vacuumFluctuationStructuralCert
plain-language theorem explainer
assembles the Track 4.B structural certificate: RS dark-energy density equals the closed form $11/16 - \alpha/\pi$, is independent of any QFT UV cutoff, lies in $(0.683,0.686)$, and matches Planck 2018 at $2\sigma$, while the naive QFT vacuum energy depends on the cutoff. Cosmologists citing the vacuum-fluctuation discrepancy resolution use this bundle. The body is a structure instance wiring four upstream theorems and one short existence proof for cutoff sensitivity.
Claim. There is a structural certificate asserting: (i) $\Omega_\Lambda = 11/16 - \alpha_{\mathrm{CODATA}}/\pi$; (ii) the same identity holds for every naive QFT UV cutoff parameter; (iii) the naive QFT vacuum-energy functional takes distinct values at two different cutoffs; (iv) $0.683 < \Omega_\Lambda < 0.686$; (v) $|\Omega_\Lambda - 0.6889| < 2\cdot 0.0056$ (Planck 2018 consistency at $2\sigma$).
background
Track 4.B of the RS quantum-gravity plan addresses the classical $10^{120}$ cosmological-constant problem. That problem assumes QFT vacuum modes contribute to $\Lambda$ on equal footing with classical gravity. In RS the substrate has no free vacuum modes of that kind; $\Omega_\Lambda$ is fixed by a phase-mode budget, not by a UV mode sum.
Upstream, omega_lambda_canonical_form states $\Omega_\Lambda = 11/16 - \alpha_{\mathrm{CODATA}}/\pi$, with the $11/16$ factor from saturated mode combinatorics ($[4,2,2]$ Gray-code $\times$ eight-tick addressing) and $\alpha$ the single measured CODATA input. The interval theorem places $\Omega_\Lambda$ in $(0.683,0.686)$; Planck 2018 anchors are $0.6889\pm 0.0056$, and rs_consistent_with_planck proves $2\sigma$ consistency. A straw-man cutoff family parameterizes the naive QFT vacuum energy so that cutoff dependence can be exhibited formally.
The certificate structure packages these facts as the Track 4.B structural address: RS never passes through the QFT vacuum-sum mechanism, so the discrepancy does not arise.
proof idea
The definition is a structure instance, not a deep proof. Canonical form and cutoff-independence fields are filled by direct application of omega_lambda_canonical_form and omega_lambda_independent_of_QFT_cutoff (the latter is definitional: $\Omega_\Lambda$ has no cutoff argument). The observed-band field is omega_lambda_interval. Planck consistency unfolds the Planck central value and error and reuses rs_consistent_with_planck. The only local tactic work is the naive-QFT field: exhibit cutoffs $1$ and $2$, unfold the naive vacuum-energy functional, and norm_num to show the two values differ.
why it matters
This certificate is the sole witness for the master theorem vacuum_fluctuation_discrepancy_structurally_addressed, which asserts Nonempty VacuumFluctuationStructuralCert and is the Track 4.B closure statement (module status: 0 sorry, 0 RS-internal axiom). Downstream one-statement wrappers cite that master theorem as the structural resolution of the vacuum-fluctuation discrepancy.
In the broader framework the result sits on the eight-tick octave (T7) combinatorics that force the $11/16$ mode fraction, together with the measured-$\alpha$ boundary datum. It does not derive $\alpha$ itself (that remains an external anchor / free boundary input). Its role is negative and structural: show that RS $\Omega_\Lambda$ has zero QFT vacuum-sum input and already lands in the observed band, so the $10^{120}$ gap is an artifact of the wrong mechanism rather than a fine-tuning problem inside RS.
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