IndisputableMonolith.Physics.Structural_Physics_mod46
Module packaging a domain-cost functional, a canonical positive threshold, and an inhabited structural-physics certificate for Recognition Science. Defines nonnegativity of the domain cost and positivity of the threshold, then bundles them as StructPhysicsM46Cert. Cited when a structural bound or certificate interface is needed upstream of physics claims. Argument is definitional plus elementary positivity lemmas over Cost and Constants.
claimThe module introduces a domain cost $C_{\mathrm{dom}}$, equality and nonnegativity facts for it, a canonical threshold $\theta>0$, and an inhabited certificate asserting those structural properties together.
background
Recognition Science measures mismatch with the J-cost $J(x)=(x+x^{-1})/2-1$ (equivalently $\cosh(\log x)-1$), developed in the Cost import. Constants supplies the RS-native tick $\tau_0=1$ and related units. This module sits in the Physics domain and specializes those primitives to a domain-level cost and a fixed positive threshold used as a structural gate.
Sibling declarations name the objects: domainCost with an evaluation identity and a nonnegativity lemma; canonicalThreshold with a positivity lemma; and StructPhysicsM46Cert / cert / cert_inhabited, which package the above into a single certificate type. No external physics dynamics are assumed here; the setting is pure structural bookkeeping on top of Cost and Constants.
proof idea
Definition-heavy module. Domain cost and the canonical threshold are introduced as defs; nonnegativity and positivity are short lemmas over the Cost/Constants API. The certificate record is assembled from those lemmas and shown inhabited. No deep tactic proof or forcing-chain step lives here.
why it matters in Recognition Science
Supplies a reusable structural-physics certificate (mod46) that downstream physics developments can require as a hypothesis interface rather than re-proving cost nonnegativity and threshold positivity. Used_by is empty in the current graph, so this is a leaf packaging layer: it closes local scaffolding around domain cost and the canonical threshold so later RS physics modules can cite one inhabited cert. Ties to the Cost layer that underpins J-uniqueness (T5) without re-deriving the Recognition Composition Law.
scope and limits
- Does not derive J-uniqueness, RCL, or any T0–T8 forcing step.
- Does not fix numerical particle masses, alpha, or rung gaps.
- Does not model dynamics, measurement, or spacetime geometry.
- Does not claim the certificate is consumed by a named parent theorem yet.
- Does not replace the general Cost API; only packages domain-level facts.