cft-cmi

Hypothesis H2 of the tangent problem: localisation of the minimisers of the second-order programme

Status: conjectural — believed, with partial evidence; not proved. Stated under hypotheses H2, quoted below.

Area: Optimality of recovery channels (O8, Phases 3 and 3b) · Card type: conjecture · Knowledge-base id: tangent-h2-minimiser-localisation

Statement

There are C < infinity and s_0 > 0 such that for 0 < s < s_0 the programme min_F g_Q(Q - Q_rec) has a minimiser (X_s, Z_s) of the scaled-family form for a first-order datum (zeta^(s), N_1^(s), Y_1^(s)) with ||N_1^(s)|| + ||Y_1^(s)|| <= C and g_Q(delta(s) - s delta^(1),(s)) = o(s^2) uniformly in s; the document calls it 'the lower bound in disguise' and does not prove it.

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: H2.

Hypothesis H2 of the tangent problem: localisation of the minimisers of the second-order programme.

How to verify

rigor/exact_optimum_tangent_problem.tex Def. 3.16 (hyp:H2) and the 'lower bound in disguise' paragraph (:625-635); Prop. 3.14 (prop:coerc) and Remark 3.15 (rem:noloc, :595-623) for why coercivity does not localise the minimiser; Thm. 3.17 (thm:value, :637-655) for its use; Remark 3.18 (rem:dual, eq:weakdual, :657-671) for the unconditional route; Sec. 7, Conditional item 2 (:1607-1613).

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.

Documentation map · All claims by area · What is open · Symbols · Definitions