{
  "abstract": "The topologically twisted index of ABJM theory captures the microscopic entropy of magnetically charged supersymmetric $\\mathrm{AdS}_4$ black holes. Building on the companion Letter arXiv:2608.04107, which reconstructed the finite-rank twisted superpotential at the universal twist, we determine the finite-rank index using high-precision Bethe-vacuum data, physics-informed symbolic regression, and integer relations. The Hessian, effective dilaton, and one-loop factors encode information beyond the on-shell twisted superpotential. The two observables share the same shifted rank. Within a declared finite class, we reconstruct the index constant map from the ABJM $S^3$ constant maps at levels $k$ and $k/2$, the constant map of the twisted superpotential, and elementary terms. We prove that it equals a convergent one-kernel integral for real $k>0$, resumming the large-$k$ expansion, fixing a previously numerical constant, and yielding type-IIA coefficients at arbitrary genus. We also prove that the Clausen expression in arXiv:2608.04107 equals an alternating Euler sum and an absolutely convergent integral, giving closed evaluations for two rational-argument Euler-sum families. At $k=1,2,4$, the exponentially suppressed sectors exhibit arithmetic structure. The reconstructed coefficients of the twisted superpotential obey a divisor-sum formula with a conjectural all-order Eichler-integral series associated with a weight-four Eisenstein form. The index coefficients reduce to two rational generators; one admits modular-product formulas reproducing every available coefficient and suggesting an all-order completion. Conditional on this continuation, modular transformations determine the nearest logarithmic singularity, radius of convergence, and leading coefficient growth. These results provide a finite-$N$ benchmark for quantum gravitational blocks and bulk black hole quantum entropy.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09273",
  "author_total": 1,
  "authors": [
    {
      "name": "Seyed Morteza Hosseini"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7gd643ft4y9h0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09273",
  "fulltext_url": null,
  "id": "7gd643ft4y9h0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09273",
  "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",
      "hep-th"
    ],
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7212148264",
  "pdf_url": "https://arxiv.org/pdf/2609.09273",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7gd643ft4y9h0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:12Z",
      "native_id": "2609.09273",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09273"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Constant Maps and Exponentially Small Sectors in ABJM Bethe Observables",
  "title_text": "Constant Maps and Exponentially Small Sectors in ABJM Bethe Observables",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:12Z",
  "url": "https://research.draconitic.com/paper/7gd643ft4y9h0",
  "venue": "arXiv",
  "versions": []
}