IndisputableMonolith.Physics.Structural_Physics_mod86
Structural physics certificate module for a domain-cost threshold package (mod 86). It packages a nonnegative domain cost, a positive canonical threshold, and an inhabited certificate record used by structural-physics audits. Definitions and elementary positivity/equality lemmas; no deep forcing-chain argument lives here.
claimA structural-physics package consisting of a domain cost $C$ (nonnegative), a canonical threshold $\theta>0$, and an inhabited certificate record asserting the structural-physics mod-86 claims built from the RS cost and constants layers.
background
Recognition Science measures mismatch with a J-cost (from the Cost import) and works in RS-native units fixed by Constants, where the fundamental time quantum is one tick ($\tau_0=1$). Structural physics statements often reduce to comparing a domain-level cost against a positive threshold so that a certificate can be discharged without reopening the full forcing chain.
This module sits in the Physics domain and imports only Mathlib, Constants, and Cost. Sibling names indicate a domain cost functional, its evaluation-at-equality and nonnegativity facts, a canonical threshold with positivity, and a certificate type StructPhysicsM86Cert with an inhabited instance. The local setting is therefore a thin structural layer: cost and threshold data plus a certificate wrapper, not a derivation of $J$, $\varphi$, or dimension.
proof idea
Definition-and-certificate module. Domain cost and canonical threshold are introduced as defs; nonnegativity and positivity are short lemmas over the Cost/Constants substrate. Equality-at-evaluation is an algebraic identity wrapper. The certificate record and its inhabited instance assemble those facts into a single dischargeable package. No multi-step tactic development or forcing-chain induction appears at module scope.
why it matters in Recognition Science
Gives Physics a reusable structural certificate (mod 86) so downstream audits can cite one inhabited record instead of re-proving domain-cost nonnegativity and threshold positivity. Upstream edges are only Constants and Cost, so the module deliberately stays below T5–T8 (J-uniqueness, $\varphi$, eight-tick octave, $D=3$). No used_by edges are recorded here; the value is local packaging for structural-physics checks that need a cost-versus-threshold gate without touching mass ladders or $\alpha$ bands.
scope and limits
- Does not derive J-uniqueness, phi, eight-tick structure, or D=3.
- Does not prove mass-ladder or fine-structure (alpha) numerics.
- Does not supply exploit-style or dynamical evolution equations.
- Does not claim downstream consumers beyond the local certificate package.
- Does not replace the full Cost theory; only uses it as substrate.