alpha_over_pi_small
plain-language theorem explainer
The declaration proves that the fine-structure correction alpha over pi stays strictly below 11/16. Cosmologists resolving the vacuum-energy discrepancy would cite this bound to confirm the electromagnetic term remains smaller than the ledger-derived geometric seed. The proof is a one-line tactic that invokes the positivity of Omega_Lambda and applies linear arithmetic to rearrange the inequality.
Claim. In the Recognition Science derivation where the vacuum energy fraction satisfies $0 < 11/16 - alpha/pi$, the fine-structure correction obeys $alpha/pi < 11/16$.
background
The module derives the cosmological constant from the ledger structure. The geometric seed 11/16 originates from the eight-tick octave (T7) combined with D=3 spatial dimensions (T8) and gap-45 synchronization, whose LCM yields the factor 11/16. The term alpha/pi supplies the infrared correction from electromagnetic physics. Upstream results include the definition of alpha as the electromagnetic coupling 1/alphaInv and ledger-factorization structures that calibrate J-cost. The positivity statement for Omega_Lambda is established in a sibling theorem.
proof idea
This is a tactic-mode proof. It first obtains the hypothesis 11/16 minus alpha over pi is positive from the omega_lambda_positive theorem. Linear arithmetic then rearranges the inequality to the required upper bound.
why it matters
The theorem supplies step C-010.6 in the cosmological-constant derivation, confirming that the alpha/pi correction is smaller than the 11/16 geometric seed. It supports the natural resolution of the vacuum-energy problem via phi-cancellation, consistent with the T8 forcing chain and the Recognition Composition Law. The result underpins subsequent bounds on Omega_Lambda and the Hubble parameter in the same module.
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