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Set-theoretic assumption dependency viewer
Family 244: The Partition Principle does not imply Choice. First application triage, 9 October 2026 Australia/Brisbane.
Problem and potential new use
Formalization teams can distinguish the Partition Principle, ordinal-indexed choice and full Choice under the stated consistency constructions.
Applicability and commercial boundary
Relative consistency and transitive-model assumptions do not create an operational resource-selection algorithm.
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
Preserve each metatheoretic hypothesis and conclusion in the provenance registry.
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.