IndisputableMonolith.Physics.RS_Physics_Module_007
Physics module 007 packages a domain cost functional, its evaluation identity and nonnegativity, and a strictly positive canonical threshold. It exposes a small inhabited certificate record so downstream physics lemmas can cite one object rather than a scatter of facts. The content is definitional plus short positivity and evaluation proofs over the imported cost layer.
claimThe module defines a domain cost $C_{\mathrm{dom}}$, proves $C_{\mathrm{dom}}\ge 0$ and an evaluation identity at equality cases, and fixes a canonical threshold $\theta>0$. It bundles these into an inhabited certificate record for RS physics module 007.
background
Recognition Science measures mismatch with the J-cost $J(x)=(x+x^{-1})/2-1$ from the cost layer, with RS-native constants (including the tick $\tau_0$) from the constants module. Physics modules specialize that cost language to concrete domains and cutoffs used in mass, coupling, and threshold arguments.
This file sits in the physics domain and imports only Constants and Cost. Sibling declarations introduce domainCost with an evaluation lemma and nonnegativity, plus canonicalThreshold with a positivity proof. The certificate constructors RSPhysics007Cert, cert, and cert_inhabited package those facts for reuse.
No forcing-chain step (T5–T8) is proved here; the module only freezes the local cost/threshold interface those later physics claims expect.
proof idea
Definition-first module. domainCost and canonicalThreshold are introduced as defs; domainCost_at_eq and the two positivity lemmas are short algebraic or inequality arguments over the imported cost primitives. The certificate is a structure (or sigma-type style record) assembled by cert, with cert_inhabited supplying a canonical instance. No deep tactic scripts or multi-hop rewriting beyond the cost API.
why it matters in Recognition Science
Gives physics consumers a single named certificate for domain-cost nonnegativity and a positive canonical threshold, instead of re-proving those facts at each call site. Downstream usage is not yet wired in this graph snapshot (used_by empty), so the module currently acts as a self-contained physics interface stub in the RS physics stack.
It does not itself force $\varphi$, the eight-tick octave, or $D=3$; those live in the unified forcing chain. Its role is narrower: freeze the cost/threshold side conditions that mass-ladder and coupling arguments typically assume when they quote J-cost and RS-native units.
scope and limits
- Does not derive J-uniqueness, phi, eight-tick structure, or D=3.
- Does not prove any mass, alpha, or coupling numerical claim.
- Does not connect domainCost to a specific physical observable beyond the local defs.
- Does not list downstream consumers; used_by is empty in this snapshot.
- Does not replace the general Cost API; it only specializes a domain slice.