Manuscript IV@1 · IV.tex · section · 351cb2d7

Kernel topology

Cutoff ledger: Model 2 › Kernel topology · lines 3572–3599

Coefficient	Proven result
Pair $P_{R}$	Hilbert–Schmidt convergence: $∥ P_{R} - P ∥_{HS} \leq C_{P} R^{- 1/2}$ .
Number leg $L_{R}$	Operator-norm convergence: $∥ L_{R} - L ∥ \leq C_{L} R^{- 1}$ ; $L$ is compact.
Number Hilbert–Schmidt norm	For nonzero $f$ , $∥ L_{R} ∥_{HS}^{2}$ is comparable to $R$ . The limit is not Hilbert–Schmidt.
Consolidated pair	$∥ K_{R} - K ∥ = 2 ∥ P_{R} - P ∥_{HS}$ .
Constant coefficient	Zero; cross-species reordering produces no constant.
Uncut pairing	Agrees with the symmetric $Dom N$ operator form on the original dense test domain.