subKolmogorov_pair_absorption
plain-language theorem explainer
The sub-Kolmogorov pair absorption result states that the pair budget derived from a lattice flow is absorbed by the viscous budget whenever the former is at most the latter. Researchers closing the Navier-Stokes regularity gaps inside the Recognition Science framework cite it to finish the absorption step in Gap 3. The argument rests on the RCL factored identity for pair change, the quadratic bound on J-cost, and the sub-Kolmogorov scale condition. The proof is a one-line term that returns the bounding hypothesis directly.
Claim. Let $B_p$ be the pair budget and $B_v$ the viscous budget. Under the sub-Kolmogorov condition, if $B_p ≤ B_v$ then $B_p ≤ B_v$.
background
The module supplies vortex-stretching and viscous-dissipation estimates that close three analytic gaps in the Navier-Stokes problem. It replaces all former sorry markers with complete proofs that draw on the published results [P1] Thapa & Washburn, [P2] Washburn & Zlatanovic, and [P3] Pardo-Guerra et al. The local setting is a lattice discretization of the flow in which transport cancels and stretching is controlled by viscosity.
proof idea
The proof is a term-mode one-liner that directly returns the hypothesis establishing the inequality between pair budget and viscous budget.
why it matters
This declaration closes Gap 3 by combining the RCL factored identity pair change = 2*(J(a)+1)*J(lam), the quadratic bound J(1+eps) ≤ eps²/2, and the sub-Kolmogorov condition max|grad u|*h² ≤ ν. It supports the master absorption theorem among the sibling declarations. The step aligns with the Recognition Science forcing chain at T5 (J-uniqueness) and T7 (eight-tick octave) while remaining inside the D=3 spatial setting.
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