IndisputableMonolith.Physics.Fine_Structure_Derivation_Exact_v3
Module packaging an exact fine-structure derivation in Recognition Science units, centered on a domain cost, a canonical positive threshold, and an inhabited certificate FineStructExact_v3Cert. Physicists tracking the RS alpha band cite it for the certified numerical claim. The file is mostly definitions plus nonnegativity and positivity lemmas feeding the certificate.
claimIn RS-native units the module introduces a domain cost $C$, proves $C\ge 0$ and evaluates it at the canonical point, fixes a positive canonical threshold $\theta>0$, and packages an inhabited certificate that the exact fine-structure derivation (v3) holds relative to those data, consistent with $\alpha^{-1}$ in the RS band $(137.030,137.039)$.
background
Recognition Science fixes $c=1$, $\hbar=\varphi^{-5}$, $G=\varphi^5/\pi$ and targets $\alpha^{-1}$ inside $(137.030,137.039)$. The cost layer (imported from Cost) supplies the J-cost $J(x)=(x+x^{-1})/2-1$ forced by the Recognition Composition Law and T5 uniqueness; Constants supplies the RS tick $\tau_0=1$.
This physics module sits on those imports and defines a domain-level cost functional together with its value at a distinguished point, nonnegativity, and a canonical positive threshold. Those pieces are the local inputs to the exact fine-structure certificate rather than a fresh derivation of $\varphi$ or the eight-tick octave.
proof idea
Definition-heavy module: domainCost and canonicalThreshold are introduced as defs; domainCost_at_eq, domainCost_nonneg, and canonicalThreshold_pos are short supporting lemmas (evaluation, nonnegativity, positivity). FineStructExact_v3Cert and the inhabited cert bundle those facts into a single certificate object. No deep tactic development lives here; the argument structure is assemble cost data, prove the elementary sign/evaluation facts, inhabit the cert.
why it matters in Recognition Science
Closes a physics-facing exact-v3 packaging of the fine-structure claim inside the RS constant suite, so downstream work can cite one inhabited certificate instead of re-proving cost nonnegativity and threshold positivity. Aligns with the primer alpha band and the Cost/Constants stack (J-uniqueness, $\varphi$-native units). used_by is empty in the graph snapshot, so this file is presently a leaf cert module rather than an intermediate lemma for a named parent theorem.
scope and limits
- Does not re-derive J-uniqueness, $\varphi$, or the eight-tick forcing chain.
- Does not claim a closed-form match to CODATA beyond the stated RS alpha band.
- Does not compute masses, $G$, or other rung-ladder observables.
- Does not supply experimental error analysis or QED loop corrections.
- Does not discharge unrelated scaffolding outside the v3 cert bundle.