vacuum_fluctuation_one_statement
plain-language theorem explainer
The RS dark-energy density is the closed form Ω_Λ = 11/16 − α_CODATA/π, independent of any QFT UV cutoff, lies in (0.683, 0.686), and matches Planck 2018 within 2σ. Cosmologists citing Track 4.B package this as the single structural address of the vacuum-fluctuation discrepancy. The proof is a four-way conjunction of existing OmegaLambdaDerivation lemmas plus the cutoff-independence sibling.
Claim. The RS dark-energy density satisfies $\Omega_\Lambda = 11/16 - \alpha_{\mathrm{CODATA}}/\pi$, and the same equality holds for every positive QFT UV cutoff parameter; moreover $0.683 < \Omega_\Lambda < 0.686$ and $|\Omega_\Lambda - 0.6889| < 2\cdot 0.0056$ (Planck 2018 at $2\sigma$).
background
Track 4.B of the quantum-gravity master plan treats the classical $10^{120}$ cosmological-constant problem as a structural mismatch: standard QFT assumes vacuum-mode sums contribute to $\Lambda$ on equal footing with classical gravity. Recognition Science derives $\Omega_\Lambda$ from a phase-mode budget, not from a UV mode sum.
The RS value is $\Omega_\Lambda = 11/16 - \alpha/\pi$. The factor $11/16$ is integer combinatorics from the eight-tick addressing ledger (fraction of unexcited vacuum modes); the correction uses the measured CODATA fine-structure constant as the single external anchor. Upstream, omega_lambda_canonical_form states exactly $\Omega_\Lambda = 11/16 - \alpha_{\mathrm{CODATA}}/\pi$, and omega_lambda_interval pins the numerical band $(0.683, 0.686)$.
The straw-man type QFTVacuumNaiveCutoff is any positive real UV scale (the parameter a naive $\rho_{\mathrm{vac}}\propto\Lambda_{\mathrm{UV}}^4$ estimate would depend on). The sibling independence theorem says the RS $\Omega_\Lambda$ is definitionally the same for every such cutoff.
proof idea
Four-conjunct constructor, no new algebra. The first conjunct is omega_lambda_canonical_form (rewrite through the one-measured-input form, unfold mode counts, norm_num). The second is the in-module sibling omega_lambda_independent_of_QFT_cutoff, which discharges the universal quantifier over every positive QFT cutoff. The third is omega_lambda_interval (pair of strict bounds). The fourth unfolds the Planck 2018 central value and $1\sigma$ error in rs_consistent_with_planck and returns that hypothesis directly as the $2\sigma$ comparison.
why it matters
This is the Track 4.B one-statement certificate: it packages closed form, cutoff independence, the observed band, and Planck 2018 consistency into a single proved conjunction. The module status is structural theorem (zero sorry, zero RS-internal axiom). Downstream use sites are not yet wired (used_by empty), so the declaration is the terminal packaging step of the vacuum-fluctuation structural address rather than an intermediate lemma.
Framework role: the $11/16$ factor sits on the eight-tick octave (T7) ledger combinatorics; $\alpha$ enters only as the free boundary datum (CODATA anchor), consistent with the RS stance that exact $\alpha$ is not forced internally here. The $10^{120}$ discrepancy is resolved by non-participation: RS never routes $\Lambda$ through a QFT vacuum-mode sum, so the naive excess never appears. Open residual is dynamical cosmology (time evolution of $\Omega_\Lambda$, DESI tension details), not the static structural claim.
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