{
  "schema_version": 1,
  "problem_number": "AIM-PROBABILITY-0086",
  "title": "Spatial Mollification of the Multilayer Stochastic Heat Equation",
  "author": {
    "name": "Alper Ferudun",
    "affiliation": "Mercury Software GmbH",
    "url": "https://github.com/AlperTheKing"
  },
  "abstract": "We give a spatial mollifier construction of the O'Connell-Warren multilayer stochastic heat equation directly from nonintersecting Brownian bridges with coalesced endpoints. Both the fully Wick-ordered exponential of the total path energy and the product of separately Wick-ordered path weights converge to the chaos partition function in every finite Lp norm. The difference between the two approximations is O(epsilon^alpha) for every 0 < alpha < 1. The proof combines the established chaos and intersection-local-time estimates with a mollifier-independent inverse-gap bound for the mutual-path counterterm. All parameters, including the number of layers, are fixed. The comparison rate is not a rate to the limiting field; uniform sample-path convergence and temporal smoothing are not claimed. This supplies the spatial smoothing construction in AIM KPZ item 2.04 (UnsolvedMath AIM-PROBABILITY-0086, imported with the label 22.04). The work relies on and explicitly credits O'Connell and Warren's machinery. It is an AI-assisted, self-audited, unrefereed preprint, without independent peer review, formal verification or an absolute-priority claim.",
  "result_type": "COMPLETE_PROOF",
  "categories": [
    "math.PR",
    "math.MP"
  ],
  "keywords": [
    "stochastic heat equation",
    "multilayer polymer",
    "spatial mollification",
    "Dyson Brownian bridge",
    "Wick exponential",
    "nonintersecting paths"
  ],
  "manuscript_version_date": "2026-10-12",
  "publication_date": "2026-10-12",
  "publication_date_kind": "first public online release",
  "version": "1.0",
  "date_modified": "2026-10-12",
  "presentation_revision_only": false,
  "doi_archived_file_version": "1.0",
  "status": "unrefereed preprint",
  "canonical_url": "https://eulersolve.org/papers/aim-probability-0086/",
  "pdf_url": "https://eulersolve.org/papers/aim-probability-0086/paper.pdf?v=f0320168ac4f",
  "doi": "10.5281/zenodo.23315978",
  "zenodo_record_url": "https://zenodo.org/records/23315978",
  "license": "https://creativecommons.org/licenses/by/4.0/",
  "scope_caveat": "Complete spatial smoothing construction at coalesced endpoints for every fixed finite layer number, real noise strength and positive time. Both Wick conventions converge in all finite Lp norms. Their comparison rate is not a rate to the limiting field. No uniform sample-path, temporal-smoothing or large-layer assertion. The O'Connell-Warren machinery is explicitly credited. AI-assisted, self-audited and unrefereed; no independent review, formal verification or absolute-priority certification is claimed.",
  "files": {
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      "sha256": "f0320168ac4fbb76e8915ffc5131b0830d12d36a40c8739a43115409420683ed"
    },
    "source.zip": {
      "sha256": "aca9f3b4a3a8a6801e8617206e69c18a41746f664c36726e1946bcbd453f82c3"
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    "verification_report.md": {
      "sha256": "a60ce12f7ef5a4424d93098ca5c7153f942e69cb7822fc7a6ce3019263a45595"
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  },
  "ai_use_disclosure": "AI-assisted tools supported research, computation, proof development, and manuscript preparation. The author remains responsible for all claims and the final text."
}