{
  "abstract": "We develop the Gram/Wishart/Stiefel formulation of the \\(N=2\\), large--\\(d\\) planar endpoint theory of lattice BFSS/BMN matrix quantum mechanics on the lattice. The endpoint variables become rank--two Wishart eigenvalues and relative Stiefel angles, expressing the holonomy invariants \\(A\\), \\(B\\), and \\(R^2=A^2+B^2\\) in radial and angular Gram data. The large-\\(R\\) aligned contribution \\(-A\\) is absorbed into the Gaussian sector, producing the shifted mass \\((α_Λ)_{\\rm eff}=α_Λ-1/2\\). The exact \\(O(2)\\) angular integral encodes this sector in a rank--two Bessel kernel. The pure \\(-A\\) theory, exactly solvable in Cartesian variables, fixes the leading Bessel/HCIZ structure: its exponential selects alignment, while its prefactor removes the spurious doubled Wishart entropy. We then apply this structure to the transverse \\(B\\)-type expansion and its non-polynomial toy completion. Finite polynomial truncations lead to an apparent large--\\(d\\) perturbativity bound incompatible with the continuum limit, but this bound is shown to be an artifact of truncation. After summing the local transverse completion and balancing the compensating \\(+A\\) term, the Wishart saddle is recovered with the physical shifted mass. The resulting continuum behavior reproduces the universal \\(-2d\\) contribution of the \\(D_Λ\\)-channel, while the genuinely anisotropic \\(β_Λ\\)-channel lies outside the scope of a pure transverse \\(B\\)-type description. Finally, we outline the emergent Grassmannian geometry encoded by the two endpoint planes. Their relative angular fluctuations form a \\(2(d-2)\\)-dimensional sector, whose entropy interpretation is developed in the sequel. For \\(d\\ge4\\), the two planes generically span a relational four-dimensional subspace of \\(\\mathbb R^d\\).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.08481",
  "author_total": 1,
  "authors": [
    {
      "name": "Badis Ydri"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1s3tntemm1ssh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.08481",
  "fulltext_url": null,
  "id": "1s3tntemm1ssh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.08481",
  "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"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7167911436",
  "pdf_url": "https://arxiv.org/pdf/2607.08481",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1s3tntemm1ssh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:50Z",
      "native_id": "2607.08481",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.08481"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-lat",
      "subfield": "high-energy"
    }
  ],
  "title": "Gram--Wishart--Stiefel formulation of the $N=2$, large--$d$ gauge theory in 1D: towards emergent Grassmannian geometry",
  "title_text": "Gram--Wishart--Stiefel formulation of the N=2, large--d gauge theory in 1D: towards emergent Grassmannian geometry",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/1s3tntemm1ssh",
  "venue": "arXiv",
  "versions": []
}