictly positive canonical threshold used as the acceptance cut for the pion-mass claim.
The local setting is therefore a pure physics certificate layer: no new forcing-chain step, only the packaging of the pion prediction into a checkable record.
proof idea
Definition module with short supporting lemmas. domainCost is introduced and shown nonnegative; domainCost_at_eq records the concrete evaluation identity needed by the certificate. canonicalThreshold is defined and proved positive. PionMassCert is a structure (or Prop bundle) whose inhabitant cert is supplied by cert_inhabited, assembling the cost value, threshold, and ladder data into one certificate object. No deep tactic proof; the work is definitional wiring to Constants and Cost.
why it matters in Recognition Science
Supplies the pion-mass certificate that any downstream RS hadron-spectrum or precision-mass audit would import. It sits downstream of the mass-formula infrastructure and the J-cost uniqueness (T5) that fixes the ladder spacing, and upstream of any global particle-data comparison that needs an inhabited, nonnegative cost witness for the lightest meson. Because used_by is presently empty in the mirror graph, the module is a leaf certificate ready for spectrum-level aggregation. It does not itself derive the rung or gap; it packages them for verification against the RS-native units ($c=1$, $\hbar=\phi^{-5}$, etc.).
scope and limits
- Does not derive the pion rung or gap from first principles; assumes ladder data.
- Does not prove numerical agreement with PDG pion mass beyond the certificate band.
- Does not address charged/neutral pion splitting or electromagnetic corrections.
- Does not export a general meson-mass constructor; only the pion certificate.
- Does not modify J-cost, RCL, or the forcing chain T0–T8.