phiLadderSum
plain-language theorem explainer
phiLadderSum defines the infinite sum over phi-ladder rungs as phi squared, equal to phi over (phi minus one). Cosmologists addressing the cosmological constant problem would cite it to quantify the geometric suppression of vacuum energy in the J-cost ledger. The definition follows at once from the closed-form sum of the geometric series with ratio 1/phi.
Claim. Let $phi$ be the golden ratio. The $phi$-ladder sum is defined by $sum_{n=0}^infty phi^{-n} = phi^2$.
background
Recognition Science treats the vacuum as a ledger carrying baseline J-cost under the Recognition Composition Law. Physical quantities sit on discrete phi-ladder tiers scaled by powers of phi, as in the nucleosynthesis tiers structure where nuclear densities scale as phi to an integer exponent times Planck density. This module derives Lambda from the J-cost ground state and notes that the observed value is 10^120 times smaller than naive QFT predictions.
proof idea
The definition is a one-line wrapper that assigns phi squared, the closed form of the geometric series sum sum phi^{-n} for n from 0 to infinity.
why it matters
This supplies the summation factor for the cosmological constant cancellation mechanism. It feeds the dark energy density and vacuum J-cost expressions in the same module. The module flags the result as central to a potential resolution of the cosmological constant problem, linking to the phi self-similar fixed point and J-uniqueness in the forcing chain.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.