# Very-general-point interpolation boundary

Family 039: Nagata’s conjecture and maximal Seshadri constants. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Audit interpolation and Seshadri claims that invoke the Nagata bound for at least ten very general points.

## Applicability and commercial boundary

Very general is stronger than an arbitrary observed point set. Strict multiplicity inequalities and characteristic regimes must be preserved.

## 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

Extract an explicit specialization with separately checked hypotheses rather than certify arbitrary data.

## 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).

[Nagata's conjecture for plane curves](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Nagatas-Conjecture-for-Plane-Curves-September-23-2026/main.pdf).