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  "slug": "two-colour-overpartition-congruences",
  "title": "Two-colour overpartitions: exact certificates and parameter families",
  "shortTitle": "Two colours, exact remainders",
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  "oneLine": "Four finite certificates and a complete modulo-eight parameter criterion reveal structured divisibility in two-colour overpartitions.",
  "abstract": "Unrefereed two-paper mathematical collection: four exact eta-quotient/Sturm certificates, an exact modulo-8 parameter classification, a modulo-16 binary-form support theorem for square/twice-square parameters, and a dyadic modulo-16 family whenever the parameter odd part is 1 modulo 8. Includes corrected earlier-statement attribution, explicit sharpness and boundary witnesses, and failure-sensitive verification. Universal conclusions require the written proofs. No formal verification, external peer review, independent reproduction, priority certification or world-leading significance is asserted.",
  "datePublished": "2026-10-12",
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    "name": "Two-colour overpartition congruences",
    "url": "https://arxiv.org/abs/2607.16608v1"
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    "Four stated arithmetic progressions have exact eta-quotient/Sturm certificates modulo32,64,64 and128.",
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    {
      "citation": "Bharadwaj, Sujatha and Chandankumar (2026), Arithmetic properties of the 2-color overpartition function: source statements, conjectures and earlier theorem overlap.",
      "url": "https://arxiv.org/abs/2607.16608v1",
      "doi": "10.48550/arXiv.2607.16608"
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    {
      "citation": "Keister, Sellers and Vary (2009), Some arithmetic properties of overpartition k-tuples: Theorem9,k=2 supplies the ell1 case.",
      "url": "https://math.colgate.edu/~integers/j17/j17.pdf",
      "doi": null
    },
    {
      "citation": "Hirschhorn and Sellers (2005), Arithmetic relations for overpartitions: Theorem2(6) supplies ordinary congruence used when4 divides ell.",
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