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Artifact ↗Source authenticated
Kirchberg-Rordam comparison question: pure infiniteness implies strong pure infiniteness, and weak equals strong for exact C*-algebras
Theorem 1.1: every complex C*-algebra in which every positive element is properly infinite is strongly purely infinite, with an arbitrary cross term in the diagonalization. Theorem 1.2: for exact algebras, proper infiniteness of for one fixed and all positive implies proper infiniteness of every positive element, hence strong pure infiniteness. Corollary: a separable nuclear algebra with this fixed-amplification property absorbs , with no unitality or simplicity assumption (via Kirchberg's central-sequence results). Not settled: whether weak pure infiniteness implies pure infiniteness for non-exact algebras, which the paper states remains outside its conclusions.
Exact FrontierDelta
Prior state unknown→proved
Scope and record
Occurred: Sep 25, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: lean-checked. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.
Canonical aliases: Kirchberg-Rordam comparison question: pure infiniteness implies strong pure infiniteness, and weak equals strong for exact C*-algebras · Pure vs strong pure infiniteness
Confidence: Not scored
Registry verification: lean checked · announcement · partial
Attribution
VibeMathed
registry · event recorded by
Unreleased internal OpenAI model
model · ai model contributor · OpenAI
Artifacts and verifiers
lean artifact · pending
Artifact ↗Compute record
No linked compute attempts recorded.
Lineage and corrections
Lean proof (OAI.WeakPureInfiniteness.exact_weaklyPurelyInfinite_stronglyPurelyInfinite) evidence for this event
Schafhauser-Tikuisis-White, Nuclear C*-algebras: 99 problems (Problem LXXII) evidence for this event
This event attributed to Unreleased internal OpenAI model
Kirchberg-Rordam comparison question: pure infiniteness implies strong pure infiniteness, and weak equals strong for exact C*-algebras evidence for this event
Lean proof (OAI.MainGap.Manuscript.individual_to_strong_main) evidence for this event
VibeMathed record: Kirchberg-Rordam comparison question: pure infiniteness implies strong pure infiniteness, and weak equals strong for exact C*-algebras evidence for this event
Kirchberg-Rordam comparison question: pure infiniteness implies strong pure infiniteness, and weak equals strong for exact C*-algebras parent of this event
Theorem 1.1: every complex C*-algebra in which every positive element is properly infinite is strongly purely infinite, with an arbitrary cross term in the diagonalization. Theorem 1.2: for exact algebras, proper infiniteness of for one fixed and all positive implies proper infiniteness of every positive element, hence strong pure infiniteness. Corollary: a separable nuclear algebra with this fixed-amplification property absorbs , with no unitality or simplicity assumption (via Kirchberg's central-sequence results). Not settled: whether weak pure infiniteness implies pure infiniteness for non-exact algebras, which the paper states remains outside its conclusions. parent of this event
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