IndisputableMonolith.Cosmology.CMBPolarization3_FromJCost
Module packaging a J-cost certificate for CMB polarization mode structure labeled "Polar3". It defines a domain cost, a positive canonical threshold, and an inhabited certificate record tying those quantities together. Cosmologists working in the RS ladder would cite the certificate when linking multipole polarization features to the unique cost J. The content is mostly definitional with elementary nonnegativity and positivity lemmas.
claimOn a cost domain built from the RS functional $J(x)=(x+x^{-1})/2-1$, define a domain cost $C$, a canonical threshold $\theta>0$, and a certificate asserting that the Polar3 CMB polarization feature is controlled by $C$ relative to $\theta$.
background
Recognition Science fixes a unique nonnegative cost $J$ on ratios by the Recognition Composition Law and the forcing chain (T5 J-uniqueness). In RS-native units the same $J$ seeds mass rungs, coupling bands, and several cosmological thresholds.
This cosmology module imports only Constants (tick quantum $\tau_0$) and Cost (the $J$ infrastructure). It introduces a domain-level cost built from $J$, records elementary facts (evaluation identity, nonnegativity), and a strictly positive canonical threshold against which a Polar3 polarization certificate is stated.
The certificate is an inhabited structure: existence of a witness bundle rather than a deep analytic derivation of the full CMB Boltzmann hierarchy.
proof idea
Definition module with light lemma support. Domain cost is introduced as a def; equality-at-point and nonnegativity are short algebraic consequences of $J\ge 0$. The canonical threshold is a positive constant def with a one-line positivity proof. The Polar3 certificate is a structure packing those ingredients; inhabitation is by direct constructor application. No multipole integral or transfer-function analysis appears here.
why it matters in Recognition Science
Places a named Polar3 CMB polarization certificate on the J-cost spine so later cosmology results can cite a single inhabited record instead of re-deriving threshold positivity. Downstream use is not yet wired in this graph snapshot (no used_by edges). In the broader RS program it sits beside other cost-derived cosmological landmarks (eight-tick cadence, $D=3$, $\phi$-ladder mass formula) as a polarization-side interface: the claim is that the same $J$ that forces T5–T8 also supplies the cost scale for the Polar3 feature once the canonical threshold is fixed.
scope and limits
- Does not derive CMB power spectra or Boltzmann transfer functions.
- Does not identify Polar3 with a specific observed multipole $\ell$ without further mapping.
- Does not prove uniqueness of the threshold beyond the local positivity lemma.
- Does not connect to $\alpha$, $G$, or mass-ladder formulae in this module.
- Does not supply observational error bars or data fits.