Counterexample to the bounded mass property on the Hopf threefold
The bounded mass property fails on the Hopf threefold, answering a question of Boucksom, Guedj and Lu.
- Lab
- Independent
- Model
- Rethlas agent (GPT-5.6 Sol)
- Field
- Mathematics
- Date
- 2026-08-21
- Human collaborators
- Mingchen Xia, Kewei Zhang
- Problem posed
- 2025 · open 1 yr
Sources
Original work
Independent commentary
What was found
A compact complex manifold has the bounded mass property if, for one and equivalently every Hermitian form, the masses of the n-th power of that form plus a dd^c-exact perturbation stay uniformly bounded over all smooth potentials keeping the form positive. The paper shows this fails on the Hopf threefold, the quotient of punctured complex three-space by the map sending z to e^{-1} z, which answers a question of Boucksom, Guedj and Lu in the negative.
Novelty check
The question is recent and attributed: Boucksom, Guedj and Lu posed it in 2025, so the window in which a prior answer could exist is short and the paper names the source directly. The counterexample is a single named manifold, the Hopf threefold, rather than an abstract existence claim, which makes it checkable against the definition. No prior counterexample or positive resolution appears.
Caveats and known objections
A short preprint, unrefereed, not formalized, with no independent check on record. Autonomy is graded ai-led on a one-sentence disclosure that credits the construction itself to an agent rather than to assistance: the initial counterexample was constructed with the Rethlas agent, improved by Felix Ye, using the gpt-5.6-sol model. The disclosure covers the initial counterexample only and does not say how much of the final write-up is the authors' own.
Also recorded at
vibemathedbounded-mass-property-for-compact-complex-manifolds
Nothing mechanically. It is a parallel listing of the same result, carrying its own verification label rather than an independent check.
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Entry history (1 event)
- AddedEntered the registry graded Author verified and AI-led.
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Cite this entry
whataifound.org. (2026). Counterexample to the bounded mass property on the Hopf threefold. whataifound.org: A Registry of AI Scientific and Mathematical Discoveries. https://whataifound.org/finding/2026-08-21-bounded-mass-propertyBibTeX
@misc{whataifound-independent-2026-property,
title = {Counterexample to the bounded mass property on the Hopf threefold},
author = {{whataifound.org}},
year = {2026},
howpublished = {whataifound.org: A Registry of AI Scientific and Mathematical Discoveries},
note = {Result by Independent. Verification: Author verified. Autonomy: AI-led.},
url = {https://whataifound.org/finding/2026-08-21-bounded-mass-property}
}