Depth-three circuit lower-bound teaching and benchmark module

Family 112: Beyond the square-root exponent for depth-three circuits. First review, 8 October 2026.

Problem and potential new use

Circuit-complexity researchers and educators could use an explicit language separating a restricted circuit model from polynomial-time decision.

Applicability and commercial boundary

The theorem does not show hard instances for unrestricted software or create a practical cryptographic primitive.

Initial business decision

Defer direct product. Buyer demand and profitability remain hypotheses. This first pass does not establish a validated commercial market.

Next verification action

Inspect the explicit language and identify a bounded demonstrator; prefer adding it to an existing research workbench.

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.