{
  "abstract": "We consider two canonical market-microstructure regularities: the long-memory of trade signs and the square-root law of meta-order impact. The point is not to propose new empirical laws, but to separate the clocks on which existing laws are defined. The sign-memory law is an event-time statement about the ordering and fragmentation of hidden orders. The square-root impact law is an operational-time statement about front motion in a locally linear latent order book. Starting from a discrete-time random-walk bid/ask reaction--diffusion order book with a separate event clock, we identify an event-time imbalance reduction, derive the operational-time front and impact equations in the locally linear regime, and then subordinate both sign and impact observables to calendar time. Fractional or tempered clock effects enter through this event-to-calendar projection, not through a different operational-time impact mechanism. This gives a compact clock-aware framework in which event-time sign persistence, operational-time square-root impact, and anomalous calendar-time effects appear as distinct but compatible consequences of a common order-book representation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: J. Stat. Mech. (2026) 103402",
  "arxiv": "2609.13715",
  "author_total": 2,
  "authors": [
    {
      "name": "Christopher Angstmann"
    },
    {
      "name": "Tim Gebbie"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c42zmdbg4m11h.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13715",
  "fulltext_url": null,
  "id": "c42zmdbg4m11h",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13715",
  "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",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "q-fin.MF"
    ],
    [
      "arxiv",
      "q-fin.TR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.13715",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c42zmdbg4m11h.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:54Z",
      "native_id": "2609.13715",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13715"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Event-Time Order-Flow Memory, Operational-Time Impact, and Subordinated Market Observables",
  "title_text": "Event-Time Order-Flow Memory, Operational-Time Impact, and Subordinated Market Observables",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/c42zmdbg4m11h",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1088/1742-5468/aeab7b",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}