IndisputableMonolith.Verification.PhiBoundsCert
Verification module that packages machine-checkable numerical bounds on the RS self-similarity fixed point φ. Auditors and coupling/mass certificates cite it to keep φ-powers inside explicit rational intervals. Structure is a thin certificate wrapper over Constants plus Mathlib inequalities, not a deep existence proof.
claimModule exporting a certificate that the Recognition Science fixed point $\varphi>1$ (unique positive solution of the self-similarity relation forced at T6) lies in stated rational bounds used by downstream $\varphi$-ladder and coupling checks.
background
Recognition Science forces a unique dimensionless scale $\varphi$ as the self-similar fixed point (forcing-chain step T6). In RS-native units the derived constants are pure powers of this scale: $\hbar=\varphi^{-5}$, $G=\varphi^5/\pi$, with $\alpha^{-1}$ required to land in a narrow numerical band near 137.03. Interval control on $\varphi$ is therefore a prerequisite for any verified numerical claim on masses or couplings.
The module imports Constants, whose documentation fixes the fundamental RS time quantum $\tau_0=1$ tick and supplies the ambient definition of $\varphi$. Mathlib supplies the ordered-field and inequality infrastructure. The local setting is the Verification domain: certificate objects that audit tooling can discharge without re-deriving the forcing chain.
proof idea
Definition and certificate module, not a deep theorem development. It assembles already-available inequalities on $\varphi$ from the Constants layer and Mathlib into a named bounds certificate (PhiBoundsCert). Argument structure is packaging and re-export: pin rational lower/upper bounds, expose them under a verification namespace, and stop. No new fixed-point analysis is performed here.
why it matters in Recognition Science
Anchors T6 ($\varphi$ forced) into the verification stack so that later numerical certificates (mass yardstick on the $\varphi$-ladder, $\alpha^{-1}$ band inside $(137.030,137.039)$, Berry threshold $\varphi^{-1}$) rest on explicit enclosures rather than informal floats. The graph snapshot shows no named used_by parents yet; the module is a leaf certificate intended for audit consumers and future coupling/mass checkers. It does not itself close the forcing chain; it only makes the numerical face of $\varphi$ quotable under Lean.
scope and limits
- Does not prove uniqueness or existence of φ (that is upstream T6).
- Does not derive mass-ladder or α-band formulas.
- Does not certify floating-point evaluation beyond stated rational bounds.
- Does not address eight-tick structure (T7) or D=3 forcing (T8).
- Does not claim physical units conversion outside RS-native normalization.