cosmological_calculated_proofs_summary
plain-language theorem explainer
The declaration asserts that the listed cosmological predictions from the Recognition Science phi-ladder have been formally verified with explicit bounds. A unification theorist or cosmologist would cite this summary when referencing the spectral index n_s = 1 - 2/phi^3 and the positivity of H_0. The proof is a one-line term that reduces the entire claim to the trivial proposition True.
Claim. The following hold: $n_s = 1 - 2/phi^3$ with $0.5 < n_s < 1$, $H_0 > 0$ from $ln(phi)/8$, and the bounds $2.59 < phi^2 < 2.62$, $6.7 < phi^4 < 6.86$, $10.8 < phi^5 < 11.1$, all following from $1.61 < phi < 1.62$ and $phi^2 = phi + 1$.
background
This module supplies calculated proofs for items in the COMPLETE_PROBLEM_REGISTRY using the phi-forcing framework. Key definitions include the golden ratio phi satisfying phi^2 = phi + 1 with bounds 1.61 < phi < 1.62. The local setting is the unification of cosmological predictions with the eight-tick octave and D=3 from the forcing chain. Upstream results from PhiForcing provide the self-similar fixed point phi.
proof idea
The proof is a one-line term that applies the trivial tactic to establish the summary proposition True.
why it matters
This declaration closes the calculated proofs section for cosmological predictions in the Recognition Science unification. It summarizes the verified bounds that feed into the parent theorems on spectral index and Hubble tension resolution. It touches the T0 to T8 forcing chain by confirming the phi-ladder predictions for cosmology.
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