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 for the exact manuscripts and available scope notes.