IndisputableMonolith.Physics.MuonMass3_FromPhiLadder
Module packaging a Recognition Science derivation of the muon mass from the golden-ratio ladder, together with a domain cost, a canonical threshold, and an inhabited certificate object. Particle-physics auditors cite it when checking the rung-gap mass formula against the muon. The argument is definitional scaffolding plus nonnegativity and positivity lemmas, not a deep tactic proof.
claimOn the $\varphi$-ladder mass formula, the module introduces a domain cost $C$, a canonical threshold $\theta>0$, and a certificate that the muon mass sits at the predicted rung (with gap correction) relative to the electron yardstick in RS-native units.
background
Recognition Science places particle masses on a discrete $\varphi$-ladder: mass equals a yardstick times $\varphi$ raised to (rung $-8+$ gap$(Z)$). Here $\varphi$ is the self-similar fixed point forced at T6, and the eight-tick octave (T7) sets the rung offset. The module imports RS constants ($\tau_0=1$ tick, and the usual $c=1$, $\hbar=\varphi^{-5}$ conventions) and the $J$-cost infrastructure.
Locally it defines a domain cost (nonnegative, with an evaluation identity) and a strictly positive canonical threshold. These bound or select the rung at which the muon is expected. The certificate type MuonMass3v2Cert packages the numerical/structural claim that the muon matches that ladder prediction; cert_inhabited asserts a witness exists.
proof idea
Definition-heavy module. Domain cost and canonical threshold are introduced as defs; nonnegativity and positivity are short lemmas. The certificate is a structure (or Prop bundle) inhabited by a concrete witness construction. No long tactic script: the work is wiring Constants and Cost into the muon rung claim and recording the certificate.
why it matters in Recognition Science
Closes a physics-facing instance of the RS mass formula for the muon (second charged lepton), the standard precision check after the electron yardstick. Feeds any downstream mass-spectrum or lepton-ladder audits that consume MuonMass3v2Cert. Anchors the primer mass rule (yardstick $\cdot\varphi^{\mathrm{rung}-8+\mathrm{gap}(Z)}$) at a named particle. No further used_by edges are recorded in the graph yet; the module stands as a leaf certificate in the Physics domain.
scope and limits
- Does not derive electron or tau masses; muon certificate only.
- Does not re-prove T5–T8 or uniqueness of $J$ and $\varphi$.
- Does not claim experimental PDG fit beyond the ladder identity encoded in the cert.
- Does not supply a full tactic derivation of the rung integer from first principles.
- Does not address neutrino or quark ladder placements.