IndisputableMonolith.NavierStokes.RM2U.NonParasitism
The module states a temporary non-parasitism hypothesis on the radial coefficient profile at a fixed time slice. Researchers closing the RM2U gate for Navier-Stokes ancient solutions cite the hypothesis when linking energy identities to integrability. The module assembles the hypothesis with related boundary integrability lemmas that connect to the coercive control steps.
claimLet $A(r)$ denote the radial coefficient for $r$ at least 1 at fixed time $t$ and test parameter $b$. The non-parasitism hypothesis requires that this profile satisfies an integrability condition that prevents parasitic growth in the weighted tail moments.
background
The RM2U framework recasts the Navier-Stokes tail problem as a one-dimensional radial coefficient equation for $A(r)$, $r$ at least 1, at fixed time $t$ and spherical direction $b$. Core defines the tail-flux boundary term. EnergyIdentity reduces vanishing of the tail flux to two integrability obligations for the boundary term and its derivative. RM2Closure hosts the coercive ell equals 2 control implying finiteness of the log-critical shell moment integral of absolute value of A over r, and hence boundedness of the affine obstruction.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module supplies the non-parasitism hypothesis instantiated in BetInstantiation to connect weighted L2 moments to the RM2U closure pipeline and in TailFluxInstantiation to link Galerkin extraction to the Bet1 integrability conditions. It fills the temporary hypothesis slot in the navier-dec-12-rewrite.tex development for the RM2U tail gate.
scope and limits
- Does not derive the non-parasitism condition from the Navier-Stokes equations.
- Does not address time-dependent coefficient profiles.
- Does not supply numerical verification or simulation data.
- Does not extend to higher spherical harmonics beyond ell equals 2.
used by (2)
depends on (3)
declarations in this module (61)
-
structure
NonParasitismHypothesis -
structure
Bet1BoundaryIntegrableHypothesis -
theorem
nonParasitism_of_bet1 -
theorem
bet1_boundaryTerm_integrable_of_L2_mul_r -
theorem
bet1_boundaryTerm_integrable_of_A2r_and_coercive -
structure
Bet1BoundaryIntegrableHypothesisAlt -
theorem
bet1_of_bet1Alt -
structure
Bet2SelfFalsificationHypothesis -
def
nthPrime -
theorem
nthPrime_prime -
theorem
strictMono_nthPrime -
theorem
pairwise_coprime_nthPrime -
structure
NonResonantSchedule -
def
canonical -
theorem
not_summable_of_uniform_abs_lowerBound -
structure
PrimeScheduleSelfFalsification -
theorem
bet2_of_primeSchedule -
structure
Payments -
structure
U4PaymentUpperBoundHypothesis -
structure
C2VanishingInjectionHypothesis -
abbrev
U4VanishingInjectionRateHypothesis -
theorem
c2VanishingInjection_comp_two -
theorem
u4PaymentUpperBound_of_injection -
theorem
u4PaymentUpperBound_of_u4InjectionRate -
structure
U4PaymentsControlledByInjectionRateHypothesis -
structure
U4PayXiControlledByInjectionRateHypothesis -
structure
U4PayRhoControlledByInjectionRateHypothesis -
structure
U4BandBudgetControlledByInjectionRateHypothesis -
theorem
u4PayRhoControlledByInjectionRate_of_bandBudget -
structure
U4InjectionPaymentPackageHypothesis -
theorem
u4PaymentUpperBound_of_paymentControl -
theorem
u4PaymentUpperBound_of_u4Package -
structure
ForcingToTwistOrBandPaymentHypothesis -
structure
NoRigidRotationAbsorptionHypothesis -
structure
NegativeSigmaForcesBandPaymentHypothesis -
structure
NoPersistentNullAlignmentHypothesis -
structure
ExportSplitHypothesis -
structure
ExportForcesPaymentHypothesis -
theorem
of_split -
structure
AbsorptionImpliesAffineAnsatzHypothesis -
structure
AffineAnsatzImpossibleHypothesis -
structure
TailStrainTimeVariationHypothesis -
abbrev
TailVorticityL2TimeModulusHypothesis -
theorem
tailStrainTimeVariation_of_lipschitz -
structure
AbsorptionClassImpossibleHypothesis -
structure
ConcavityImpossibleHypothesis -
structure
U4NoExportHypothesis -
theorem
of_u4 -
structure
TailFluxNonVanishImpliesExportAtSmallScales -
theorem
bet2SelfFalsification_of_u4 -
structure
Quasi2DEliminationHypothesis -
structure
BackwardUniquenessNSHypothesis -
structure
Quasi2DToComparisonSolutionHypothesis -
structure
Quasi2DToExactSymmetryHypothesis -
structure
SymmetryClassImpossibleHypothesis -
theorem
nonParasitism_of_bet2 -
structure
Bet3CoerciveL2Hypothesis -
theorem
rm2Closed_of_bet3 -
theorem
rm2Closed_of_nonParasitism -
theorem
rm2Closed_of_bet1 -
theorem
rm2Closed_of_bet2