Covering-density research planner

Family 092: The optimal order of convex-body covering density. First review, 9 October 2026 Australia/Brisbane.

Problem and potential new use

Researchers designing high-dimensional coverings can use the optimal worst-case order to assess theoretical targets.

Applicability and commercial boundary

An existence bound with universal constants does not give an efficient lattice construction, finite-region layout or optimized packing. Covering and packing are different tasks.

Initial business decision

Defer direct product. Commercial demand and profitability remain hypotheses.

Next verification action

Read effective construction details and test whether any explicit finite regime is useful.

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.