IndisputableMonolith.Physics.Physics
Physics-layer definitions that attach the Recognition cost functional to domain-scale observables: a domain cost, a canonical positive threshold, and the RS-native Planck energy. Experimental and continuum-limit arguments cite these as the bridge from abstract J-cost to dimensionful physics. The module is mostly definitional, with nonnegativity and positivity lemmas and an inhabited certificate type.
claimThe module introduces a domain cost $C_{\mathrm{dom}}$, a canonical threshold $\theta_{\mathrm{can}}>0$, the RS-native Planck energy $E_{\mathrm{P}}^{(\mathrm{RS4})}$, and a certificate type witnessing the basic positivity and evaluation identities for these quantities (built from the RS cost $J$ and the constants module).
background
Recognition Science measures mismatch by the unique cost $J(x)=(x+x^{-1})/2-1$ forced at T5, with composition law $J(xy)+J(x/y)=2J(x)J(y)+2J(x)+2J(y)$. The Cost import supplies that functional; Constants supplies the RS time quantum $\tau_0=1$ tick and the native unit system ($c=1$, $\hbar=\varphi^{-5}$, $G=\varphi^5/\pi$).
This Physics module sits above those foundations. It packages domain-level cost evaluations, a canonical positive threshold used as a comparison scale, and an RS4 Planck energy so continuum and particle-physics statements can quote a single named energy yardstick rather than raw $\varphi$-ladder expressions.
Sibling lemmas record evaluation at equality, nonnegativity of domain cost, positivity of the threshold, and that the certificate type is inhabited.
proof idea
Definition module with thin supporting lemmas, not a long derivation. Domain cost is defined from the imported $J$-cost; equality and nonnegativity follow by unfolding and the known $J\ge 0$ facts. The canonical threshold is a positive constant expression; positivity is a short arithmetic check. Planck energy is an RS-native closed form. The certificate bundles these facts and is shown inhabited by constructing a witness from the lemmas above.
why it matters in Recognition Science
Gives the Physics domain a stable vocabulary for cost-at-domain, threshold comparisons, and Planck-scale energy in RS units, so later continuum or particle results need not re-derive those bindings. No downstream edges are recorded on this page yet; the natural consumers are higher Physics and phenomenology modules that quote domain cost, the canonical threshold, or $E_{\mathrm{P}}^{(\mathrm{RS4})}$. Ties to the forcing chain only indirectly: $J$-uniqueness (T5) and the $\varphi$-native constants underwrite the definitions, while the eight-tick and $D=3$ steps live elsewhere.
scope and limits
- Does not derive $J$-uniqueness, RCL, or the T0–T8 forcing chain.
- Does not prove mass formulae, $\alpha^{-1}$ bounds, or ladder rung assignments.
- Does not claim experimental matches beyond naming RS-native Planck energy.
- Does not export continuum field equations or scattering amplitudes.
- Does not record downstream consumers on this module page.