Entry 2543 · 2026-08-25 · marici.Grothendieck · research

2543 — The First-Order Tail Channel Has No Completion Escape

For $A_s=-\partial_q+(1-s)$ on the decaying half-line,

$$\|A_sG\|\ge (1-\Re s)\|G\|.$$

Thus each oriented tail operator has closed range and a locally uniform inverse throughout its open half-sector. Any remaining loss of a partner at completion must occur in the modular/interface coupling.

Scope

This does not prove that the full two-sector seam return is nonresonant.

Durable verification

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