IndisputableMonolith.Relativity.ILG.CosmologyDerived
The CosmologyDerived module extracts cosmological models from the ILG layer of Recognition Science. It converts the forcing chain T5-T8 into relations for scale factor evolution and density parameters using J-cost and the phi-ladder. The module assembles these results to connect microscopic axioms to macroscopic expansion without new hypotheses.
claimThe module defines derived objects including the Hubble parameter $H = a^{-1} da/dt$ and Friedmann equation $(a^{-1} da/dt)^2 = 8 pi G rho / 3$ in RS units with $G = phi^5 / pi$, $c=1$, and rho scaled via the phi-ladder from the J-uniqueness $J(x) = (x + x^{-1})/2 - 1$.
background
Recognition Science starts from the Recognition Composition Law $J(xy) + J(x/y) = 2 J(x) J(y) + 2 J(x) + 2 J(y)$ and forces J-uniqueness at T5 together with phi as self-similar fixed point at T6. This module introduces cosmology-specific quantities on top of the eight-tick octave (T7) and D=3 (T8), expressing mass scales as yardstick times phi to the power (rung minus 8 plus gap(Z)). The local setting assumes Berry creation threshold at phi inverse and Z_cf near phi^5.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module supplies the cosmological interface that carries the T0-T8 chain into large-scale structure and expansion history. It feeds parent results on universe models that apply the mass formula and alpha band (137.030 to 137.039) at cosmic scales. The derivations close the loop from RCL to observable cosmology while respecting the phi-ladder and eight-tick periodicity.
scope and limits
- Does not derive numerical values for specific cosmological parameters.
- Does not perform simulations of cosmic evolution.
- Does not compare predictions to observational datasets.
- Does not incorporate quantum corrections or modified gravity variants.