LambdaFalsifier
plain-language theorem explainer
LambdaFalsifier packages the four empirical conditions that would invalidate the Recognition Science derivation of the cosmological constant from the J-cost vacuum ground state. A cosmologist testing the model would cite the structure to list the precise observations capable of refuting COS-013. The declaration is a direct structure definition that assembles the propositions and their logical consequence without lemmas or tactics.
Claim. A structure consisting of the propositions $w ≠ -1$, $Λ$ varies with time, no $φ$-structure present in the value, and a different cancellation mechanism, together with the requirement that $(w ≠ -1) ∨ (Λ$ varies$) → ⊥$.
background
The Cosmology.CosmologicalConstant module derives $Λ$ from the J-cost ground state of the vacuum ledger under Recognition Science. Observed $Λ ≈ 10^{-52} m^{-2}$ is $10^{120}$ times smaller than naive QFT vacuum energy, posing the worst fine-tuning problem in physics. The RS approach treats the vacuum as carrying a nonzero baseline J-cost fixed by the Recognition Composition Law and $φ$-ladder scaling from the T5–T8 forcing chain.
proof idea
The declaration is a direct structure definition that enumerates the four falsifying propositions and encodes their disjunctive implication as a single field.
why it matters
The structure supplies the explicit falsifiability criteria for the COS-013 claim that $Λ$ emerges from the J-cost ground state. It identifies the observational tests (equation-of-state deviation, time variation, absence of $φ$-scaling, alternative mechanism) that would defeat the derivation. No downstream theorems reference it, leaving open the integration of these criteria with current cosmological data sets.
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