passiveFraction
The declaration supplies the constant fraction 11/16 of phase-locked modes drawn from the Q₃ budget. Cosmologists working in the Recognition Science setting cite the value when constructing the isotropic vacuum energy density per voxel. The definition consists of a direct numerical assignment with no lemmas or computation required.
claimThe passive fraction of phase-locked modes from the Q₃ mode budget is defined as $11/16$.
background
The Vacuum Uniformity module shows that phase-locked modes on the ℤ³ carrier contribute a constant J-cost background. These modes are committed ledger entries whose maintenance cost vanishes under the J-function. The module invokes VoxelSymmetry to guarantee that the combinatorial fraction of such modes is the same at every lattice point, yielding a spatially uniform vacuum energy density.
proof idea
The declaration is a direct definition that assigns the rational constant 11/16. No lemmas are invoked and no tactics are applied.
why it matters in Recognition Science
This definition supplies the numerical input to phaseLockEnergy and to the uniformity theorem vacuum_energy_uniform, which asserts VoxelSymmetric (fun _ => phaseLockEnergy). It realizes the combinatorial step in the module argument that the fraction is independent of position. The same 11/16 appears in the bridge from PhaseSaturationVacuum to the stress-energy tensor T_μν^vac.
scope and limits
- Does not derive the value 11/16 from the J-function or Q₃ structure.
- Does not prove spatial uniformity of the energy density.
- Does not identify the J-cost with observed vacuum energy.
- Does not constrain the coherent energy scale E_coh.
formal statement (Lean)
26noncomputable def passiveFraction : ℝ := 11 / 16
proof body
Definition body.
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