lambda_exponent
plain-language theorem explainer
Recognition Science sets the cosmological constant scaling exponent to the integer 583 so that phi to this negative power reproduces the observed 10^{-122} suppression. Workers on the vacuum energy fine-tuning problem cite this number when building the J-cost ground state model. The definition is a direct numerical assignment obtained from the logarithmic ratio 122 log(10)/log(phi).
Claim. The exponent $n$ in the scaling relation $Λ ∝ φ^{-n}$ equals the integer 583, chosen so $φ^{-583}$ matches the factor $10^{-122}$ that reconciles the observed vacuum energy with the Planck scale.
background
The module COS-013 frames the cosmological constant problem as the 10^{120}-fold mismatch between naive quantum field theory expectations and the measured value $Λ_obs ≈ 10^{-52}$ m^{-2}. Recognition Science replaces the empty vacuum with a J-cost ground state whose baseline energy is set by phi-mismatch; the cosmological constant then emerges from this ledger cost via phi-scaling. The supplied definition fixes the concrete power required for hypothesis 3.
proof idea
Direct numerical definition. The integer 583 is obtained by evaluating the ratio 122 log(10)/log(phi) and rounding to the nearest natural number, as stated in the declaration comment.
why it matters
The definition supplies the explicit power appearing in hypothesis3, which asserts $Λ = 1/φ^{583}$ and links the vacuum energy directly to the J-cost ground state. It fills the scaling step inside the COS-013 derivation of the cosmological constant from Recognition Science principles. The module comment flags this route as a potential resolution of the worst fine-tuning problem in physics.
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