IndisputableMonolith.Verification.PhiSquaredCert
Verification module that packages a machine-checkable certificate for the golden-ratio identity $\varphi^2=\varphi+1$ in RS-native constants. Cited by anyone auditing numeric or algebraic uses of $\varphi$ downstream of the Constants layer. Structure is a named certificate object over the imported constant $\varphi$, not a deep proof development.
claimA verification certificate $\mathrm{PhiSquaredCert}$ asserting the golden-ratio fixed-point identity $\varphi^2 = \varphi + 1$ for the RS constant $\varphi$ (self-similar fixed point of the forcing chain), in the units and conventions of the Constants module.
background
Recognition Science forces a unique dimensionless scale $\varphi$ (T6) as the self-similar fixed point tied to the J-cost $J(x)=(x+x^{-1})/2-1$. Algebraically $\varphi$ is the golden ratio, so $\varphi^2=\varphi+1$ and $\varphi^{-1}=\varphi-1$. The Constants module supplies the RS-native base quantities (including the time quantum $\tau_0=1$ tick) against which such identities are stated.
This module lives in the Verification domain: thin, auditable wrappers that pin elementary constant facts so later mass-ladder, coupling, and dimension arguments need not re-prove schoolbook $\varphi$ algebra. It imports Mathlib and IndisputableMonolith.Constants only.
proof idea
Definition and certificate module rather than a multi-lemma development. It exposes a certificate object (sibling name PhiSquaredCert) whose content is the identity $\varphi^2=\varphi+1$ relative to the imported $\varphi$ from Constants. Any proof obligation is discharged by the standard golden-ratio equation already fixed upstream, not by a new forcing argument.
why it matters in Recognition Science
Keeps $\varphi$-arithmetic out of physics-facing proofs: mass rungs, $\alpha$ band checks, and eight-tick timing all assume $\varphi^2=\varphi+1$ without local sorry. No downstream edges are recorded in the current graph (used_by empty), so the module is a leaf certificate for auditors rather than a parent of named theorems. It supports the T6 landmark (phi forced) at the verification layer without reopening the UnifiedForcingChain.
scope and limits
- Does not re-derive T6 or force $\varphi$ from the J-cost equation.
- Does not certify numeric decimal bounds on $\varphi$ or $\alpha^{-1}$.
- Does not define mass-ladder rungs, $c$, $\hbar$, or $G$.
- Does not feed any recorded downstream theorem in the current dependency graph.