cosmic_ratio_large
plain-language theorem explainer
The declaration shows that the ratio of the universe's age to the Planck time exceeds 10^60. Researchers deriving the cosmological constant from ledger tension cite this scale separation to explain why dark energy appears so small. The proof reduces the claim to numerical verification after unfolding the ratio definition.
Claim. Let $t_u$ denote the age of the universe in seconds and $t_p$ the Planck time. Then $t_u / t_p > 10^{60}$.
background
In the Cosmology.DarkEnergy module, cosmicRatio is defined as the quotient t_universe / t_planck. The upstream definitions fix t_planck at 5.4e-44 seconds and t_universe at 4.3e17 seconds (approximately 13.8 billion years). The module derives dark energy from ledger tension: the requirement that total J-cost sums to zero globally while expansion creates new spacetime volume produces a residual energy density identified with the cosmological constant. Upstream results include the structure of nuclear densities from NucleosynthesisTiers and the hypothesis that Lambda scales as (tau_0 / t_universe)^2 from CosmologicalConstant.
proof idea
The term proof unfolds cosmicRatio to the explicit quotient of t_universe and t_planck, then applies norm_num to discharge the numerical inequality.
why it matters
This result supplies the scale separation (Gap-45) required for the module's target derivation of Lambda approximately 10^{-122} in Planck units from the ratio of Planck to Hubble scales. It fills the COS-006 step that links ledger balance under expansion to the observed dark energy density. The enormous ratio mediates the suppression of vacuum energy through the golden-ratio structure already fixed in the forcing chain.
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