StructPhysicsM86Cert
plain-language theorem explainer
Packages three structural properties required of the Physics-domain certificate at recognition rung 86: domain cost vanishes on the diagonal, is nonnegative for positive mass and energy arguments, and the canonical threshold is strictly positive. Downstream code cites the inhabited instance to discharge the certificate interface. The declaration is a pure structure type; no proof body.
Claim. A structural physics certificate at recognition rung 86 is a record of three facts: (i) for every nonzero real $r$, the domain cost of $(r,r)$ is zero; (ii) for all positive reals $m,e$, the domain cost of $(m,e)$ is nonnegative; (iii) the canonical threshold is strictly positive.
background
Module Structural_Physics_mod86 records a structural Recognition Science prediction for the Physics domain at recognition rung 86. Status is a structural theorem package with zero sorry and zero axiom. The local objects are a domain cost functional on pairs of reals, and a canonical threshold scalar used as a positivity gate.
Domain cost is the Physics-side specialization of the recognition cost. Upstream, ObserverForcing proves that every recognition event has nonnegative cost via the J-cost nonnegativity lemma (0 ≤ e.cost from Jcost_nonneg at positive state). The certificate fields mirror that nonnegativity, plus a diagonal vanishing condition (cost of matching arguments is zero) and a positive threshold.
Rung 86 sits on the phi-ladder mass/yardstick hierarchy used throughout RS structural physics certificates. The three fields are the minimal interface the module exposes before constructing a concrete witness.
proof idea
No proof: this is a structure declaration (type former) with three propositional fields. Inhabitation is deferred to the sibling definition cert, which fills the fields by domainCost_at_eq, domainCost_nonneg, and canonicalThreshold_pos, and to cert_inhabited, which wraps that witness as Nonempty.
why it matters
Gives the typed interface for the Physics structural certificate at rung 86. Downstream, cert builds a concrete value and cert_inhabited proves the type is nonempty, closing the module's structural claim (0 sorry, 0 axiom).
In the RS forcing picture this is bookkeeping, not a new forcing step: it packages cost nonnegativity (aligned with the J-cost minimum and ObserverForcing) and a positive threshold so later physics lemmas can assume a single certificate object rather than three loose hypotheses. It does not itself derive D = 3, the eight-tick octave, or the alpha band; it only standardizes the Physics-domain side conditions at this rung.
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