# Abundance and Iitaka dependency evidence

Family 034: Log abundance for compact Kähler spaces under logarithmic Iitaka subadditivity. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Record when a claimed log-abundance result permits a semiample multiple and an Iitaka fibration.

## Applicability and commercial boundary

The result uses log Iitaka; a uniform existence or index bound is not an implemented section constructor or a runtime guarantee.

## 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 effective bounds and the exact dependence on rational coefficient sets before proposing a CAS extension.

## 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).

[Log abundance for compact Kähler spaces under logarithmic Iitaka subadditivity](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Log-abundance-for-compact-Kahler-spaces-under-logarithmic-Iitaka-subadditivity-October-6-2026/main.pdf).