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IndisputableMonolith.NavierStokes.RM2U.TailFluxInstantiation

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The module instantiates tail-flux vanishing for ancient Navier-Stokes solutions whose ℓ=2 radial coefficient satisfies the decay bound |A(r)| ≤ C r^{-3/2} (r ≥ 1) that follows from finite energy. Researchers closing the RM2U gate in the Navier-Stokes regularity problem would cite this wiring step. It assembles the radial spec, energy identities, non-parasitism hypothesis, and coercive closure lemmas into a single import chain without introducing new proofs.

claimFinite-energy ancient solutions yield the decay $|A(r)| \leq C r^{-3/2}$ for $r \geq 1$, which forces the tail-flux boundary term and its derivative to be integrable, thereby closing the RM2U tightness gate under the non-parasitism hypothesis.

background

The module sits inside the RM2U reduction of the Navier-Stokes regularity problem to a one-dimensional radial coefficient problem. Core supplies the definition of the scalar radial coefficient A(r) for fixed time and spherical test direction b. EnergyIdentity reduces vanishing of the tail-flux boundary term at infinity to two integrability obligations on that term and its derivative. NonParasitism isolates the single hard hypothesis that must remain open. RM2Closure supplies the classical steps from coercive ℓ=2 control to finiteness of the log-critical shell moment and boundedness of the affine obstruction.

proof idea

This is an instantiation module. It imports the four upstream modules and wires the decay hypothesis through the energy-identity reduction and the RM2Closure steps to obtain the tail-flux vanishing statements used downstream. No new lemmas are proved inside the module itself.

why it matters in Recognition Science

The module supplies the concrete tail-flux instantiation required by BetInstantiation, which in turn connects the weighted L² moment hypothesis to the full RM2U closure pipeline. It therefore occupies the precise slot between the algebraic energy identities and the Bet1 route in the navier-dec-12-rewrite.tex argument.

scope and limits

used by (1)

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depends on (4)

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declarations in this module (22)