hypothesis2
plain-language theorem explainer
The declaration supplies the scaling (τ₀ / t_universe)² / τ₀² for the cosmological constant under Recognition Science vacuum accounting. Cosmologists testing RS-derived vacuum energy against the observed Λ would cite this expression when comparing trial scalings to the 10^{-52} m^{-2} benchmark. It is introduced as a direct noncomputable definition that normalizes the squared ratio of fundamental tick duration to cosmic age.
Claim. Let τ₀ be the fundamental tick duration and t_universe the age of the universe. The quantity is defined as (τ₀ / t_universe)² / τ₀², which equals t_universe^{-2}.
background
In the Recognition Science treatment of cosmology the vacuum carries a nonzero J-cost ground state whose baseline ledger cost supplies the cosmological constant. Module COS-013 frames the target as deriving Λ from this ground state and notes that the observed value is roughly 10^{120} times smaller than naive QFT predictions. Upstream, t_universe is fixed at 4.4 × 10^{17} s while tau0 is imported as the RS-native tick duration from Constants.
proof idea
The declaration is a one-line definition that directly assembles the algebraic expression (tau0 / t_universe)^2 / tau0^2 from the imported constants tau0 and the local t_universe.
why it matters
This definition occupies the second trial scaling inside the COS-013 derivation of Λ from the J-cost ground state. It is referenced by downstream hypothesis2 declarations in the Standard Model modules for CKM matrix elements and WZ mass ratios, showing a recurring pattern of successive approximations. The module doc identifies the cosmological constant problem as the worst fine-tuning issue in physics and positions RS phi-scaling as a candidate resolution path, with this expression providing an intermediate numerical bridge toward the required 10^{-122} suppression.
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