IndisputableMonolith.Foundation.Electron_Mass_RS5
Module packaging the RS5 electron-mass certificate: a nonnegative domain cost, a positive canonical threshold, and an inhabited certificate record tying them together. Mass-ladder and foundation workers cite it when they need a named, checkable electron-mass witness rather than an ad-hoc inequality. The file is mostly definitions plus elementary nonnegativity and positivity lemmas over the Cost and Constants imports.
claimDefine a domain cost $C$ on the electron-mass parameter domain, prove $C \ge 0$ and $C$ agrees with its pointwise evaluation, introduce a canonical threshold $\theta > 0$, and package an inhabited certificate $\mathrm{ElectronMassRS5Cert}$ asserting the RS5 electron-mass claim relative to $(C,\theta)$.
background
Recognition Science places particle masses on a $\varphi$-ladder: mass equals a yardstick times $\varphi^{r_{\mathrm{ung}}-8+\mathrm{gap}(Z)}$. The electron is the lightest charged rung and is the natural first mass certificate after the forcing chain fixes $J$, $\varphi$, the eight-tick period, and $D=3$.
This module sits in Foundation and imports only Constants (RS-native units, including the tick $\tau_0$) and Cost (the $J$-cost infrastructure). It does not re-derive the ladder; it supplies the local cost and threshold objects that a later mass theorem can discharge against.
Sibling names indicate a domain cost functional, its pointwise agreement and nonnegativity, a strictly positive canonical threshold, and a certificate structure ElectronMassRS5Cert with an inhabited instance cert.
proof idea
Definition-heavy module. Domain cost and canonical threshold are introduced as defs; nonnegativity and positivity are short lemmas over the imported Cost primitives. The certificate is a structure (or Prop bundle) bundling those facts; cert_inhabited supplies a concrete witness. No deep tactic proof of the physical mass value lives here: the file stages the interface that a full electron-mass theorem would inhabit.
why it matters in Recognition Science
Gives Foundation a named RS5 electron-mass certificate rather than scattering inequalities across mass-ladder files. Downstream mass and $\alpha$-band arguments can depend on one inhabited cert instead of re-proving cost nonnegativity and threshold positivity. In the broader chain this is the mass-side counterpart to T5–T8: once $J$, $\varphi$, the octave, and $D=3$ are forced, the electron rung is the first quantitative mass check. Used-by edges are empty in the current graph, so the module is a leaf interface waiting on mass-formula consumers.
scope and limits
- Does not derive the numerical electron mass from first principles inside this file.
- Does not prove the general $\varphi$-ladder mass formula for arbitrary $Z$.
- Does not fix $\alpha^{-1}$ or other gauge couplings.
- Does not discharge global forcing-chain steps T0–T8.
- Does not assert uniqueness of the certificate beyond inhabitation.