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The Inverse Generator Problem on Hilbert Spaces
One finite-dimensional construction settles several related questions. Besides the inverse generator problem, it gives a generator whose Cayley transforms satisfy the ordinary Kreiss resolvent condition but are neither strongly Kreiss bounded nor power bounded, and it shows the Crank-Nicolson scheme is unstable in operator norm both over long times at fixed step size and under mesh refinement at fixed final time. Version 2 adds Theorem 1.4, whose part (i) solves Question 6.1 of Chalmoukis, Tsikalas and Yakubovich; that question is tracked as its own entry.
Exact FrontierDelta
Prior state unknown→disproved
Scope and record
Occurred: Aug 6, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: unreviewed. Publication: preprint. AI contribution: ai-assisted. Editorial metadata: CC BY 4.0; linked content retains its own rights.
Canonical aliases: The Inverse Generator Problem on Hilbert Spaces · Inverse generator problem
Confidence: Not scored
Registry verification: unreviewed · preprint · resolved
Attribution
VibeMathed
registry · event recorded by
Emiel Lorist
human · human collaborator
Martin Meyries
human · human collaborator
Mark Veraar
human · human collaborator
ChatGPT 5.6 Pro
model · ai model contributor · OpenAI
Claude Fable
model · ai model contributor · Anthropic
Artifacts and verifiers
Compute record
No linked compute attempts recorded.
Lineage and corrections
This event attributed to Mark Veraar
This event attributed to Martin Meyries
This event attributed to Emiel Lorist
This event attributed to Claude Fable
This event attributed to ChatGPT 5.6 Pro
One finite-dimensional construction settles several related questions. Besides the inverse generator problem, it gives a generator whose Cayley transforms satisfy the ordinary Kreiss resolvent condition but are neither strongly Kreiss bounded nor power bounded, and it shows the Crank-Nicolson scheme is unstable in operator norm both over long times at fixed step size and under mesh refinement at fixed final time. Version 2 adds Theorem 1.4, whose part (i) solves Question 6.1 of Chalmoukis, Tsikalas and Yakubovich; that question is tracked as its own entry. parent of this event
The Inverse Generator Problem on Hilbert Spaces parent of this event
VibeMathed record: The Inverse Generator Problem on Hilbert Spaces evidence for this event
Lean 4 formalization repository evidence for this event
Separation Between the Ordinary and Strong Kreiss Constants evidence for this event
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