IndisputableMonolith.Physics.RS_Physics_Module_001
Physics module 001 packages a domain cost functional, its nonnegativity and evaluation identities, and a positive canonical threshold into a single certificate bundle. A physicist citing early RS cost geometry or threshold comparisons would land here. The file is mostly definitions plus short positivity lemmas, closed by an inhabited certificate record.
claimOn the RS cost layer, define a domain cost $C_{\mathrm{dom}}$, prove $C_{\mathrm{dom}}\ge 0$ and the pointwise evaluation identity, fix a canonical threshold $\theta_*>0$, and bundle these facts as an inhabited physics certificate for module 001.
background
Recognition Science measures mismatch with a nonnegative cost built from the J-functional $J(x)=(x+x^{-1})/2-1$ (equivalently $\cosh(\log x)-1$). The Cost import supplies that layer; Constants fixes the RS-native tick $\tau_0=1$.
This module sits in the Physics domain and introduces a domain-level cost together with a canonical numerical threshold. Sibling declarations name the cost, its evaluation identity, nonnegativity, the threshold and its positivity, then wrap them in RSPhysics001Cert with an inhabited instance.
The local setting is therefore definitional scaffolding for later physics comparisons (thresholds, gaps, or rung placements) rather than a forcing-chain step such as T5–T8.
proof idea
Definition-heavy module. The cost and threshold are introduced as defs; nonnegativity and positivity are short lemmas (likely direct from the Cost layer or elementary arithmetic). Evaluation-at-equality is an identity lemma. The certificate is a structure packing those facts, discharged by an inhabited instance that assembles the proved fields. No deep tactic script or multi-hop forcing argument.
why it matters in Recognition Science
Gives the Physics stack a named, certifiable handle on domain cost and a positive canonical threshold in RS-native units. Downstream used-by edges are empty in the graph snapshot, so the module presently anchors local physics certificates rather than feeding a named parent theorem. It aligns with the broader cost geometry (J-cost, RCL) that later supports mass-ladder and coupling work, without itself claiming T5 J-uniqueness, the eight-tick octave, or $D=3$.
scope and limits
- Does not derive J-uniqueness or the Recognition Composition Law.
- Does not fix numerical values of c, hbar, G, or alpha.
- Does not prove mass-ladder or rung-gap formulas.
- Does not assert eight-tick periodicity or spatial dimension D = 3.
- Does not supply exploit-style or experimental protocols; pure formal defs and lemmas.