IndisputableMonolith.Cosmology.RS_Cosmo_Module_003
Cosmology certificate module 003 packages a domain cost functional and a positive canonical threshold, with elementary nonnegativity and positivity lemmas. A researcher citing RS cosmology cost bounds or threshold gates would import it. The module is mostly definitions plus short algebraic checks that the cost is nonnegative and the threshold is positive, then wraps them in an inhabited certificate record.
claimDefine a domain cost $C$ on the RS cost structure, prove $C \ge 0$ and $C$ agrees with its pointwise evaluation, fix a canonical threshold $\theta > 0$, and package $(C,\theta)$ into an inhabited RS cosmology certificate record for module 003.
background
Recognition Science measures mismatch with the J-cost from the Cost layer (the unique cost forced by the Recognition Composition Law and T5). Cosmology modules specialize that cost to geometric or expansion domains and gate statements by a positive threshold so that only configurations above a fixed recognition scale count as events.
This file sits in the Cosmology domain and imports Constants (including the RS time quantum $\tau_0 = 1$ tick) and Cost. Sibling declarations introduce domainCost (the specialized cost), its pointwise agreement and nonnegativity, canonicalThreshold with positivity, and the certificate bundle RSCosmo003Cert with an inhabited instance.
No external physics data enter here: the objects are pure RS-native cost and threshold scaffolding for later cosmological claims.
proof idea
Definition-heavy module. The cost and threshold are introduced as defs; nonnegativity and positivity are short lemmas (typically unfolding the Cost primitives and applying standard nonnegative or positivity facts). Equality-at-evaluation is a one-line unfolding. The certificate is a structure packing those facts, discharged by an inhabited instance that assembles the proved fields.
why it matters in Recognition Science
Gives the local cost-and-threshold interface for RS cosmology certificate 003 so later cosmology theorems can cite a single inhabited record rather than re-proving nonnegativity and positivity. Downstream use is not yet wired in this graph (no used_by edges), but the pattern matches other RS cert modules that feed forcing-chain or observational-gate arguments. It does not itself force $D=3$, the eight-tick octave, or the $\alpha$ band; it only supplies the cost/threshold package those arguments may consume.
scope and limits
- Does not derive cosmological observables or fit data.
- Does not prove uniqueness of the domain cost beyond the imported Cost axioms.
- Does not force spatial dimension, eight-tick period, or fine-structure bounds.
- Does not connect the threshold to Berry creation or mass-ladder rungs.
- Does not assert any sorry-free global cosmology theorem beyond the local cert record.