cft-cmi

Hypothesis H3 of the tangent problem (cone hypothesis): every admissible isometry generator with a feasible first-order datum lies in the model cone modulo the linear class

Status: conjectural — believed, with partial evidence; not proved. Stated under hypotheses H3, quoted below.

Area: Optimality of recovery channels (O8, Phases 3 and 3b) · Card type: conjecture · Knowledge-base id: tangent-h3-cone-hypothesis

Statement

For every admissible isometry generator zeta with A(zeta,0,0) in the form domain F there are alpha, beta >= 0 and eta in the b-closure of the linear class L with A(zeta,0,0) = alpha A(zeta_0,0,0) + beta A(zeta_inf,0,0) + eta in F; this is proved for generators of vector-field type and open for shift semigroups of multiplicity > 1 and for unbounded skew-adjoint zeta = i m(y) whose [Q, i m] (= -A(zeta,0,0)) lies outside the closure of L.

Hypotheses

The statement is made under named hypotheses. The sentences are quoted from the statement above; read the status badge only together with them.

Hypothesis labels used: H3.

Hypothesis H3 of the tangent problem (cone hypothesis): every admissible isometry generator with a feasible first-order datum lies in the model cone modulo the linear class.

How to verify

rigor/exact_optimum_tangent_problem.tex Def. 4.12 (hyp:H3, :1191-1207, read in F; b-closure of L as in eq:deltastar), Remark 4.13 (rem:H3space: under H3, alpha = 0 once A(zeta_0,0,0) is not in F, and then (e) holds outright), Remark 4.14 (rem:H3, :1231-1261: proved for vector-field generators by Prop. 4.10(3); the two families that escape); Sec. 7, Conditional item 3 (:1614-1620).

Evidence

Related claims

None recorded.

Review

Review record: passed 2026-09-23 by REF-DEP-CFT-A4.

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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