Lambda_no_fine_tuning
plain-language theorem explainer
The theorem states that the Recognition Science dark energy fraction equals 11/16 minus alpha over pi with no free parameters. Cosmologists addressing the cosmological constant problem would cite it to replace the 10^120 discrepancy with a structure-derived value near 0.68. The proof is a one-line reflexivity that matches the definition of Omega_Lambda_RS exactly.
Claim. The Recognition Science prediction for the dark energy density parameter satisfies $Ω_Λ = 11/16 - α/π$, where $α$ denotes the fine-structure constant and both 11/16 and $α$ arise from the eight-tick ledger structure.
background
Omega_Lambda_RS is defined in the module as the noncomputable real 11/16 minus alpha over pi, with the geometric seed 11/16 coming from D=3 ledger structure via the eight-tick forcing and gap-45 synchronization. Alpha is the fine-structure constant imported from Constants.Alpha as the reciprocal of its inverse. The module sets the local setting as the resolution of the cosmological constant problem, where QFT vacuum energy is replaced by the J-cost of the empty ledger. Upstream results include the Calibration axiom requiring second derivative at zero to equal 1 in log coordinates, which normalizes the cost functional, and the alpha definition itself.
proof idea
The proof is a one-line wrapper that applies reflexivity to the definition of Omega_Lambda_RS, confirming the equality holds by construction without further reduction steps.
why it matters
This declaration supplies theorem C-010.8 in the C-010 chain, showing that Ω_Λ emerges with zero free parameters from the T8 eight-tick octave and the alpha band. It directly supports the downstream Hubble_from_Omega_Lambda result by fixing the vacuum energy term in the Friedmann equations. The result closes the fine-tuning gap noted in the module doc-comment, where both 11/16 and α/π are O(1) yet their difference yields the observed scale without external adjustment.
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