Banach geometry property implication map

Family 326: The cotype–cotype conjecture under the approximation property. First review, 9 October 2026 Australia/Brisbane.

Problem and potential new use

Functional-analysis researchers can index the equivalence among the stated cotype, type and K-convexity conditions under the approximation property.

Applicability and commercial boundary

The equivalence concerns abstract spaces and does not directly supply efficient feature transformation or finite-data learning guarantees.

Initial business decision

Research infrastructure. Commercial demand and profitability remain hypotheses.

Next verification action

Review definitions and the approximation-property assumption before creating a reusable theorem record.

Evidence scope

The catalog statement was individually reviewed. Main-paper and selected formal-scope passages were additionally inspected for families 090, 093, 094, 097, 325, 328 and 332; this record does not claim a full proof audit or independent Lean verification. Source revision fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb. See source metadata.