IndisputableMonolith.Cosmology.CMBTemp3_FromJCost
Certification module that ties the CMB temperature scale (~3 K) to the Recognition Science J-cost. Cosmologists in the RS program would cite it for the temperature-from-cost claim. It packages a domain cost, a positive canonical threshold, and an inhabited certificate rather than a single deep derivation.
claimThe module defines a domain cost built from the J-cost, a positive canonical threshold $T_*$, and a certificate asserting that the CMB temperature scale of order $3\,\mathrm{K}$ arises from that cost structure in RS-native units.
background
Recognition Science measures mismatch with the J-cost $J(x)=(x+x^{-1})/2-1$, brought in from the Cost module. Constants supplies the RS time quantum $\tau_0=1$ tick and the native unit conventions ($c=1$, and related scalings).
In the cosmology layer one asks whether the observed CMB temperature is forced by the same cost geometry that drives the forcing chain (J-uniqueness through dimension and octave structure). This module sets up the cost-on-domain and threshold objects used to state that claim cleanly.
proof idea
Definition-heavy module, not a single deep proof. It introduces a domain cost and records elementary facts (pointwise evaluation identity, nonnegativity), defines a positive canonical threshold, then packages a CMB-temperature certificate type together with an inhabited instance. The module-level argument is structural packaging of cost and threshold into a cert, not a multi-step analytic derivation.
why it matters in Recognition Science
Places the ~3 K CMB temperature inside the RS cost framework, linking a primary cosmological observable to J-cost. The dependency graph currently shows no downstream consumers, so the module stands as a self-contained Cosmology-domain certificate. It complements mass-ladder and coupling-band results elsewhere in the monolith by extending the same cost language to the thermal sky.
scope and limits
- Does not derive the precise 2.725 K COBE/FIRAS value from first principles alone.
- Does not treat CMB anisotropies, acoustic peaks, or polarization.
- Does not claim uniqueness of the temperature scale outside the stated certificate.
- Does not connect to late-time parameters such as H0 or matter density.