Arithmetic circuit restriction benchmark

Family 135: Homogeneous depth-five lower bounds for iterated matrix multiplication. First review, 8 October 2026.

Problem and potential new use

Circuit-complexity researchers can reproduce a sharp lower bound for a constrained homogeneous depth-five representation.

Applicability and commercial boundary

Restricted circuit lower bounds do not imply slow unrestricted matrix multiplication or a security guarantee.

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

Review the homogeneous gate model and add a bounded teaching example to the feasibility 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.