Katsumasa–Roff–Yoshinaga conjecture on Hausdorff continuity of magnitude
Yes, with a quantitative bound: magnitude is Hausdorff-continuous at every nonempty finite subset of a finite-dimensional positive definite normed space, with a local Lipschitz-type estimate in the Hausdorff distance whose constants depend on the number of points, the dimension and the least eigenvalue of the similarity matrix, and with compact approximants allowed. The paper also obtains convergence of aggregated weights and a continuity criterion in L_1 by local order oscillation, and, in the other direction, a compact convex subset of L_1[0,1] whose finite subsets approach a singleton with magnitudes tending to 3/2, which refutes an implication stated in Kalisnik and Lesnik's preprint from the one-point property to singleton continuity.
Exact FrontierDelta
Scope and record
Occurred: Sep 20, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: unreviewed. Publication: preprint. AI contribution: ai-co-developed. 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: Katsumasa–Roff–Yoshinaga conjecture on Hausdorff continuity of magnitude · Magnitude continuity at finite sets
Confidence: Not scored
Registry verification: unreviewed · preprint · candidate
Attribution
VibeMathed
registry · event recorded by
GPT-6 Astra Pro
model · ai model contributor · OpenAI
Claude Fable 5.1
model · ai model contributor · Anthropic
Mingchang Liu
human · human collaborator
Lineage and corrections
This event attributed to Claude Fable 5.1
This event attributed to GPT-6 Astra Pro
Yes, with a quantitative bound: magnitude is Hausdorff-continuous at every nonempty finite subset of a finite-dimensional positive definite normed space, with a local Lipschitz-type estimate in the Hausdorff distance whose constants depend on the number of points, the dimension and the least eigenvalue of the similarity matrix, and with compact approximants allowed. The paper also obtains convergence of aggregated weights and a continuity criterion in L_1 by local order oscillation, and, in the other direction, a compact convex subset of L_1[0,1] whose finite subsets approach a singleton with magnitudes tending to 3/2, which refutes an implication stated in Kalisnik and Lesnik's preprint from the one-point property to singleton continuity. parent of this event
Katsumasa, Roff and Yoshinaga (2025), Conjecture 1.3 evidence for this event
This event attributed to Mingchang Liu
Katsumasa–Roff–Yoshinaga conjecture on Hausdorff continuity of magnitude evidence for this event
Katsumasa–Roff–Yoshinaga conjecture on Hausdorff continuity of magnitude parent of this event
Kalisnik and Lesnik (2025), the skew-subset partial result evidence for this event
VibeMathed record: Katsumasa–Roff–Yoshinaga conjecture on Hausdorff continuity of magnitude evidence for this event
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