IndisputableMonolith.Physics.RS_Physics_Module_003
Physics module 003 packages a domain-level cost functional, its nonnegativity and evaluation identities, and a positive canonical threshold into a single certificate type. Anyone wiring RS cost bounds into continuum or lattice physics layers would cite it. The file is mostly definitional: cost and threshold are introduced, then wrapped by an inhabited certificate record.
claimIntroduce a domain cost $C_{\mathrm{dom}}$, prove $C_{\mathrm{dom}}\ge 0$ and the pointwise evaluation identity for $C_{\mathrm{dom}}$, fix a canonical threshold $\theta_*>0$, and package these facts as an inhabited certificate $\mathrm{RSPhysics003Cert}$.
background
Recognition Science measures mismatch with the J-cost from the Cost layer (the unique symmetric cost forced by the Recognition Composition Law, $J(x)=(x+x^{-1})/2-1$). Constants supplies the RS-native tick $\tau_0=1$. This module lifts that scalar cost language to a domain-level functional suitable for physics bookkeeping.
Sibling definitions name the objects: domainCost is the domain cost; domainCost_at_eq and domainCost_nonneg record evaluation and sign; canonicalThreshold with canonicalThreshold_pos fix a strictly positive cutoff. The certificate bundle RSPhysics003Cert (with cert / cert_inhabited) is the export surface for downstream physics modules that need a single inhabited proof object rather than loose lemmas.
proof idea
Definition-and-certificate module, not a deep derivation. Domain cost and the canonical threshold are defined from Cost/Constants primitives; nonnegativity and the evaluation identity are short lemmas; positivity of the threshold is immediate from the definition. The certificate record assembles those facts and is shown inhabited, so later files can depend on one structure rather than a scatter of names.
why it matters in Recognition Science
Gives the physics tree a reusable, certified domain-cost interface tied to the RS J-cost stack (T5 uniqueness of $J$, RCL). No downstream edges are recorded yet (used_by is empty), so the module is an export stub: later continuum, lattice, or threshold arguments can import the certificate instead of re-proving nonnegativity and threshold positivity. It does not itself advance the forcing chain (T0–T8) or fix constants such as $\alpha$ or the mass ladder; it only standardizes cost bookkeeping for those layers.
scope and limits
- Does not derive J-uniqueness or the Recognition Composition Law; those live upstream in Cost/Foundation.
- Does not fix numerical RS constants (c, hbar, G, alpha) beyond the imported tick.
- Does not prove continuum or particle-physics identities; only domain-cost and threshold packaging.
- Does not list downstream consumers yet; used_by is empty in the graph.
- Does not claim the threshold equals a named RS landmark (Berry gate, Z_cf, etc.) without further proof.