rs_mass_MeV
plain-language theorem explainer
Recognition Science mass in MeV for a particle sector and integer species rung: the sector yardstick times φ to that rung, scaled eV→MeV by 10^{-6}. Mass-verification and electroweak modules cite it for PDG comparisons (electron, muon, Z, etc.). The body is a pure definition expanding 2^{B(s)} φ^{r_0(s)+r-5}/10^6.
Claim. For a mass sector $s$ and integer species rung $r$, the RS predicted mass in MeV is $m(s,r)=2^{B(s)}\,\varphi^{r_0(s)+r-5}/10^6$, where $B(s)$ and $r_0(s)$ are the sector anchor integers, $\varphi$ is the golden-ratio fixed point, and the factor $10^{-6}$ converts the native eV-scale coherence energy into MeV.
background
This module compares RS mass predictions to PDG 2024 values. It is quarantined from the certified surface: it imports experimental numbers and depends on the φ-ladder anchor system rather than deriving masses from the forcing chain alone.
The native mass formula is $m=\mathrm{yardstick}(s)\times\varphi^{r}$, with yardstick $2^{B(s)}\cdot E_{\mathrm{coh}}\cdot\varphi^{r_0(s)}$ and coherence energy $E_{\mathrm{coh}}=\varphi^{-5}$ (order $0.09,\mathrm{eV}$). $B$ and $r_0$ are sector integers from cube geometry in the Anchor module; $r$ is the species rung on the φ-ladder.
rs_mass_MeV packages that product in MeV by dividing by $10^6$. Downstream lepton and electroweak code specialize the sector (e.g. lepton, electroweak) and a fixed rung, then compare to experimental anchors such as $m_e$.
proof idea
Definition, not a proved theorem. The body writes the yardstick formula explicitly as $2^{B(s)}\cdot\varphi^{-5}\cdot\varphi^{r_0(s)}\cdot\varphi^{r}/10^6$, which is algebraically $2^{B(s)}\varphi^{r_0(s)+r-5}/10^6$. No tactics or lemmas; downstream equalities (e.g. lepton_pred_eq_aux, z_pred_eq) unfold this def and combine the φ-powers with the sector equations for $B$ and $r_0$.
why it matters
Single entry point for numerical RS masses in MeV across the verification stack. Downstream: electron_pred_eq and muon_pred_eq identify lepton rungs with closed φ-power forms; electron_relative_error bounds the PDG residual; z_pred / z_pred_eq give the Z boson as rs_mass_MeV on the electroweak sector at rung 1; MassVerificationCert aggregates species checks.
In the framework this is the concrete MeV realization of the φ-ladder mass formula (yardstick times a rung power), with $E_{\mathrm{coh}}=\varphi^{-5}$ matching the RS-native $\hbar=\varphi^{-5}$ scale. It does not itself close the forcing chain (T5–T8); it only exposes the anchor formula for machine comparison. The module remains quarantined until experimental imports and anchor rungs are separated from certified core.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.