{
  "abstract": "Let $f:Y\\to\\prod_λΣ^{d_λ}H\\mathbb F_2$ be a locally finite family of positive-degree stable operations, where $Y=H\\mathbb F_2$ or $H\\mathbb Z$; in the integral case assume $d_λ\\geq2$. We determine the Adams filtration of its fiber from the minimal generators of $\\operatorname{im}(f^*)$ as a left Steenrod module. An explicit target automorphism separates a minimal subfamily from the redundant coordinates and gives a noncanonical stable splitting. Combining this reduction with the Bruner--Rognes two-extension theorem and an acyclic cancellation gives $E_3=E_\\infty$. In positive homotopy degrees, the filtration-one subgroup is the image of the dual of the induced map on minimal-generator quotients, and the redundant coordinates account for filtration zero. We also specify the zero-stem filtration and its possible cyclic extension of order four. A terminating Adem recursion realizes the splitting for the full positive even-square family and its finite truncations. Separately, for a crossed bimodule and fixed lifts of the differentials of a free primary complex, we construct a class in the third cohomology of an explicit Hom complex. Its vanishing is equivalent to the existence of coherent null-composite tracks with those fixed differential lifts.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.18906",
  "author_total": 1,
  "authors": [
    {
      "name": "Dang Vo Phuc"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5jadw4gjrbq53.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.18906",
  "fulltext_url": null,
  "id": "5jadw4gjrbq53",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.18906",
  "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.AT"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7161803076",
  "pdf_url": "https://arxiv.org/pdf/2605.18906",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5jadw4gjrbq53.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2605.18906",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.18906"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Adams filtrations and secondary coherence for fibers of Steenrod operations",
  "title_text": "Adams filtrations and secondary coherence for fibers of Steenrod operations",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/5jadw4gjrbq53",
  "venue": "arXiv",
  "versions": []
}