The BFSS exclusion of positive-energy normalizable states in the relative SU(2) model

Theorem 1.1: the relative $\mathrm{SU}(2)$ BFSS Hamiltonian has infinitely many positive eigenvalues $E_j\to\infty$ with square-integrable eigenvectors, so $\sigma_p(H)\cap(0,\infty)$ is infinite. This contradicts, for this exact operator at $N=2$ , the BFSS paper's sentence excluding other normalizable bound states. It concerns only $N=2$ , says nothing about $N\ge3$ , and does not bear on the zero-energy state (the companion entry) or on large- $N$ matrix theory.

Exact FrontierDelta

Prior state unknown→disproved

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Occurred: Oct 5, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.

Canonical aliases: The BFSS exclusion of positive-energy normalizable states in the relative SU(2) model · BFSS positive-energy bound states (SU(2))

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Registry verification: unreviewed · announcement · candidate

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VibeMathed record: The BFSS exclusion of positive-energy normalizable states in the relative SU(2) model

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No independent mathematician has checked this yet. Checked here: abstract, introduction and Theorem 1.1 of the TeX source, read against the BFSS sentence quoted in the manuscript. Theorem 1.1 gives an orthonormal sequence of eigenvectors in the domain of $H$ with eigenvalues $E_j>0$ , $E_j\to\infty$ , for the closed gauge-invariant supercharge form at $N=2$ . The mechanism is symmetry: $\mathrm{Spin}(9)$ sectors with large second highest-weight coordinate exclude low transverse oscillator levels, so those sectors are confined. The manuscript says the large- $N$ matrix-theory conjecture is a separate question. Not refereed here. No Lean formalization.

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The BFSS exclusion of positive-energy normalizable states in the relative SU(2) model

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

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