What was already known
Choice implies the Partition Principle, but an injection reversing a surjection need not select a member of each fiber. The unresolved target asks whether the cardinal comparison can recover full Choice.
What changed and why it matters
Separates the Partition Principle from full Choice under the stated relative-consistency hypothesis.
The AI contribution
OpenAI attributes these manuscripts to its internal model. The entry does not infer individual human contributions beyond that publisher attribution.
Limitations
This is a relative-consistency assertion under consistency of ZF. The companion transitive-model formulation has a stronger starting-model hypothesis; it is not an unconditional existence claim. Preprint. This is a source-statement and significance assessment, not a proof audit. No independent checking or successful formal compilation is asserted by this entry.
Verification evidence
Evidence labels show what supports the claim. Importance rates its impact if correct.
Author claim
The publisher reports the scoped result. AIProofWatch has not independently validated its correctness.
Accessible artifact / proof
The original written argument is accessible. Availability does not establish a successful proof check or Lean verification.
Correction and publication history
Historical report added after statement, scope, and importance review. No proof audit or formal checking asserted; subscriber alerts disabled.
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