# Rational constraint solver completeness contract

Family 004: Hilbert’s tenth problem over ℚ. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Symbolic solver teams can distinguish supported decidable subclasses and unknown outcomes from an impossible universal decision promise.

## Applicability and commercial boundary

The undecidability statement concerns arbitrary-variable integer polynomials with rational zeros. It does not rule out complete algorithms for restricted families or validated answers for particular inputs.

## Initial business decision

Research infrastructure or conditional engineering until a computable implementation, effective bounds and a recurring buyer need are demonstrated. No commercial novelty or profitability is established.

## Next verification action

Add rational-domain, supported-class and unknown-result fields to the evidence workbench; inspect the reduction before relying on the new claim.

## Evidence scope

The catalog statement was individually reviewed. Main-paper abstracts and available selected formal scope notes were also inspected. No independent Lean verification was run. Source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json).

[Hilbert’s tenth problem over the rational numbers](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Hilberts-tenth-problem-over-the-rational-numbers-October-6-2026/main.pdf).