Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 370-01. The Subcritical Hénon–Lane–Emden Conjecture
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OpenAI@2026-10-07#rem:oai-p-370-01
Authors: OpenAI. Family 370.
Title: The Subcritical Hénon–Lane–Emden Conjecture.
Abstract: We prove the subcritical Hénon–Lane–Emden conjecture: for every dimension n ≥ 2, positive powers p, q, and real weights A, B, the system has no strictly positive entire solution when $(n+A)/(p+1)+(n+B)/(q+1){}gt n-2$. Solutions need only be continuous at the origin and classical elsewhere, without a condition at infinity. For n ≥ 3 and $A,B{}gt -2$, combining this result with the radial existence theorem of Bidaut-Véron and Giacomini proves Phan's Conjecture C in full: a positive radial entire solution exists whenever the strict inequality fails.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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