vacuum_energy_uniform
plain-language theorem explainer
Phase-locked vacuum energy density is translation-invariant across the integer lattice. Cosmologists deriving the cosmological constant from Recognition Science phase saturation would cite this to establish isotropy of the vacuum J-cost contribution. The proof is a one-line term that directly exhibits shift invariance of the constant function via reflexivity.
Claim. Let $f : {Z}^3 {to} {R}$ be the constant function $f(v) = (11/16) E_{coh}$. Then $f(v + d) = f(v)$ for all lattice vectors $v, d$.
background
VoxelSymmetric is the structure asserting translation invariance on the Z^3 carrier: no voxel is distinguished by location. phaseLockEnergy is the constant per-voxel value passiveFraction times E_coh, with passiveFraction fixed at 11/16 by the combinatorial Q_3 mode budget. The module shows phase-locked modes are committed ledger entries carrying zero J-maintenance cost, so their contribution forms a uniform background density.
proof idea
The term constructs the VoxelSymmetric record by supplying the shift_invariant field as a lambda that returns rfl for every displacement, since the input function ignores its voxel argument entirely.
why it matters
This supplies the uniformity field required by vacuumUniformityCert, which packages the full vacuum uniformity statement including fraction sums and positivity. It completes the structural half of the argument that phase-locked J-cost yields an isotropic background, directly supporting the bridge from PhaseSaturationVacuum to T_mu nu^vac. The physical identification step remains a separate hypothesis.
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