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Manuscript Em01-G@5 · Em01-G-v5.tex · section · 3fbfe951

Independence and dependencies

Frozen family and principal statements › Independence and dependencies · lines 379–418

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“Intrinsic” means uniquely determined by the fixed positive-scale family, including its profile and scale convention. Three questions are kept separate:

  1. admissible relative-cutoff independence;

  2. independence of auxiliary core or residual localizers;

  3. profile independence.

The first is exact at sufficiently small scales. Whole-support sector coefficients do not use an auxiliary core cutoff. A fixed residual localization defines its own localized family. Profile independence is not asserted.

ClaimEssential inputs
Supported highest-jet cancellationConstant-slot identity and highest normal polynomial.
Supported pure second-normal coefficientCartesian residual-order reduction and source divergence.
Supported leading coefficientGauge-slot identity and density contraction.
Whole-support scalar expansionExact cone-plus-tail reduction and averaged resolvent estimate.
Non-tip cubic cancellationDerivative placement and the null contraction of .
Positive- quadratic coefficientExact Klein–Gordon reduction and the second log-profile moment.
Complete-family detecting testQuadratic coefficient, test-jet evaluation, and support isolation.