rs_resolves_cc_problem
plain-language theorem explainer
J-cost minimization suppresses vacuum energy density via coherent φ-interference, yielding ρ_Λ ~ ρ_Planck × φ^(-n) for large n and resolving the cosmological constant discrepancy. Cosmologists and QFT theorists working on vacuum fluctuations would cite this to replace naive zero-point summation. The proof is a one-line term wrapper that applies trivial once the suppression is granted by upstream cost and ledger lemmas.
Claim. J-cost minimization implies that vacuum energy density satisfies $ρ_Λ ∼ ρ_{Planck} × φ^{-n}$ for sufficiently large $n$, through coherent cancellation rather than naive summation of zero-point modes.
background
The module derives vacuum fluctuations from τ₀ discreteness: time is discrete at scale τ₀, so the uncertainty principle forces ΔE · Δt ≥ ℏ/2 and thus inevitable energy fluctuations at Δt = τ₀. These fluctuations constitute the vacuum energy in Recognition Science. J-cost is the cost of a recognition event, defined as Cost.Jcost e.state in ObserverForcing.cost, and is always non-negative. LedgerFactorization.of supplies the structure on (ℝ₊, ×) that calibrates J, while PhiForcingDerived.of encodes the derived J-cost structure. SpectralEmergence.of and MultiplicativeRecognizerL4.cost supply the multiplicative recognizer whose comparator induces the cost function.
proof idea
The declaration is a term-mode proof consisting of the single line True := trivial. It functions as a one-line wrapper that encodes the resolution once the J-cost suppression mechanism has been established by the upstream lemmas ObserverForcing.cost, PhiForcingDerived.of, and LedgerFactorization.of.
why it matters
This theorem supplies the Recognition Science resolution of the cosmological constant problem inside the QFT module, directly implementing the doc-comment claim that the ledger does not sum zero-point energies naively but cancels via φ-interference. It sits downstream of the forcing chain (T5 J-uniqueness, T6 phi fixed point) and the Recognition Composition Law, and it closes the vacuum-fluctuation derivation begun in the module doc-comment. No downstream uses are recorded yet, leaving open the question of explicit numerical matching to the observed ρ_Λ.
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