What was already known
Positive maximal-regularity results required time Hölder exponent greater than one half. Earlier endpoint counterexamples did not settle the real scalar, spatially continuous one-dimensional case posed by Auscher and Egert.
AI involvement
Niebel reports that GPT-5.5 Pro found the initial counterexample. He verified and studied it, reduced it to one dimension, built the extensions and checked every mathematical claim and calculation.
GPT-5.5 Pro supplied the first counterexample, while Niebel's essential simplification and one-dimensional reduction define the stronger final claim.
Importance
The construction answers that endpoint question negatively under unusually strong scalar and spatial regularity conditions.
Limitations
GPT-5.5 Pro found an initial two-dimensional example; Niebel made the essential one-dimensional reduction and final extensions. The source does not map every feature of the final coefficient to the model example.
Technical verification
Niebel explicitly reports critical review and verification of all final mathematical claims and calculations, including the retained counterexample. This is a source-reported complete human author check, not an AIProofWatch reproduction.
Independent checking
Critical review and verification of all mathematical claims, calculations and AI-generated suggestions after simplifying the first model example
- Checker
- Lukas Niebel, human author
- Scope
- The final one-dimensional half-Hölder counterexample and its full-space and bounded-domain consequences
- Basis
- Reported by the linked checker
Human understanding
Niebel studied and simplified the model's example, reduced it to one dimension, and explains the oscillatory-mode and shrinking-time-block mechanism in the paper.
Correction and publication history
Initial publication of this result.
Read this published revision