hypothesis3
plain-language theorem explainer
This definition sets the cosmological constant hypothesis to one over phi to the power 583 in RS units. Cosmologists testing Recognition Science against the observed vacuum energy scale of order 10^{-52} m^{-2} would cite it when quantifying the required phi-scaling suppression. The declaration is a direct one-line assignment that pulls the precomputed exponent from the sibling lambda_exponent definition.
Claim. The hypothesis states that the cosmological constant satisfies $Λ = φ^{-583}$, where $φ$ is the golden ratio self-similar fixed point and the exponent 583 is chosen so that $φ^{-583}$ reproduces the observed suppression factor of order $10^{-122}$ relative to the Planck scale.
background
The module COS-013 derives the cosmological constant from the J-cost ground state of the vacuum ledger. J-cost is the recognition cost function induced by a multiplicative recognizer, given explicitly as $J(x) = (x + x^{-1})/2 - 1$, and equals the cost of any recognition event. The local setting begins from the observed mismatch $Λ_obs ≈ 10^{-52} m^{-2}$ and seeks a phi-scaling mechanism to explain the $10^{120}$ discrepancy with naive QFT predictions. Upstream, lambda_exponent supplies the concrete integer 583 obtained by solving $φ^{-n} ≈ 10^{-122}$ via $n = 122 × log(10) / log(φ)$.
proof idea
The declaration is a one-line definition that substitutes the precomputed lambda_exponent value of 583 into the expression 1 / phi raised to that power.
why it matters
This supplies the concrete numerical hypothesis for the cosmological constant within the Recognition Science framework, directly addressing the cosmological constant problem via phi-scaling as anticipated by the T5 J-uniqueness and T6 phi fixed-point landmarks. It feeds the same hypothesis pattern used in downstream Standard Model declarations for the CKM matrix and WZ mass ratio. The open question it leaves is whether the exponent 583 can be derived from the J-cost ground-state mechanism without external tuning.
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