Kernel clustering hardness and Gaussian partition benchmark

Family 096: The Gaussian propeller conjecture in every dimension. First review, 9 October 2026 Australia/Brisbane.

Problem and potential new use

Clustering researchers can evaluate Gaussian first-moment partitions and the stated identity-target kernel objective.

Applicability and commercial boundary

The Gaussian partition optimum and reduction assumptions do not promise improved arbitrary clustering accuracy or determine the practical difficulty of a dataset.

Initial business decision

Research infrastructure. Commercial demand and profitability remain hypotheses.

Next verification action

Reproduce the three-sector extremizer and review the reduction's rational positive-semidefinite input model.

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.