What was already known
Bogoliubov and Lee–Huang–Yang predicted this profile and coefficient. Earlier rigorous results treated energy, condensation, other limits or approximate correlation equations, rather than this momentum law for exact hard-sphere ground states in the stated limits.
AI involvement
OpenAI is named as author and its math release attributes the manuscripts to an internal model. The degree of human direction for this proof is not described; the argument uses separate human results on energy and condensation.
OpenAI is the credited author and the repository identifies its manuscripts as internal-model products; independent generation is not established for this item.
Importance
Reports the predicted momentum law and depletion fraction for exact hard-sphere ground states in the ordinary fixed-density thermodynamic limit.
Limitations
The order of limits matters. A companion Lean development checks an earlier condensation theorem, not this depletion or momentum-profile result. No completed check of this specific theorem is documented.
Technical verification
The paper gives a proof, but the repository says collection results have varied verification and documents no completed check of this depletion theorem. Family 267's Lean scope covers the earlier ground-state condensation result only.
Human understanding
Default for missing evidence: the manuscript explains its local-excitation and long-wavelength strategy, but no named human explanation of this model-produced argument was found.
Correction and publication history
First report of the hard-sphere ground-state depletion result.
Read this published revision