geometric_seed
plain-language theorem explainer
The geometric seed supplies the explicit value 128 ln(π/2) + 45 ln φ as the base input for constant derivations. Researchers assembling the inverse fine-structure constant from geometric and logarithmic contributions cite this definition. The declaration proceeds by direct assignment of the closed-form expression.
Claim. The geometric seed is defined as $128 ln(π/2) + 45 ln φ$.
background
The RRF foundation derives all constants from φ through gate identities in the chain φ to coherent energy to τ₀ to c to ℏ to G to α inverse. Key identities include the IR gate ℏ = E_coh · τ₀ and the Planck gate (c³ λ_rec²)/(ℏ G) = 1/π. The geometric seed enters the alpha assembly step as the explicit logarithmic starting value. Upstream results establish equivalent geometric forms: one as the product of solid angle of ∂Q₃ and passive field edges equaling 4π·11, and another as the ratio 11/16 from the D=3 ledger and eight-tick structure.
proof idea
The declaration is a direct definition that assigns the indicated linear combination of natural logarithms to the geometric seed.
why it matters
This definition supplies the concrete logarithmic value that feeds alphaInv_derived, where α inverse equals the geometric seed minus gap and curvature corrections and lands inside the observed band (137.030, 137.039). It closes the derivation from the phi fixed point and eight-tick octave to the alpha band. The parent result is the alpha seed structural theorem that factorizes the seed into solid angle times passive channels from Q₃ geometry.
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