{
  "abstract": "We study the singlet-sector structure of mass-deformed BFSS$_{d+1}$ matrix quantum mechanics by combining the large--\\(d\\) Gaussian reduction with the Molien--Weyl projection. The Gaussian reduction captures the bulk matrix dynamics through a gauged harmonic oscillator, while the Molien--Weyl integral imposes the Gauss law and reorganizes the physical Hilbert space into holonomy-projected singlet excitations. We show that the very-low-temperature bosonic singlet spectrum is universally controlled by the quadratic Gram operators \\(\\Tr(X_aX_b)\\), whose number is \\(d(d+1)/2\\). For \\(N=2\\), this result is established by explicit residue computations and character methods; for \\(N>2\\), it is supported by the character analysis. Thus the infrared spectrum begins as a collection of BFSS$_2$--like Gram towers, although higher invariant structures generally modify the full partition function. We also give a Hamiltonian derivation of the exceptional exact factorization at \\((d,N)=(2,2)\\), where the BFSS$_3$ singlet partition function equals the cube of the BFSS$_2$ one for all temperatures. This rigidity is special to the \\(SU(2)\\) invariant tensor structure and distinguishes exact singlet factorization from the possibility of smooth deconfinement--like holonomy crossovers at finite $N$. Finally, we extend the Gram-counting picture to supersymmetric BFSS/BMN models and indicate how the Molien--Weyl formulation can benchmark Monte Carlo simulations in both \\(X_a\\)-space and holonomy space.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.04621",
  "author_total": 1,
  "authors": [
    {
      "name": "Badis Ydri"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0at3qyyxt0fh3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.04621",
  "fulltext_url": null,
  "id": "0at3qyyxt0fh3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.04621",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "gr-qc"
    ],
    [
      "arxiv",
      "hep-lat"
    ],
    [
      "arxiv",
      "hep-ph"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7160555875",
  "pdf_url": "https://arxiv.org/pdf/2605.04621",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0at3qyyxt0fh3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:28Z",
      "native_id": "2605.04621",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.04621"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-lat",
      "subfield": "high-energy"
    }
  ],
  "title": "Molien--Weyl Singlet Counting and BFSS$_2$--Factorization in Gaussian Matrix Quantum Mechanics",
  "title_text": "Molien--Weyl Singlet Counting and BFSS_2--Factorization in Gaussian Matrix Quantum Mechanics",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:47Z",
  "url": "https://research.draconitic.com/paper/0at3qyyxt0fh3",
  "venue": "arXiv",
  "versions": []
}