# Hyperbolicity-to-projectivity evidence ledger

Family 051: Kobayashi’s canonical-ampleness conjecture. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Track the claimed implication from absence of entire curves on a compact Kähler manifold to an ample canonical bundle.

## Applicability and commercial boundary

Absence of all entire curves is not certified by a finite sample; the result supplies no terminating general recognition test.

## 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

Inspect whether any effective restricted-class hyperbolicity test is available.

## 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).

[Canonical ampleness of compact hyperbolic Kähler manifolds](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Canonical-ampleness-of-compact-hyperbolic-Kahler-manifolds-September-23-2026/canonical-ampleness.pdf).