IndisputableMonolith.Physics.RS_Physics_Module_001
First physics-layer module packaging a domain cost functional and a positive canonical threshold, together with a small certificate that both are well-formed. Physicists tracing how the J-cost enters continuum physics would land here. The file is mostly definitions plus elementary nonnegativity and positivity lemmas, closed by an inhabited certificate record.
claimIntroduce a domain cost $C_{\mathrm{dom}}$ built from the Recognition cost $J$, prove $C_{\mathrm{dom}}\ge 0$ and an evaluation identity, fix a canonical threshold $\theta_*>0$, and package these facts as an inhabited certificate $\mathrm{RSPhysics001Cert}$.
background
Recognition Science measures mismatch by the unique cost $J(x)=(x+x^{-1})/2-1$ forced at T5 of the unified forcing chain (equivalently $\cosh(\log x)-1$). The Cost import supplies that $J$ and its elementary calculus; Constants supplies the RS-native tick $\tau_0=1$.
This module sits at the physics boundary: it lifts the scalar cost to a domain-level functional domainCost and names a positive cutoff canonicalThreshold against which continuum or lattice defects can later be compared. Sibling lemmas record evaluation at equality cases and nonnegativity of the domain cost, plus positivity of the threshold.
The certificate record RSPhysics001Cert (with cert and cert_inhabited) is the module's export surface: a single inhabited bundle asserting the cost and threshold facts needed by later physics layers.
proof idea
Definition-heavy module, not a deep theorem file. domainCost is introduced from the imported $J$-cost; domainCost_at_eq and domainCost_nonneg are short algebraic or order lemmas. canonicalThreshold is a named positive constant; canonicalThreshold_pos is its positivity proof. The certificate is assembled by bundling those facts and discharging inhabitance with a concrete witness (cert_inhabited).
why it matters in Recognition Science
Gives the physics tree a first certified handle on domain-level cost and a canonical positive threshold, so later continuum or particle constructions can cite one certificate rather than re-proving $J$-nonnegativity and cutoff positivity. No downstream edges are recorded yet (used_by empty), so this is an entry stub for the Physics domain rather than a leaf of a finished forcing argument. It sits downstream of T5 J-uniqueness and the Cost library, and upstream of any mass-ladder, defect, or threshold comparisons that need a packaged physics-001 certificate.
scope and limits
- Does not derive $J$ itself; assumes Cost/T5 uniqueness.
- Does not fix numerical continuum limits or couple to $c,\hbar,G$.
- Does not prove mass-ladder or $\alpha$ bounds.
- Does not assert uniqueness of the canonical threshold beyond positivity.
- Does not yet feed named parent theorems (no used_by edges).