# Model-theory threshold and axiom provenance

Family 240: Shelah's eventual categoricity and the prescribed-threshold obstruction. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Logic researchers can track uniform eventual categoricity thresholds and the separate CH obstruction to a prescribed threshold.

## Applicability and commercial boundary

Infinite-cardinal categoricity is not finite database uniqueness or a schema-matching algorithm. ZFC and conditional claims need separate records.

## Initial business decision

Research reference or conditional symbolic/verification engineering. No practical implementation, recurring buyer need or profitability has been demonstrated; a weak business bridge is explicitly deferred.

## Next verification action

Map cardinal and set-theoretic assumptions to exact statements.

## Evidence scope

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

[A CH obstruction to a prescribed categoricity threshold](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-CH-Obstruction-to-a-Prescribed-Categoricity-Threshold-September-24-2026/paper.pdf).