# Algebraic cancellation counterexample fixture

Family 047: Zariski cancellation and affine fibrations over the complex numbers. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Test the inference that a variety whose product with the affine line is affine five-space must itself be affine four-space.

## Applicability and commercial boundary

The complex affine example concerns algebraic isomorphism, not cancellation of finite numeric vectors or database columns.

## Initial business decision

Research reference or conditional symbolic/verification engineering. No recurring buyer need, practical implementation or profitability has been demonstrated. Defer a standalone commercial product until a constructive example and a measurable workflow improvement exist. These records also identify unsupported inferences that an evidence platform could flag.

## Next verification action

Read explicit equations and maps before building an exact symbolic fixture.

## Evidence scope

The repository catalog statement was individually read. Main-paper construction, effectiveness and selected formal-scope comparison remain queued for this record. No independent Lean verification was run. Source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json).

[An explicit failure of complex affine-space cancellation](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/An-explicit-failure-of-complex-affine-space-cancellation-September-23-2026/paper.pdf).