# 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](source.json).