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 for the exact manuscripts and available scope notes.