{
  "abstract": "The square-root impact law (SRIL), $I = Yσ\\sqrt{Q/V}$, bundles two facts that a single mechanism must explain at once: a shape (impact proportional to square-root of traded volume $Q$) and an amplitude ($Y=O(1)$, independent of the participation rate $φ$). Bonart has recently proposed an elegant solution: if realized and counterfactual prices are both diffusive, information-neutral impact must have white increments and the SRIL follows without the wart. We reformulate and simplify his argument, and foreground the ingredient he himself regards as essential --- that the market whitens the stationary stream of each participant's metaorders, not any isolated one. The Lillo--Mike--Farmer model satisfies his premises, yet gives an isolated metaorder the super-square-root impact $φ^{(1-γ)/2}Q^{(1+γ)/2}$, $γ\\in(0,1)$, because single metaorders (i.e. not part of a stream) are statistically invisible and thus priced mechanically. We then construct an explicit multi-agent propagator that realizes Bonart's whitening, and show it reproduces the clean SRIL precisely when the market can attribute trades to their issuer. But correct re-attribution of anonymous trades is a formidable task, which requires markets to behave as implausibly efficient signal processing machines. The stream hypothesis makes a sharp, falsifiable prediction --- isolated metaorders, well separated in time, should not obey the SRIL --- that does not seem agree with empirical data known to us. Independently, a volume-conservation argument singles out the square-root law and lays bare the step the diffusivity route must assume: diffusivity fixes the variance of impact --- an additive, stationary, age-blind quantity --- whereas the SRIL is a law for the mean impact, which marginally decays as $1/\\sqrt{\\text{age}}$ and therefore demands an origin of time.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10053",
  "author_total": 3,
  "authors": [
    {
      "name": "J. -P. Bouchaud"
    },
    {
      "name": "I. Mastromatteo"
    },
    {
      "name": "B. Toth"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aphs8sss6vb15.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10053",
  "fulltext_url": null,
  "id": "aphs8sss6vb15",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10053",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "q-fin.TR"
    ],
    [
      "openalex",
      "2002|Complex Systems and Time Series Analysis"
    ]
  ],
  "openalex": "W7220933330",
  "pdf_url": "https://arxiv.org/pdf/2610.10053",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aphs8sss6vb15.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:37Z",
      "native_id": "2610.10053",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10053"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "On Bonart's interpretation of the Square-Root Impact Law",
  "title_text": "On Bonart's interpretation of the Square-Root Impact Law",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:37Z",
  "url": "https://research.draconitic.com/paper/aphs8sss6vb15",
  "venue": "arXiv",
  "versions": []
}