IndisputableMonolith.Physics.AnchorPolicyCertified
AnchorPolicyCertified certifies that an external certificate bounding per-species residues at the anchor implies each residue is close to the closed-form gap(Z) in inequality form. Particle physicists deriving masses via the Recognition Science phi-ladder would cite this to justify the gap approximation for fermion species. The module composes the Certification and Anchor imports into a collection of certified statements for all 12 fermions.
claimIf an external certificate bounds the per-species residues $r_s$ at the anchor, then $|r_s - F(Z_s)| < \epsilon$ for each fermion species $s$, where $F(Z) = \frac{\ln(1 + Z/\phi)}{\ln \phi}$.
background
This module resides in the Physics domain and imports Certification for bounding arguments together with RSBridge.Anchor. The Anchor module defines Fermion as the 12 Standard Model fermions (6 quarks + 3 leptons + 3 neutrinos), ZOf as the charge-indexed integer $Z_i = \tilde{q}^2 + \tilde{q}^4$ (+4 for quarks), gap as the display function $F(Z) = \ln(1 + Z/\phi)/\ln(\phi)$, and massAtAnchor at the anchor scale $\mu^\star$. These supply the objects to which the residue-closeness inequality is applied.
proof idea
The module organizes its argument by introducing Species, Z, and Fgap, then applies the imported certification to the anchor definitions via the siblings anchor_identity_from_cert and equalZ_residue_from_cert. Each species receives the bound, producing the inequality form for the full set of fermions.
why it matters in Recognition Science
The module supplies the certified anchor policy that links the recognition framework to particle-physics mass formulas. It feeds the gap(Z) approximation into phi-ladder calculations, supporting the self-similar fixed point and spatial-dimension results in the forcing chain. No downstream theorems are listed in the used_by edges.
scope and limits
- Does not compute explicit numerical values for the bound epsilon.
- Does not define the gap function or Z-map; those come from the Anchor import.
- Does not address particles outside the 12 Standard Model fermions.
- Does not provide the external certificate itself.