IndisputableMonolith.Foundation.AllPhysics5
Foundation module packaging a domain cost functional, a positive canonical threshold, and an inhabitation certificate for an All-Physics-5 bundle. Physicists tracing how RS cost structure underwrites a five-part physics package would land here. The file is largely definitional: nonnegativity and positivity lemmas plus a trivial certificate witness.
claimA nonnegative domain cost $C$ on the RS cost structure, a strictly positive canonical threshold $\tau_\ast$, and an inhabited certificate type asserting that the five-part All-Physics package is well-formed relative to those data.
background
Recognition Science routes physics through a single cost functional $J$ forced by the Recognition Composition Law, with native units fixed by the golden ratio $\varphi$. The Constants import supplies the RS time quantum $\tau_0=1$ tick; the Cost import supplies the ambient $J$-cost calculus used throughout the monolith.
This module sits in the Foundation layer and introduces a domain-level cost $C$ together with a canonical positive threshold. The siblings domainCost_nonneg and canonicalThreshold_pos record the elementary analytic facts needed before any downstream physics packing. The certificate objects then bundle those facts into a single inhabitable Prop-level witness.
proof idea
Definition-heavy module. Domain cost and canonical threshold are introduced by def; nonnegativity and positivity are short analytic lemmas off the Cost import. The AllPhysics5 certificate is a structure or Prop bundle; inhabitation is a one-line constructor or ⟨⟩-style witness. No deep forcing-chain argument lives here.
why it matters in Recognition Science
Gives Foundation a single named place for the five-part physics packaging relative to domain cost and threshold. Downstream consumers (none listed yet in the graph) can import the certificate rather than re-proving nonnegativity and positivity. Ties to the broader RS program that all physics is forced from the $J$-cost and $\varphi$-ladder data, without itself discharging T5--T8.
scope and limits
- Does not derive the J-cost uniqueness theorem (T5).
- Does not force $\varphi$, the eight-tick period, or $D=3$.
- Does not compute masses, $\alpha$, or continuum limits.
- Does not claim the certificate implies empirical completeness.
- Does not discharge any sorry outside this file's own defs.