# Symbolic representation complexity audit

Family 108: A cubic permanent–determinant lower bound. First review, 8 October 2026.

## Problem and potential new use

Computer-algebra teams could check whether a proposed determinant-based encoding of the permanent is compatible with known size limits.

## Applicability and commercial boundary

The cubic lower bound is specific to border determinantal representations over complex numbers; it is not a general lower bound for all permanent algorithms.

## Initial business decision

Research infrastructure. Buyer demand and profitability remain hypotheses. This first pass does not establish a validated commercial market.

## Next verification action

Review the representation model and identify whether any actual rewrite or encoding workflow needs this audit.

## Evidence scope

Catalog statement reviewed; inspect linked opportunity dossier for any deeper source review. This record alone does not establish full manuscript or proof verification.

Source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json) for the exact manuscripts and available scope notes.