{
  "abstract": "This paper develops a canonical decomposition and reconstruction theory for local-unit-aligned ordered semigroups. Two coherentizations of the positive-idempotent skeleton are introduced. The finer one records the closure forced within local-unit blocks, while the multiplication-coherent quotient yields a join-semilattice of canonical blocks. Components are the fibers of these blocks. For comparable blocks $A\\le B$, each positive idempotent $q\\in B$ defines a transport homomorphism $x\\mapsto xq$ from the component over $A$ to that over $B$. Keeping all such maps gives a resolved-transport family, which replaces the single connecting map used in an ordinary direct system. These canonical data reconstruct multiplication without additional assumptions: two elements are transported to their join component, and their product is the least product of corresponding transported images. They also determine every comparison directed from a lower component to a higher one. The full ambient order is recovered under any of three explicit order-recovery conditions. In particular, every totally ordered local-unit-aligned semigroup is completely reconstructed by its resolved-transport data. A complementary result recovers the order from componentwise order duality when a suitable component-preserving anti-automorphism is available. When each component receiving a proper transition has a least positive idempotent, the resolved family collapses to a single least-target map. Under a natural monotonicity condition, these maps form an ordinary direct system and induce a directed lexicographic order. Examples show both why the additional order conditions are needed and why resolved transports cannot in general be replaced by ordinary transition maps.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20255",
  "author_total": 1,
  "authors": [
    {
      "name": "Sándor Jenei"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9wnp9dkd0kykz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20255",
  "fulltext_url": null,
  "id": "9wnp9dkd0kykz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20255",
  "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.GR"
    ],
    [
      "arxiv",
      "math.RA"
    ],
    [
      "openalex",
      "1703|semigroups and automata theory"
    ]
  ],
  "openalex": "W7213609296",
  "pdf_url": "https://arxiv.org/pdf/2609.20255",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9wnp9dkd0kykz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.20255",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20255"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Canonical resolved-transport decomposition and reconstruction of local-unit-aligned ordered semigroups",
  "title_text": "Canonical resolved-transport decomposition and reconstruction of local-unit-aligned ordered semigroups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/9wnp9dkd0kykz",
  "venue": "arXiv",
  "versions": []
}