IndisputableMonolith.Physics.Foundation
Foundation layer for RS physics: domain cost functionals, a canonical positive threshold, and an RS4 mass certificate for the W boson. Physicists cite it when wiring mass-ladder or threshold arguments to the J-cost. The module is mostly definitions and elementary positivity lemmas over Constants and Cost.
claimThe module introduces a domain cost $C_{\mathrm{dom}}$, its nonnegativity, a canonical threshold $\theta_*>0$, and an RS4 certificate for the $W$ boson mass on the $\varphi$-ladder (yardstick times $\varphi^{r-8+\mathrm{gap}(Z)}$).
background
Recognition Science builds physics from the unique cost $J(x)=(x+x^{-1})/2-1$ fixed by the Recognition Composition Law, with $\varphi$ the self-similar fixed point (forcing chain T5–T6). Constants supplies the RS time quantum $\tau_0=1$ tick; Cost supplies the J-cost infrastructure.
This module sits at the physics entry point. It packages a domain-level cost (evaluation and nonnegativity), a strictly positive canonical threshold used as a creation or acceptance cutoff, and an RS4 mass certificate for the $W$ boson. Masses are read on the $\varphi$-ladder via yardstick $\cdot,\varphi^{\mathrm{rung}-8+\mathrm{gap}(Z)}$, with RS-native units $c=1$, $\hbar=\varphi^{-5}$.
Sibling names indicate the local API: domain cost equalities, threshold positivity, and an inhabited certificate object rather than a deep dynamical derivation.
proof idea
Definition-and-lemma module, not a single theorem. Domain cost is defined and shown equal at evaluation points; nonnegativity is inherited from the underlying J-cost. The canonical threshold is a positive constant (positivity lemma). The W-boson RS4 entry and cert/cert_inhabited are certificate scaffolding: inhabited proof objects that package the mass claim for downstream use, not a full forcing-chain derivation inside this file.
why it matters in Recognition Science
Gives the physics layer a thin, reusable foundation so mass and threshold arguments do not re-import raw Cost/Constants each time. Downstream pages (none listed on the import graph yet) would cite the domain cost, the positive threshold, and the W-boson RS4 certificate when closing particle-mass or acceptance-threshold claims. Ties to the primer mass formula and to T5–T6 uniqueness of $J$ and $\varphi$; it does not itself re-prove the forcing chain or the eight-tick/D=3 steps (T7–T8).
scope and limits
- Does not derive J-uniqueness or force phi; those live in the UnifiedForcingChain.
- Does not prove the full Standard Model mass spectrum; only packages a W-boson RS4 certificate.
- Does not establish eight-tick periodicity or D=3 spatial dimensions.
- Does not compute alpha or fix G; only uses Constants/Cost primitives.
- Does not supply dynamical evolution; only cost, threshold, and certificate objects.