IndisputableMonolith.Cosmology.PrimordialGW3_FromJCost
Packages a domain cost built from the J-functional, a positive canonical threshold, and an inhabited PrimGW3 certificate for a primordial gravitational-wave signature forced by recognition cost. Cosmologists in the RS program cite it when tying early-universe tensor structure to J rather than to free inflationary parameters. The module is mostly definitions plus nonnegativity and positivity lemmas; the certificate is a thin inhabited wrapper.
claimIntroduce a domain cost $C$ from the J-cost, a canonical threshold $\theta>0$, and an inhabited certificate that the primordial GW3 signature lies at or above threshold under that cost.
background
Recognition Science measures mismatch with the J-cost $J(x)=(x+x^{-1})/2-1$ (equivalently $\cosh(\log x)-1$), fixed uniquely by the recognition composition law and the T5 step of the forcing chain. The Cost import supplies that functional; Constants supplies the RS time quantum $\tau_0=1$ tick used to normalize cosmological scales.
This cosmology module specializes those primitives to a primordial gravitational-wave channel labeled GW3. It defines a domain cost on the relevant configuration space, records that the cost is nonnegative, and fixes a canonical positive threshold against which the GW3 mode is compared.
The certificate type bundles those facts into a single inhabitable record so downstream cosmology developments can assume a single named witness rather than re-proving threshold positivity at each use site.
proof idea
Definition-and-certificate module, not a deep derivation. Domain cost is introduced as a J-derived quantity; equality-at-a-point and nonnegativity are recorded as short lemmas. The canonical threshold is a positive constant (positivity lemma immediate from the algebraic form). PrimGW3Cert is a structure packing those ingredients; cert and cert_inhabited supply a canonical inhabitant so the certificate is available as a fact rather than a hypothesis.
why it matters in Recognition Science
Places a named, inhabitable bridge between the abstract J-cost (T5 uniqueness, RCL) and a concrete primordial tensor signature in the cosmology layer. No downstream consumers are wired in the graph yet; the module is an upstream certificate source for later GW or early-universe arguments that need a cost-threshold witness rather than a free amplitude. It keeps the GW3 claim inside the same cost language used for mass ladders and eight-tick structure, instead of importing an external inflationary power spectrum.
scope and limits
- Does not derive a full primordial power spectrum or tensor-to-scalar ratio.
- Does not prove observational detection of GW3; only a cost-threshold certificate.
- Does not fix inflationary potentials or reheating dynamics.
- Does not connect to late-time GW observatories or strain amplitudes.
- Does not discharge broader cosmology forcing beyond the local certificate.