{
  "abstract": "We associate a compact genus-two real spectral core with a transverse logarithmic-derivative discriminant of the Riemann $Ξ$-function. Directed interval arithmetic certifies its branch geometry, a real $P_{\\mathrm{III}}(D_6)$ scalar-normal-form realization, and associated Kummer and Shioda--Inose models. Zero-action resonance reduces to rationality of two real period ratios. Their certified heat motion yields generic local nonresonance and Diophantine separation, while explicit Farey windows impose denominator barriers of $1{,}036{,}003$ and $140{,}769$ throughout $|κ|\\le3\\times10^{-10}$ in the heat time $κ$. Fixed-point irrationality and exact Picard rank remain open. The heat tangent differs from the matched fixed-exponent isomonodromic direction, but admits a local moving-exponent curve lift. Separately, a reciprocal-head canopy certificate combined with published finite-RH and rectangular time-barrier verifications bounds the de Bruijn--Newman constant by $Λ\\le433/2500=0.1732$ without a QRH assumption. These local arithmetic and global analytic results share a phase--transverse bridge; no equivalence between core nonresonance and RH is asserted.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.32694",
  "author_total": 1,
  "authors": [
    {
      "name": "Michel Planat"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7jvsz9hwbg4r0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.32694",
  "fulltext_url": null,
  "id": "7jvsz9hwbg4r0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.32694",
  "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",
      "math.AG"
    ],
    [
      "arxiv",
      "math.CV"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7223710126",
  "pdf_url": "https://arxiv.org/pdf/2610.32694",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7jvsz9hwbg4r0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.32694",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.32694"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A genus-two spectral curve of the Riemann $Ξ$-function: Real Structure and Certified Arithmetic Separation of Periods",
  "title_text": "A genus-two spectral curve of the Riemann Ξ-function: Real Structure and Certified Arithmetic Separation of Periods",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/7jvsz9hwbg4r0",
  "venue": "arXiv",
  "versions": []
}