IndisputableMonolith.Physics.ElectronMass3_FromPhiLadder
Physics module that packages the electron mass as a φ-ladder certificate in RS-native units. It defines a domain cost, a positive canonical threshold, and an inhabited ElectronMass3v2 certificate witnessing the ladder match. Mass-spectrum auditors cite the cert when checking the lightest charged lepton against the RS mass formula. The module is mostly definitional, with nonnegativity and positivity lemmas plus an inhabited witness.
claimIntroduce a domain cost $C$, a canonical threshold $T>0$, and an inhabited certificate that the electron mass equals the $\varphi$-ladder prediction $m_e = y\,\varphi^{r-8+g(Z)}$ in RS-native units (yardstick $y$, rung $r$, gap $g(Z)$).
background
Recognition Science puts rest masses on a discrete $\varphi$-ladder. The mass formula is yardstick times $\varphi$ to the power (rung $-8+$ gap$(Z)$), with $\varphi$ forced as the self-similar fixed point (forcing step T6). Constants are RS-native: $c=1$, and the time quantum $\tau_0$ is one tick.
This Physics module imports Constants and the $J$-cost layer. Sibling definitions supply a domain cost (deviation from the predicted ladder seat), its pointwise evaluation identity and nonnegativity, a canonical acceptance threshold with positivity, and the ElectronMass3v2 certificate bundle together with an inhabited witness.
The local setting is certification, not derivation from the RCL functional equation: the ladder seat for the electron is packaged so downstream spectrum checks can consume a single Prop-level object.
proof idea
Definition-and-witness module, not a deep tactic proof. Domain cost is introduced, shown equal under evaluation, and proved nonnegative. The canonical threshold is defined and proved positive. The electron-mass certificate is a structure (or Prop bundle) that is inhabited, so the ladder match is a concrete witness rather than an open hypothesis. No multi-step algebraic reduction of the RCL appears here; the work is packaging and sign/positivity lemmas around the mass formula instance.
why it matters in Recognition Science
Pins the electron, the lightest charged lepton, to the RS $\varphi$-ladder mass formula. That formula is a framework landmark (yardstick $\cdot\varphi^{\mathrm{rung}-8+\mathrm{gap}(Z)}$), and $\varphi$ itself is forced at T6. Even with no recorded used_by edges in the mirror graph, the inhabited certificate is the natural parent input for spectrum tables, charged-lepton comparisons, and any later link from ladder rungs to $\alpha$-band or $Z_{\mathrm{cf}}$ checks.
The v2/v3 naming marks iterative tightening of the electron rung certificate inside the Physics layer. Closing this instance removes one free mass parameter from the RS ledger and makes falsification concrete: a mismatch between the certified ladder value and the RS-native electron mass would break the certificate.
scope and limits
- Does not derive the full SM mass spectrum or other lepton/hadron rungs.
- Does not prove uniqueness of the electron seat among all particles.
- Does not convert the certificate into CODATA SI values outside RS-native units.
- Does not re-derive $\varphi$, the eight-tick octave, or $D=3$ here.
- Does not discharge $\alpha$-band or gravitational constraints.