IndisputableMonolith.Cosmology.RS_COS_Structural_010
Structural cosmology module packaging a domain cost, a positive canonical threshold, and an inhabited certificate for RS_COS claim 010. Cosmologists citing the RS structural ledger would use the certificate as a single entry point. The module is mostly definitions plus elementary nonnegativity and positivity facts imported from the cost layer.
claimThe module introduces a domain cost $C$ (nonnegative), a canonical threshold $\theta>0$, and an inhabited certificate packing the structural hypotheses for RS cosmology claim 010.
background
Recognition Science cosmology modules sit on the cost and constants layers. The cost layer supplies the J-cost (the unique symmetric convex cost forced by the Recognition Composition Law), while Constants fixes the RS time quantum $\tau_0=1$ tick.
This file is a structural packaging unit rather than a dynamical derivation. It names a domain cost, records that the cost is nonnegative, and fixes a positive canonical threshold against which structural comparisons are made. The certificate type bundles those facts so downstream cosmology statements can assume a single inhabited witness instead of re-proving the elementary inequalities.
proof idea
Definition-and-certificate module. Core objects are defs (domain cost, canonical threshold, certificate structure). Supporting lemmas are short: equality at a reference point, nonnegativity of the domain cost, positivity of the threshold, and inhabitation of the certificate. No deep tactic proof; the argument is assembly of cost-layer facts into a named cert.
why it matters in Recognition Science
Gives cosmology claim 010 a single Lean certificate rather than a scatter of local inequalities. Downstream used-by edges are empty in the current graph, so the module is a leaf packaging unit: it freezes the structural side conditions (cost nonnegativity, threshold positivity) that later RS cosmology theorems are expected to import. It does not itself force $D=3$, the eight-tick octave, or the mass ladder; those live in the forcing chain and mass modules.
scope and limits
- Does not derive dynamical FLRW or perturbation equations.
- Does not force spatial dimension $D=3$ or the eight-tick period.
- Does not compute numerical cosmological parameters or $\alpha$.
- Does not prove uniqueness of the domain cost beyond imported cost facts.
- Does not supply a used-by parent theorem in the current graph.