{
  "abstract": "We develop nonreciprocal spherical attention as a mathematical framework for coarsening and compressed nearest-neighbor retrieval. For two shrinking acute blocks whose centers have zero skew pairing and whose total mass ratio is subexponential in inverse temperature, we prove $\\lim_{β\\to\\infty}β^{-1}\\log T_β=1-\\cosϕ$, without restricting particle-count growth. An explicit three-body flow has two rigorously separated metastable exponents. For finite compression, mass centering yields a sharp $O(r^2)$ attention-output error bound at fixed temperature, with an explicit spherical-normalization correction. We formulate skew query-side score calibration as a strictly convex moment problem and derive a unique normal equation, residual-based optimization certificates, and bounded low-rank projections. A norm-aware margin objective calibrates native squared-distance rankings. Experiments use semantic retrieval data, one million visual descriptors with three codebook seeds, and a ten-million-vector FAISS IVF-PQ index with recomputed exact cosine ground truth. On SIFT1M, skew margin calibration raises native-L2 hit@10 from 0.8926 to 0.8948; symmetric calibration reaches 0.8996. The ten-million-vector index reaches 0.8827 hit@10 at 0.1794 ms per query in a four-thread batch benchmark, while validation selects no skew update. Exact streamed attention over ten million keys evaluates compressed memory on 1,024 held-out queries. Independent matrix solves, automatic differentiation, finite differences, interval arithmetic, full-flow tests, and nine Rocq-checked algebra lemmas support reproducibility. Directionality alone does not establish retrieval superiority.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02237",
  "author_total": 2,
  "authors": [
    {
      "name": "Faruk Alpay"
    },
    {
      "name": "Taylan Alpay"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dqsh44r0r84ws.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02237",
  "fulltext_url": null,
  "id": "dqsh44r0r84ws",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.02237",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.IR"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.DS"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.02237",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dqsh44r0r84ws.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.02237",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02237"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Nonreciprocal Spherical Attention and Retrieval: Sharp Coarsening Clocks and Certified Score Correction",
  "title_text": "Nonreciprocal Spherical Attention and Retrieval: Sharp Coarsening Clocks and Certified Score Correction",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/dqsh44r0r84ws",
  "venue": "arXiv",
  "versions": []
}