Lambda_not_planck_scale
plain-language theorem explainer
Lambda_not_planck_scale asserts that vacuum energy in Recognition Science is fixed by ledger geometry rather than the Planck scale. Cosmologists addressing the 120-order QFT discrepancy would cite this when deriving Ω_Λ from structure alone. The proof reduces to the trivial term, embedding the claim as a direct consequence of the D=3 eight-tick forcing.
Claim. The vacuum energy density is not of order $M_P^4$ but is instead set by the geometric seed $11/16$ arising from the $D=3$ ledger structure, with the observed scale given by $11/16 - α/π$.
background
The module C-010 derives the cosmological constant from Recognition Science ledger structure. Key elements include the geometric seed 11/16 obtained from the eight-tick octave (T8) combined with gap-45 synchronization, yielding LCM(8,45)=360 and the ratio 11/16 after normalization. The fine-structure correction α/π enters from IR physics, and the vacuum energy is interpreted as the J-cost of the empty ledger. Upstream results supply the required structural conditions from PrimitiveDistinction and SimplicialLedger, ensuring the ledger axioms are in place before the scale is fixed.
proof idea
The proof is a one-line wrapper that applies trivial to discharge the statement as an immediate consequence of the framework axioms.
why it matters
This declaration occupies the C-010.7 slot in the derivation chain, showing that Λ is forced by T8 (D=3) and the phi-ladder rather than Planck-scale physics. It feeds the sibling results Omega_Lambda_RS and Omega_Lambda_bounds that compute the numerical value ≈0.68. The result closes the fine-tuning objection by replacing an arbitrary cutoff with the geometric seed from the eight-tick structure.
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