What was already known
Boundedness was known for several manifold families, including spheres and tori. Unbounded Hamiltonian spectral norm did not by itself establish unbounded Lagrangian distance for these zero-section orbits.
AI involvement
GPT 6 Astra supplied an initial negatively curved Z₂-coefficient counterexample after prompting by the second and third authors. The authors credit earlier human ideas and report doing all subsequent proofs, generalizations, applications and writing themselves.
Retain the initial negatively curved Z2-coefficient counterexample supplied by GPT; all subsequent generalizations, applications and proofs are human work.
Importance
Gives counterexamples to the proposed generalized boundedness statement and extends understanding of the dependence on the base manifold and coefficient ring.
Limitations
The hypotheses on topology, Euler characteristic and coefficients are essential to the stated theorem. The paper also classifies closed surfaces over Z₂, but the result is not a disproof of every version of a Viterbo conjecture or of the separate capacity–volume conjecture. GPT’s initial example overlapped with prior human ideas and a previously considered diffeomorphism. No formal proof or independent audit by AIProofWatch is claimed.
Technical verification
The primary source reports the contribution, but the reviewed source passages do not document a completed full rigorous check. Proof availability, authorship and publication status are not treated as completed checking.
Human understanding
Named human researchers explain or reconstruct the scoped central mechanism in the cited paper/account; credit for that explanation is separate from technical checking. GPT 6 Astra supplied an initial negatively curved Z₂-coefficient counterexample after prompting by the second and third authors. The authors credit earlier human ideas and report doing all subsequent proofs, generalizations, applications and writing themselves.
Correction and publication history
Primary statement, hypotheses, prior bounds, AI role and evidence scope reviewed on 16 October 2026 against every current catalog/update page and existing immutable revisions. New recent scoped contribution; ordinary notifying editor publication.
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