# Real constraint complexity scope explorer

Family 141: Existential–universal real sentences in the counting hierarchy. First review, 8 October 2026.

## Problem and potential new use

Symbolic-verification researchers can classify certain existential and existential-universal real decision problems within the counting hierarchy.

## Applicability and commercial boundary

Membership in a complexity hierarchy does not produce a fast practical solver or remove representation and numerical-conditioning challenges.

## 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 constructive decision procedure and compare its operations with existing real-algebraic solving workflows.

## 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.