geometric_seed
plain-language theorem explainer
The geometric seed is the rational 11/16 that encodes the D=3 ledger geometry arising from the eight-tick octave combined with gap-45 synchronization. Cosmologists deriving the dark energy density fraction cite this constant as the base term before the fine-structure correction. The definition is a direct abbreviation that fixes the ratio without further reduction.
Claim. The geometric seed equals the real number $11/16$, the ratio obtained from the three-dimensional ledger with eight-tick period $2^3$ and gap-45 synchronization via lcm$(8,45)=360$.
background
The Cosmological Constant Derivation module resolves the vacuum energy discrepancy by writing the observed dark energy fraction as the difference between a geometric seed and the fine-structure correction. The geometric seed 11/16 originates from the D=3 vacuum ledger: 11 counts the passive energy quantum from cube geometry while 16 follows from the eight-tick octave. Upstream results in AlphaDerivation establish the related full geometric seed as the product of solid angle and passive edge count, here specialized to the cosmological ratio.
proof idea
The declaration is a direct definition that assigns the rational 11/16 to the geometric seed, with no lemmas or tactics applied beyond the abbreviation itself.
why it matters
This definition supplies the leading term for the cosmological constant formula realized as 11/16 minus alpha over pi, which reproduces the observed value near 0.68. It feeds directly into the Omega_Lambda_RS bounds and the alpha inverse derivation in the same module. The construction realizes the T8 forcing of three spatial dimensions together with the eight-tick octave from the unified forcing chain, closing the ledger-to-observed-Lambda step without external tuning.
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