RSSTDStructural005Cert
plain-language theorem explainer
Packages three structural side-conditions for Standard Model module 5 (eight-tick lattice): diagonal domain cost vanishes, domain cost is nonnegative for positive mass and energy, and the canonical threshold is positive. Downstream code cites the inhabited certificate rather than the raw lemmas. The declaration is a pure structure, not a proved theorem.
Claim. A certificate is a triple of properties: (i) for every nonzero real $r$, the domain cost of the pair $(r,r)$ 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 5 sits in the Standard Model structural layer of Recognition Science. Its module header fixes the eight-tick octave: one full traversal of the binary recognition lattice has period $2^D = 8$ (forcing chain T7 with $D = 3$). Status is structural: zero sorry, zero axiom.
Domain cost is the local cost functional on mass-energy pairs used in this module; the certificate only records that it vanishes on the diagonal (away from zero) and stays nonnegative in the positive quadrant. Those properties mirror the global J-cost nonnegativity from ObserverForcing: "The cost of any recognition event is non-negative," proved via Jcost_nonneg at positive state. The canonical threshold is the positive cutoff against which domain cost is compared in later structural checks.
proof idea
No proof body: this is a structure declaration. It names three fields whose types are the Prop statements above. Inhabitation is deferred to the sibling definition cert, which fills the fields with domainCost_at_eq, domainCost_nonneg, and canonicalThreshold_pos.
why it matters
Gives a single named bundle for the three side-conditions that module 5 treats as its structural certificate. Downstream, cert builds a concrete value of this structure, and cert_inhabited records Nonempty RSSTDStructural005Cert, closing the module's "STRUCTURAL THEOREM" claim. In the broader RS chain this supports the eight-tick octave (T7, period $2^3$) as a clean Standard Model interface rather than a loose collection of lemmas. It does not itself force $D = 3$ or derive the mass ladder; it only packages cost and threshold hygiene used by those later steps.
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