Pith Number

pith:3BHSV4B6

pith:2025:3BHSV4B6RVWKHKOFGUWDXRB7DV

not attested not anchored not stored refs pending

On the spatio-temporal increments of nonlinear parabolic SPDEs and the open KPZ equation

Cheuk Yin Lee, Jingwu Hu

Nonlinear parabolic SPDEs on bounded intervals have exact local and uniform spatio-temporal moduli of continuity.

arxiv:2508.05032 v3 · 2025-08-07 · math.PR

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\pithnumber{3BHSV4B6RVWKHKOFGUWDXRB7DV}

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Record completeness

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We identify the exact local and uniform spatio-temporal moduli of continuity for the sample functions of the solutions to nonlinear parabolic SPDEs on a bounded interval with Dirichlet, Neumann, or Robin boundary conditions.

C2weakest assumption

The results rest on new strong local non-determinism properties for the linear stochastic heat equation under the various boundary conditions, together with detailed control of linearization errors for the nonlinear increments, as stated in the abstract.

C3one line summary

Exact spatio-temporal moduli of continuity, small-ball estimates, and iterated logarithm laws are established for nonlinear parabolic SPDEs and extended to the open KPZ equation on the unit interval.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-06-11T01:09:16.017181Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d84f2af03e8d6ca3a9c5352c3bc43f1d6cf36f8103a6cb82327b494f2c2bdb21

Aliases

arxiv: 2508.05032 · arxiv_version: 2508.05032v3 · doi: 10.48550/arxiv.2508.05032 · pith_short_12: 3BHSV4B6RVWK · pith_short_16: 3BHSV4B6RVWKHKOF · pith_short_8: 3BHSV4B6

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/3BHSV4B6RVWKHKOFGUWDXRB7DV \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: d84f2af03e8d6ca3a9c5352c3bc43f1d6cf36f8103a6cb82327b494f2c2bdb21

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5ea1a260aba99d858b1b6f39b51b50dd38c8d36ce1ea01ecbffaed01d1119a19",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2025-08-07T05:12:52Z",
    "title_canon_sha256": "7bdb5c02199e8095aa1662f06c5a918731e3025aee396176dec217fcff28201f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.05032",
    "kind": "arxiv",
    "version": 3
  }
}