{
  "abstract": "Branching stochastic mechanics (BSM) provides a reciprocal branching representation of the Schrödinger--Nagasawa pair. Its centered forward--backward kernel $C_{\\rm FB}=\\mathbb E_ω[ψ_Fψ_B]$ resolves an organized connected sector, with weight $ρ_{\\rm BSM}=-C_{\\rm FB}(x,x)$ on the anticorrelated branch. Here we investigate how this sector forms, localizes, and propagates under Bohm/Fisher feedback. We retain the branching covariance on the prescribed background as the bare noise kernel and truncate the nonlinear interaction to Bohm/Fisher drift vertices. A Martin--Siggia--Rose--Janssen--de Dominicis formulation and a causal two-loop two-particle-irreducible (2PI) closure determine response and correlation functions self-consistently. While the free connected theory exhibits secular growth and ultraviolet accumulation, the dressed theory develops a finite relative screening length. A reduced numerical evolution shows bounded formation of the localized sector, and a self-similar Fisher construction defines a saturated information velocity $c_\\star$. A Born--Oppenheimer separation connects this internal organization to collective propagation. The instantaneous adiabatic kernel has two pole families at fixed internal momentum: a gapless difference branch and a gapped sum branch. Projecting both inverse response kernels onto the same localized internal profile defines their collective coefficients. If both propagation speeds match $c_\\star$ and the projected gap matches $mc_\\star^2/\\hbar$, the gapped branch takes the infrared Klein--Gordon form. These matching conditions define a candidate relativistic fixed point whose dynamical realization remains to be tested.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02520",
  "author_total": 2,
  "authors": [
    {
      "name": "Benoit Bischoff"
    },
    {
      "name": "Eric Dumonteil"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/57cqhtq7fhtmz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02520",
  "fulltext_url": null,
  "id": "57cqhtq7fhtmz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02520",
  "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",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum Mechanics and Applications"
    ]
  ],
  "openalex": "W7207541246",
  "pdf_url": "https://arxiv.org/pdf/2609.02520",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/57cqhtq7fhtmz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:19Z",
      "native_id": "2609.02520",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02520"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Branching stochastic mechanics: Relative localization and collective poles from Bohm/Fisher feedback",
  "title_text": "Branching stochastic mechanics: Relative localization and collective poles from Bohm/Fisher feedback",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:19Z",
  "url": "https://research.draconitic.com/paper/57cqhtq7fhtmz",
  "venue": "arXiv",
  "versions": []
}