Manuscript Em01-B@3 · Em01-B-v3.tex · section · 69189992

Estimate ledger

An actual estimate for the complete retained family › Estimate ledger · lines 1393–1430

Estimate	Complete expression controlled	Status
Finite test order with polynomial smoothing growth	All internal blocks and all vertex terms	Proved: order five and loss $δ^{- q - 13}$ .
Normalized two-parameter growth	Tests scaled toward $N$ , including the normal origin	Proved: (eq:two-parameter); still has smoothing loss.
Smoothing-uniform finite-order bound	The named complete sum near $N$	Not proved. Internal order alone does not remove $δ^{- q - 13}$ .
Fourier decay off a selected output cone	Localized complete crossed sum	Conditional criterion below; no characteristic cone estimate is verified.
Summable complete-sum differences	Dyadic regularizations of $K_{ret}$	Not proved. This would establish a fixed-kernel limit.
Uniform input continuity for a limit map	Every reconstructed input	Stronger than a limit for $K_{ret}$ ; remains conditional.

The proved row is not relabeled as the missing smoothing-uniform estimate. A future improvement must preserve the complete tensor and branch sum before asserting a cancellation or a smaller growth exponent.