geometric_seed_pos
plain-language theorem explainer
The theorem establishes positivity of the geometric seed 11/16 that supplies the leading term in the Recognition Science expression for dark-energy density. Cosmologists deriving Ω_Λ from ledger geometry cite it to confirm the base contribution before the α/π subtraction. The proof is a direct term-mode reduction that unfolds the constant definition and applies numerical normalization.
Claim. The geometric seed defined by the ratio 11/16 arising from the D=3 ledger structure satisfies 11/16 > 0.
background
In the C-010 module the cosmological constant problem is resolved by writing Ω_Λ = 11/16 - α/π, where 11/16 is the geometric seed extracted from the eight-tick forcing chain (T8) and the gap-45 synchronization of the simplicial ledger. The upstream definition in Constants.AlphaDerivation expresses the same seed as solid_angle_Q3 times a geometric factor, while the local definition specializes it to the rational 11/16. This seed encodes the passive energy quantum of the cube geometry (11 edges after removing one active edge) normalized by the 2^4 factor from the 8-tick octave.
proof idea
The proof is a one-line term-mode wrapper. It unfolds the local definition of geometric_seed to the literal constant 11/16 and invokes norm_num to discharge the strict inequality.
why it matters
The result supplies the positivity anchor for the entire C-010 chain and is referenced by the sibling statements Omega_Lambda_positive, Omega_Lambda_bounds and Omega_Lambda_RS. It confirms the structural positivity forced by T8 (D=3) and the eight-tick octave before the small α/π correction is subtracted, thereby closing the fine-tuning objection at the level of the geometric seed.
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