# Conic formulation scope checker

Family 095: Hyperbolicity cones without semidefinite lifts. First review, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Optimization teams can flag promises to encode every hyperbolicity cone exactly by a finite semidefinite lift.

## Applicability and commercial boundary

A counterexample to universal representability does not prohibit approximations or efficient algorithms for specific cones.

## Initial business decision

Research infrastructure. Commercial demand and profitability remain hypotheses.

## Next verification action

Extract an explicit cone and identify an existing modeling claim that the counterexample would challenge.

## 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).