{
  "abstract": "We present a rigorous strong-coupling Birman-Schwinger analysis of the three-boson lattice Schroedinger operator on Z^2 at the exceptional quasimomentum K = pi. First, we provide an exact closed-form benchmark for the fiber Fredholm determinant, valid for every quasimomentum K, obtained via a uniform elliptic reduction. Second, we formulate and prove a general order-matching criterion determining whether a leading-order Fredholm determinant asymptotic, with relative error O(1/mu), suffices to fix the constant-order additive energy correction, or if the next-order refinement is required. Applying the criterion to the formal branch z = -2mu + d, we identify an algebraic crossing -2mu + 6 + 8/mu + O(mu^{-2}), but demonstrate that this crossing does not correspond to a true eigenvalue of the full Hamiltonian. The actual ground state obeys the rigorous variational bounds -3mu <= z_1^{pi,s}(mu) <= -3mu + 6, so that z_1^{pi,s}(mu) = -3mu + O(1), the same leading branch as at K = 0; direct finite-volume diagonalisation confirms the refined asymptotic -3mu + 6 + O(mu^{-1}) and spectral gap 2mu - 2 + O(mu^{-1}). We independently confirm that the known K = 0 constant C approximately 3.96458 requires no analogous refinement. Finally, we compare the asymptotic precision levels achieved across recent lattice few-body models and draw a structural parallel with the parity-based classification of topological band insulators at time-reversal-invariant momenta.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.11848",
  "author_total": 1,
  "authors": [
    {
      "name": "Mikhail Dolgopolov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e440ktgw6tcrh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.11848",
  "fulltext_url": null,
  "id": "e440ktgw6tcrh",
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  "landing_url": "https://arxiv.org/abs/2608.11848",
  "language": null,
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  "metadata_licence": "CC0-1.0",
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      "2610|Spectral Theory in Mathematical Physics"
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  "openalex": "W7202347616",
  "pdf_url": "https://arxiv.org/pdf/2608.11848",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e440ktgw6tcrh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:48Z",
      "native_id": "2608.11848",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.11848"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "A uniform elliptic reduction, an order-matching criterion, and precision benchmarks for the strong-coupling Birman-Schwinger analysis of the lattice three-boson trimer",
  "title_text": "A uniform elliptic reduction, an order-matching criterion, and precision benchmarks for the strong-coupling Birman-Schwinger analysis of the lattice three-boson trimer",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:57Z",
  "url": "https://research.draconitic.com/paper/e440ktgw6tcrh",
  "venue": "arXiv",
  "versions": []
}