The first-order compression defect is a commutator with the vacuum symbol: ddelta = [Q, E_I D_chi E_I] (F1 Lemma 6.1)

Status: proved — a complete structured proof.

Area: Optimality of recovery channels (O8, Phases 3 and 3b) · Card type: result · Knowledge-base id: compression-defect-commutator-form

Statement

With d := E_I D_chi E_I one has ddelta = E_I[P, D_chi]E_I = [Q, d], and on the isometric orbit the first-order defect is delta^(1)(zeta,0,0) = [Q, d - zeta] for anti-self-adjoint zeta = E_D zeta E_D, so the tangent problem is expressed through (Q, E_D) and the single operator d.

How to verify

No verification recipe recorded on this card.

Evidence

• rigor/exact_optimum_tangent_problem.tex — document, at lem:commQ

Related claims

None recorded.

Review

Review record: passed 2026-09-23 by REF-DEP-CFT-A1.

The referee's report and the card's event log stay in the private knowledge base; only the verdict, the date and the referee are published here.

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