hypothesis1
This definition supplies the baseline hypothesis that the cosmological constant equals the inverse square of the fundamental tick duration tau0. Cosmologists testing Recognition Science vacuum scales against the observed Lambda would reference it as the naive starting point before suppression factors. The declaration is a direct noncomputable assignment that pulls tau0 from the imported Constants module.
claim$Λ_1 := τ_0^{-2}$, where $τ_0$ is the fundamental tick duration in RS-native units.
background
The Cosmology.CosmologicalConstant module targets derivation of the cosmological constant from Recognition Science via the J-cost ground state of the vacuum ledger. It opens by stating the observed value Λ_obs ≈ 10^{-52} m^{-2} is 10^{120} times smaller than naive QFT predictions, framing this as the worst fine-tuning problem in physics. Upstream results supply tau0 as the tick duration (Constants.tick and its derivations from hbar, G, c) together with t_universe ≈ 4.4 × 10^{17} s.
proof idea
One-line definition that directly assigns the reciprocal square of the imported tau0 constant.
why it matters in Recognition Science
This supplies the initial trial scale for the COS-013 program on the cosmological constant problem, feeding the subsequent hypothesis2 that multiplies by (tau0 / t_universe)^2. It instantiates the RS approach in which vacuum energy emerges from baseline J-cost rather than empty space, and it parallels the hypothesis-testing pattern used in Standard Model modules for CKM and WZ parameters. The declaration highlights the need for additional phi-ladder suppression to reach the observed 10^{-52} m^{-2} scale.
scope and limits
- Does not incorporate universe age or any (tau0 / t_universe) suppression.
- Does not equate the expression to observed vacuum energy density.
- Does not invoke J-cost cancellation or phi-ladder summation.
- Does not derive the numerical value 6 × 10^{53} m^{-2} inside the declaration.
formal statement (Lean)
72noncomputable def hypothesis1 : ℝ := 1 / tau0^2
proof body
Definition body.
73
74/-- Hypothesis 2: Λ ∝ (τ₀ / t_universe)²
75
76 t_universe ~ 4.4 × 10¹⁷ s
77 (τ₀ / t_u)² ~ (1.3e-27 / 4.4e17)² ~ 10⁻⁸⁸
78
79 Λ ~ τ₀⁻² × 10⁻⁸⁸ ~ 10⁻³⁵ m⁻²
80
81 Getting closer but still too large. -/