IndisputableMonolith.Physics.Structural_Physics_mod76
Module packaging a structural-physics cost on domains together with a positive canonical threshold and an inhabitation certificate (StructPhysicsM76Cert). Physicists tracking RS domain energetics and threshold positivity would cite it. Content is definitional plus short nonnegativity and positivity lemmas over the Cost and Constants imports.
claimDefines a domain cost $C_{\mathrm{dom}}$, proves $C_{\mathrm{dom}}\ge 0$ and an evaluation identity, introduces a canonical threshold $\theta>0$, and packages these into an inhabited structural-physics certificate for the mod-76 layer.
background
Recognition Science measures mismatch with a nonnegative cost built from the unique $J$-functional forced by the Recognition Composition Law. The Cost import supplies that infrastructure; Constants supplies the RS-native tick $\tau_0=1$ and related units.
This module sits in the Physics domain and specializes those primitives to a domain-level cost (sibling domainCost) with an evaluation identity and a nonnegativity lemma. It also fixes a canonical positive threshold used as a structural cutoff.
The certificate bundle StructPhysicsM76Cert (with cert and cert_inhabited) is the module's export surface: a single inhabited record that downstream physics layers can assume rather than re-proving local positivity and cost facts.
proof idea
Definition-heavy module, not a deep proof development. Domain cost and the canonical threshold are introduced as defs; nonnegativity and positivity are short lemmas over the Cost/Constants API. The certificate is assembled as a structure instance and shown inhabited, so callers obtain the package by inhabitation rather than by replaying the lemmas.
why it matters in Recognition Science
Gives the Physics layer a named, inhabitable certificate for structural cost and threshold facts at the mod-76 slice, so later RS physics developments can depend on one object instead of scattered lemmas. No downstream edges are recorded in the graph yet; the module is an export surface over Cost and Constants rather than a step in the T0–T8 forcing chain. It supports structural bookkeeping (nonnegative domain cost, positive cutoff) needed before mass-ladder or coupling arguments that consume cost positivity.
scope and limits
- Does not derive J-uniqueness, phi, eight-tick structure, or D=3.
- Does not prove mass-ladder or alpha-band numerical claims.
- Does not connect domain cost to experimental observables.
- Does not list downstream consumers; used_by is empty in the graph.
- Does not replace the general Cost API; it only specializes and packages it.