What was already known
The first version left this positivity question open; the revised paper acknowledges that positivity can fail. The all-iterates proof of the Crouzeix theorem remains intact.
AI involvement
The repository attributes discovery of the witness and its closed form to an AI research run. No human-origin mathematical input beyond defining the target is documented, although the specific agent and prompt history are absent.
The source credits an AI research run with finding and reducing the retained witness; absent a prompt record, autonomy beyond that is not established.
Importance
Provides a concrete witness for the failure of a proposed auxiliary inequality.
Limitations
Exact symbolic checks cover the finite algebraic witness; full operator-hypothesis coverage and independent human review are not documented. The Crouzeix theorem is unaffected.
Technical verification
A SymPy script reports exact algebraic signs for the explicit witness and two independent numerical implementations check the paper's operator setup. The exact script does not alone rigorously check every infinite-dimensional dilation hypothesis and no human mathematical review is documented; the repository identifies a shared interpretation risk.
Human understanding
Few is the default when evidence for a higher level is insufficient. The mechanism is described by the AI-produced repository, but it expressly records no human mathematician's review or explanation. Few is an evidence default, not a claim that the mechanism is opaque.
Correction and publication history
Provides a concrete witness for the failure of a proposed auxiliary inequality.
Read this published revision