IndisputableMonolith.Physics.Muon_Lifetime_RS
Module packaging the Recognition Science treatment of the muon lifetime: a domain cost functional, its nonnegativity and evaluation identities, a positive canonical threshold, and an inhabited certificate type MuonLifetimeCert. A particle-physics reader cites it when matching the observed muon mean life to an RS cost-threshold comparison in native units. Structure is definitional plus short positivity and evaluation lemmas, not a long derivation.
claimIn RS-native units the module introduces a domain cost $C_{\mathrm{dom}}$, proves $C_{\mathrm{dom}}\ge 0$ and an evaluation identity at a distinguished point, fixes a canonical threshold $\theta>0$, and supplies an inhabited certificate type asserting that the muon lifetime sits in the predicted cost-threshold relation (with $\tau_0=1$ tick from the constants layer).
background
Recognition Science works in units where the fundamental time quantum is one tick: $\tau_0=1$ (Constants). Costs are built from the J-cost of the Recognition Composition Law, imported here via the Cost module; the usual closed form is $J(x)=(x+x^{-1})/2-1$.
This physics module specializes that cost language to a domain cost for the muon channel. Sibling definitions name domainCost, an equality for its value at a canonical argument, nonnegativity, and a strictly positive canonicalThreshold. The certificate bundle MuonLifetimeCert (with cert and cert_inhabited) is the interface object a downstream checker would inhabit when the lifetime matches the threshold prediction.
No forcing-chain step (T5–T8) is re-proved here; the module assumes the global RS constants and cost calculus already fixed upstream.
proof idea
Definition-heavy module. Domain cost and canonical threshold are introduced as defs; short lemmas record evaluation at the distinguished point, nonnegativity of the cost, and positivity of the threshold. The certificate is a structure (or Prop bundle) with an inhabitation witness cert_inhabited, so the logical content is “the named numerical relation is realized,” not a multi-step analytic derivation of the PDG lifetime from first principles inside this file.
why it matters in Recognition Science
Gives the physics layer a named, checkable handle on the muon lifetime in RS units, parallel to other particle certificates in the monolith. Downstream used-by edges are empty in the current graph, so this module is a leaf packaging layer: it concentrates Cost and Constants into a muon-specific cert rather than feeding a larger named theorem yet. In the broader framework it sits with mass-ladder and lifetime comparisons that use $\phi$-scaled yardsticks and tick-normalized times; it does not itself re-derive $\phi$, the eight-tick octave, or $D=3$.
scope and limits
- Does not derive the PDG muon lifetime from the forcing chain T0–T8 inside this module.
- Does not prove uniqueness of the domain cost among all possible RS cost functionals.
- Does not treat muon g-2, branching ratios, or other flavor observables.
- Does not export a closed-form mass-ladder rung for the muon; only lifetime-cert machinery.
- Does not claim experimental error bars or unit conversions beyond RS-native ticks.