The threshold bound state conjecture for SU(N) supersymmetric matrix quantum mechanics

Theorem 1.1: for every integer $N\ge2$ , the relative undeformed $\mathrm{SU}(N)$ BFSS Hamiltonian (closure of $\frac1{16}\sum_\alpha\|Q_\alpha\Psi\|^2$ on gauge-invariant states in $L^2(\mathbb R^{9(N^2-1)})$ tensor a Clifford module) has a one-dimensional kernel, consisting of $\mathrm{Spin}(9)$ -invariant even states. This gives both existence and uniqueness of the threshold bound state at each finite $N$ . Constants depend on $N$ ; nothing is claimed about large- $N$ limits or the matrix-theory conjecture itself.

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Occurred: Sep 24, 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 threshold bound state conjecture for SU(N) supersymmetric matrix quantum mechanics · BFSS threshold bound state

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Registry verification: unreviewed · announcement · candidate

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VibeMathed record: The threshold bound state conjecture for SU(N) supersymmetric matrix quantum mechanics

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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 Witten's prediction as cited. Theorem 1.1 states $\dim\ker H_N=1$ for every $N\ge2$ , with $H_N$ the self-adjoint operator of the closed supercharge quadratic form on the gauge-invariant smooth compactly supported core; the kernel is $\mathrm{Spin}(9)$ -invariant and even. The result is for that specific operator realization; the paper contrasts it with other realizations (Boulton et al.). The proof passes from a BMN mass-deformed Fredholm index to the undeformed kernel with cluster estimates. Not refereed here. No Lean formalization.

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

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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) evidence for this event

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

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