IndisputableMonolith.Cosmology.ThermodynamicSelectionCert
The Cosmology.ThermodynamicSelectionCert module certifies an entropy floor by showing J-cost is non-negative. Cosmologists applying Recognition Science to early-universe bounds would cite it when linking cost functions to thermodynamic selection on the phi-ladder. The module assembles direct consequences from imported Cost definitions and the RS time quantum without internal derivations.
claim$J(x) = (x + x^{-1})/2 - 1$ satisfies $J(x) > 0$ except at the fixed point, establishing the entropy floor for thermodynamic selection certification.
background
The module sits in the cosmology domain and imports the RS time quantum τ₀ = 1 tick from Constants together with the cost functional from the Cost module. It defines supporting objects including jcost_entropy_floor, jcost_ground_state, jcost_unbounded_near_zero, jcost_unbounded_at_infinity, and sublevel_set_has_bounds before reaching ThermodynamicSelectionCert. These rest on the Recognition Composition Law and the J-function properties already fixed in the upstream Cost module.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the entropy floor required for thermodynamic selection in cosmology and thereby supports downstream derivations that connect J-cost bounds to the forcing chain steps T5 through T8. It supplies the non-negativity needed to close cost arguments on the phi-ladder when deriving spatial dimension D = 3 and the alpha band.
scope and limits
- Does not derive explicit mass spectra on the phi-ladder.
- Does not address interactions with the Berry creation threshold.
- Does not extend the floor to non-RS units or external fields.