IndisputableMonolith.Physics.FinalModule_1396
Packages a physics milestone certificate built from a domain cost functional and a positive canonical threshold. Imports only Constants and Cost, then exposes equality at evaluation, positivity of the threshold, and an inhabited MilestoneCert record. Cite when closing a physics ledger step that needs a single named certificate rather than raw cost inequalities. The module is definitional scaffolding plus elementary positivity and equality lemmas.
claimDefine a domain cost $C$, a canonical threshold $\theta>0$, and a milestone certificate $\mathsf{Cert}$ asserting the cost-threshold relation used at this physics ledger step; the certificate is inhabited.
background
Recognition Science measures mismatch with a nonnegative cost (the $J$-cost lineage from the Cost import). Constants supplies the RS-native tick $\tau_0=1$. This module sits in the Physics domain and does not re-derive $J$; it only names a domain-level cost, a fixed positive threshold, and a certificate type that packages their relation for downstream ledger checks.
Sibling definitions introduce domainCost (the cost functional on the relevant domain), canonicalThreshold with a positivity lemma, and MilestoneCert together with an explicit inhabitant cert. The equality lemma records that evaluating the domain cost at the designated point matches the expected closed form, so later proofs can rewrite rather than recompute.
proof idea
Definition module with thin lemmas. Cost and threshold are introduced by def; positivity of the canonical threshold is a short arithmetic or constant-unfolding argument. The equality lemma is a direct evaluation identity. MilestoneCert is a structure (or Prop bundle); cert builds one inhabitant, and cert_inhabited is the corresponding Nonempty/Inhabited witness. No deep forcing-chain reasoning occurs here.
why it matters in Recognition Science
Gives Physics a single named milestone certificate instead of ad-hoc cost inequalities at this ledger index (1396). Upstream it only needs Constants ($\tau_0$) and Cost. Downstream edges are empty in the current graph, so the module is a terminal packaging point: other physics developments can import cert rather than reconstruct the threshold and cost side conditions. It does not advance T5–T8 (J-uniqueness, $\phi$, eight-tick, $D=3$); it only freezes a cost-threshold checkpoint for audit.
scope and limits
- Does not derive the J-cost functional equation or RCL identities.
- Does not force $\phi$, the eight-tick period, or $D=3$.
- Does not compute particle masses or the fine-structure band.
- Does not supply a used-by parent theorem in the current graph.
- Does not claim experimental falsification criteria beyond the certificate packing.