StructPhysicsM46Cert
plain-language theorem explainer
Bundles three structural properties for Recognition Science physics at rung 46: domain cost vanishes on the diagonal, is nonnegative for positive mass and energy, and the canonical threshold is positive. Anyone citing the inhabited structural certificate for this module uses this pack. It is a pure structure definition with no proof body; the fields are discharged by sibling lemmas when the certificate is built.
Claim. A structural physics certificate at recognition rung 46 is a triple of properties: (i) for every nonzero real $r$, the domain cost satisfies $C(r,r)=0$; (ii) for all positive mass $m$ and energy $e$, $C(m,e)\ge 0$; (iii) the canonical threshold $T$ obeys $T>0$.
background
This module is the Recognition Science structural certificate for the Physics domain at recognition rung 46 (Plan v7, 120th pass). Status is structural theorem: zero sorry, zero axiom. The certificate packages the local cost and threshold facts that the physics-side structural prediction needs.
Domain cost is the real-valued cost assigned to a mass/energy pair in this module; sibling facts assert it vanishes when the two arguments agree (nonzero) and is nonnegative on the positive orthant. The canonical threshold is the positive real cutoff used as the structural acceptance level for the domain. Upstream, the foundation layer already has nonnegativity of recognition-event cost via the J-cost: "The cost of any recognition event is non-negative," proved from Jcost_nonneg on positive state.
The structure itself does not compute masses or coupling constants; it only records the three inequalities and identities the certificate consumer will demand.
proof idea
No proof body: this is a structure declaration. The three fields are Prop-valued requirements (diagonal vanishing of domain cost, nonnegativity on positive mass and energy, positivity of the canonical threshold). Inhabitation is separate: the sibling cert fills the fields by domainCost_at_eq, domainCost_nonneg, and canonicalThreshold_pos, and cert_inhabited wraps that as Nonempty.
why it matters
Gives a single named type for the structural physics pack at rung 46 so downstream code can demand one object rather than three loose lemmas. Immediate consumers are cert (the concrete inhabitant) and cert_inhabited (nonemptiness). In the RS forcing picture this sits on the physics side of the structural certificates, not on the T0–T8 foundation chain itself; it records cost-shape and threshold positivity once the domain cost and threshold are fixed by the module’s siblings. It does not close mass-ladder or alpha-band claims; it only certifies the local cost/threshold interface those claims may later use.
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