Threshold and positive-energy bound states of the BFSS matrix model

What OpenAI claims

Proves that the undeformed relative SU(N) BFSS model has exactly one normalizable zero-energy state for every finite N ≥ 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.

Papers (2)

1. The unique threshold bound state of the SU(N) BFSS model

   24 September 2026 · Preprint, not peer reviewed · PDF

   For every finite N ≥ 2, we prove that undeformed SU (N) BFSS matrix quantum mechanics has exactly one normalizable zero-energy state after removing the center of mass. This establishes the threshold-bound-state conjecture.

2. Positive eigenvalues of the relative SU(2) BFSS Hamiltonian

   5 October 2026 · Preprint, not peer reviewed · PDF

   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.

Status

Preprint. The papers have not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.