{
  "abstract": "Let $p$ be an odd prime and let $K/\\mathbb{Q}_p$ be a finite unramified extension. From a finite presentation by roots of unity of order prime to $p$, we construct a localized Iwasawa pseudomeasure on $\\mathbb{Z}_p^\\times$. Although the pseudomeasure depends on the chosen presentation, its image modulo bounded measures depends only on the associated Bloch class: it is the Frobenius-depleted Coleman regulator of that class multiplied by a universal half-shifted zeta principal part. Consequently, every nonexceptional weight component is bounded, while the exceptional component has at most a simple pole with explicitly determined residue. For $p>3$ and $\\mathbb{Z}_p$-valued coefficients, vanishing of the principal part is equivalent to vanishing of the corresponding class in $K_3(K;\\mathbb{Z}_p)$. Cyclotomic refinements preserve the Bloch class and act on the associated pseudomeasures by explicit Iwasawa multipliers. Normalized finite linear combinations of refinements interpolate arbitrary finite jets of the bounded weight-space data, subject only to the normalization at the exceptional point. We also establish a half-shifted complex Mellin factorization, compare the construction with the GSWZ germ family, and derive, at simple degree-one places above primes $p>3$, a finite-polylogarithm criterion for the local $K_3$-class of the knot $5_2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.29587",
  "author_total": 2,
  "authors": [
    {
      "name": "Honghuai Fang"
    },
    {
      "name": "Zekun Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e4r3h5mx1994r.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.29587",
  "fulltext_url": null,
  "id": "e4r3h5mx1994r",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.29587",
  "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",
      "math.KT"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "arxiv",
      "math.QA"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7204950578",
  "pdf_url": "https://arxiv.org/pdf/2608.29587",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e4r3h5mx1994r.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.29587",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.29587"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.KT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Bloch-regulator Principal Parts of Cyclotomic Iwasawa Pseudomeasures",
  "title_text": "Bloch-regulator Principal Parts of Cyclotomic Iwasawa Pseudomeasures",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/e4r3h5mx1994r",
  "venue": "arXiv",
  "versions": []
}