IndisputableMonolith.Physics.AnomalousMoments
Defines lepton anomalous magnetic moments in Recognition Science: Schwinger term plus an RS ladder correction fixed by the lepton Z and gap. Equal-Z leptons share one dimensionless target, so electron and tau corrections match on the φ-ladder. Cite when comparing RS a_ℓ predictions to PDG values or when closing the e–τ universality claim.
claimFor each lepton species $\ell$, the RS anomalous moment is $a_\ell = a_{\mathrm{Schwinger}}(\alpha) + \delta_{\mathrm{RS}}(Z_\ell,\mathrm{gap}(Z_\ell))$, with $Z$ and gap from the $\varphi$-ladder anchor map. If $Z_e = Z_\tau$ then the dimensionless RS targets coincide (e–τ universality).
background
Recognition Science places fermion masses on a φ-ladder: mass scales as a yardstick times $\varphi^{r-8+\mathrm{gap}(Z)}$, where $Z$ is the charge-indexed integer from the RSBridge anchor and $\mathrm{gap}(Z)=\ln(1+Z/\varphi)/\ln\varphi$. The same $Z$ and gap control dimensionless radiative targets once $\alpha$ is fixed in RS-native units.
This module sits in the physics layer above Constants, Alpha, and RSBridge.Anchor. Anchor supplies the twelve SM fermions, $Z_i=\tilde q^2+\tilde q^4$ (+4 for quarks), the gap display, and mass-at-anchor. Alpha supplies the fine-structure input to the classical Schwinger piece $\alpha/(2\pi)$.
The local claim flagged in the module doc is universality: equal $Z$ on the φ-ladder forces the same dimensionless RS correction, independent of the species label.
proof idea
Definition-and-identity module, not a deep proof stack. It introduces lepton tags, their anchor $Z$ and gap, the Schwinger baseline, an additive RS correction built from those ladder data, and the combined anomalous moment. Universality is the algebraic identity that equal $Z$ (hence equal gap) yields equal dimensionless RS targets for $e$ and $\tau$. Numerical side definitions expose PDG $a_e$ and the RS predicted $a_e$ for comparison; no heavy tactic proof is required beyond unfolding and equality of equal-$Z$ inputs.
why it matters in Recognition Science
Anomalous moments are a precision stress test of the RS bridge: the same $Z$ and gap that set lepton masses must also fix the dimensionless magnetic corrections once $\alpha$ is taken from the RS band. The module isolates that correction and records e–τ universality as equal-$Z$ equality on the φ-ladder, tying radiative observables to the Anchor fermion map and the Constants/Alpha layer.
No downstream used_by edges are recorded yet; the natural parents are precision-QED comparison theorems and any global “RS matches PDG moments” reports. Framework landmarks in play are the φ-ladder mass formula, the anchor $Z$/gap map, and the RS value of $\alpha$ (inverse in the narrow 137.03x window). Open surface: quantitative closure against full PDG $a_e$, $a_\mu$, $a_\tau$ once higher-order and hadronic pieces are specified.
scope and limits
- Does not derive the Schwinger term from the Recognition Composition Law; it imports the classical $\alpha/(2\pi)$ baseline.
- Does not claim a full Standard-Model $a_\mu$ prediction including hadronic vacuum polarization.
- Does not prove numerical equality to PDG beyond the exposed predicted/PDG constants.
- Does not treat quark or neutrino magnetic moments; scope is lepton tags only.
- Does not re-derive $Z$ or gap; those are taken from RSBridge.Anchor.