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The Kirchberg-Rordam character question: does absence of characters on the central sequence algebra characterize Jiang-Su stability?

Theorem 1.1: for every nonzero unital separable complex C*-algebra $A$ and every free ultrafilter $\omega$ , $F_\omega(A)$ has no characters iff $A\cong A\otimes_{\min}\mathcal Z$ ; no nuclearity, simplicity, trace or comparison hypothesis. Theorem 1.2: every nonzero unital characterless $D$ admits a unital map $I(2,3)\to D^{\otimes_{\max}m}$ for some $m$ . Corollary: the infinite minimal tensor power of a nonzero unital separable characterless algebra is $\mathcal Z$ -stable (bearing on Kirchberg-Rordam Question 3.7, via Dadarlat-Toms). Not shown: any finite tensor power is $\mathcal Z$ -stable, or nonseparable cases.

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Prior state unknown→proved

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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: The Kirchberg-Rordam character question: does absence of characters on the central sequence algebra characterize Jiang-Su stability? · Kirchberg-Rordam character question

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VibeMathed record: The Kirchberg-Rordam character question: does absence of characters on the central sequence algebra characterize Jiang-Su stability?

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No independent mathematician has checked this yet. Checked here: abstract, introduction and Theorem 1.1, read against Question 3.1 as the paper quotes it; proof not refereed. Lean-checked on Comparator challenge CharacterCriterion, declaration OAI.KirchbergRordam.character_criterion in OAI/Analysis/CharacterCriterion/Main.lean, listed in lean/formalization.yaml; statement read here, not rebuilt. The challenge file builds the norm ultrapower, central sequence algebra, minimal tensor product and the Jiang-Su algebra itself (about 2,100 lines of definitions), and states: for every nontrivial separable unital C*-algebra and free ultrafilter, no characters on the central algebra iff $A\cong A\otimes_{\min}\mathcal Z$ . That is the headline. The infinite tensor power corollary is not in the formal statement. The proof uses a companion OpenAI lemma (catalog entry robert-tikuisis-conjecture-c1).