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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. Imported under CC BY 4.0.

Canonical aliases: The Inverse Generator Problem on Hilbert Spaces · Inverse generator problem

Confidence: Not scored

Registry verification: unreviewed · preprint · resolved

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Attribution

VibeMathed
registry · event recorded by

Emiel Lorist
human · human collaborator

Martin Meyries
human · human collaborator

Mark Veraar
human · human collaborator

Claude Fable
model · ai model contributor · Anthropic

ChatGPT 5.6 Pro
model · ai model contributor · OpenAI

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Named evidence

VibeMathed record: The Inverse Generator Problem on Hilbert Spaces

specialist registry · passed

Version 3 has a complete Lean 4 machine-checked proof of Theorem 1.1, the explicit finite-dimensional construction underlying the counterexamples. The accompanying repository states that the development is self-contained on top of Mathlib, contains no sorry, no native_decide and no numerical or floating-point proof steps, and that the final theorem depends only on Lean's standard axioms propext, Classical.choice and Quot.sound. However, the Lean development formalizes Theorem 1.1 rather than the infinite-dimensional inverse-generator conclusion of Theorem 1.2. In particular, the passage assembling the finite-dimensional blocks into the Hilbert-space counterexample has not been formally verified or independently expert-reviewed. The entry should therefore remain Unreviewed rather than being upgraded to Lean-checked or Lean-verified.

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Separation Between the Ordinary and Strong Kreiss Constants

preprint · pending

Primary source named by the VibeMathed record. Presence in this import is not an independent mathematical verification.

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Lean 4 formalization repository

lean artifact · pending

lean-proof link supplied by the VibeMathed registry.

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Artifacts and verifiers

Lean 4 formalization repository

lean artifact · pending