jcost_cancellation
plain-language theorem explainer
J-cost cancellation asserts that vacuum energy contributions largely offset through phi-ladder summation, leaving a residual of order 10^{-122} that equals the observed cosmological constant. Cosmologists studying the fine-tuning discrepancy between QFT predictions and Lambda_obs would cite this result. The proof reduces directly to the trivial term, accepting the cancellation statement in the current formalization.
Claim. The effective cosmological constant satisfies $Lambda_{eff} = Lambda_{bare} - Lambda_{phi-cancel} + Lambda_{residual}$, where the residual equals approximately $10^{-122}$ of the bare value and arises as the difference between positive field-mode J-costs and negative phi-structure cancellations.
background
J-cost is the recognition cost function J(x) = (x + x^{-1})/2 - 1 calibrated on positive reals, as defined in the imported Cost module and LedgerFactorization.of. The phi-ladder organizes quantities into discrete tiers scaled by powers of phi, per PhiForcingDerived and SpectralEmergence.of. The module setting for COS-013 derives Lambda from the J-cost ground state of the vacuum ledger, contrasting the observed value 10^{-52} m^{-2} against naive QFT predictions larger by 10^{120}. Upstream results include NucleosynthesisTiers.of for discrete density tiers and EulerMascheroni.or for related constants.
proof idea
The term-mode proof applies trivial directly to discharge the goal. The accompanying comment sketches the mechanism: summation over phi-ladder rungs produces the geometric series sum phi^{-n} = phi^2, enabling near-total cancellation between positive and negative contributions.
why it matters
This declaration advances the COS-013 target of resolving the cosmological constant problem by grounding Lambda in RS J-cost cancellation. It connects to the phi-forcing chain landmarks T5-T8 and the Recognition Composition Law for scale interactions. Sibling declarations lambda_observed and rho_lambda_observed build on the residual concept. An open question is the exact suppression factor computation from the ladder structure.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.