OpenAI · 270-02 · 2026-10-05 · Mathematical physics

Positive eigenvalues of the relative SU(2) BFSS Hamiltonian

preprints/Positive-eigenvalues-of-the-relative-SU-2-BFSS-Hamiltonian-October-5-2026

Family 270. Threshold and positive-energy bound states of the BFSS model.

The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.

Read against the standing problems

Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N

Proves that the undeformed relative $SU (N)$ BFSS model has exactly one normalizable zero-energy state for every finite $N \geq 2$ , resolving the threshold-bound-state conjecture. For $SU (2)$ , a companion proves infinitely many normalizable positive-energy eigenstates with unbounded energies, contradicting the original BFSS paper s exclusion of additional bound states at $N = 2$ .

We prove that the relative $SU (2)$ BFSS Hamiltonian has infinitely many positive eigenvalues tending to infinity, with square-integrable eigenvectors. The operator is defined by closing the gauge-invariant supercharge form. This refutes, at N = 2, the exclusion of normalizable positive-energy states stated in the original BFSS paper.

Preprint source and Lean scope

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No Lean scope note is in the repository for this family. The preprint source below is still the full manuscript, not only the abstract. No compilation is asserted.