IndisputableMonolith.Cosmology.Reionization_Redshift_RS
RS packaging of the cosmic reionization redshift as a nonnegative domain cost compared against a positive canonical threshold, with an inhabited certificate object. Cosmologists checking the RS redshift band cite the certificate and the threshold lemmas. The module is mostly definitions plus elementary nonnegativity and positivity facts imported from Cost and Constants.
claimThe module defines a domain cost $C$ (nonnegative), a canonical threshold $\theta>0$, and a reionization certificate asserting the RS cost-threshold relation used to locate the reionization redshift on the $\varphi$-ladder.
background
Recognition Science measures mismatch with the J-cost $J(x)=(x+x^{-1})/2-1$ from the forcing chain (T5) and the Recognition Composition Law. Cosmology modules import Constants (RS-native units, $\tau_0=1$ tick) and Cost to place epoch markers on the $\varphi$-ladder rather than fitting $\Lambda$CDM free parameters.
Reionization is the late-universe transition when the IGM becomes transparent again. In this file that epoch is encoded as a domain cost evaluated against a canonical positive threshold, not as a free $z_{\mathrm{re}}$ prior. Sibling names indicate equality and nonnegativity lemmas for the cost, positivity of the threshold, and a ReionizationCert bundle with an inhabited instance.
The local setting is certificate-style cosmology: small Lean objects that pin an RS-native numerical claim so downstream reports can cite a single inhabited cert rather than ad hoc numerics.
proof idea
Definition-heavy module. It introduces the domain cost and canonical threshold, then records elementary facts (evaluation equality, nonnegativity of cost, positivity of threshold) by reduction to Cost/Constants. The certificate type packages those inequalities; inhabitance is a one-shot construction of a default cert value. No deep tactic proof of a redshift formula appears at module scope.
why it matters in Recognition Science
Gives cosmology pages a named RS handle for reionization redshift instead of an external $z\sim6$–$10$ quote. Feeds any parent report that needs an inhabited reionization certificate (no used_by edges are recorded yet). Sits beside other RS epoch markers that use $\varphi$-ladder rungs, eight-tick structure, and J-cost thresholds. Does not itself force $D=3$ or $\alpha$; those remain upstream (T8, alpha band).
scope and limits
- Does not derive a numerical $z_{\mathrm{re}}$ from first principles inside this module alone.
- Does not prove agreement with Planck or JWST optical-depth posteriors.
- Does not model bubble growth, UV luminosity functions, or hydrodynamics.
- Does not discharge global RS forcing (T0–T8); it only packages a cost-threshold cert.
- Does not assert observational uniqueness of the canonical threshold choice.