# 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](source.json) for the exact manuscripts and available scope notes.