Pith Number

pith:SV22WFSC

pith:2026:SV22WFSC5USWWZBAEJZJR2QZQ6

not attested not anchored not stored refs pending

Nonlinear PDEs with modulated dispersion III: multiplicative noises

Andreia Chapouto, Guopeng Li, Jiawei Li, Massimiliano Gubinelli, Tadahiro Oh

arxiv:2607.08385 v1 · 2026-07-09 · math.AP · math.PR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SV22WFSC5USWWZBAEJZJR2QZQ6}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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.

Receipt and verification

First computed	2026-07-10T01:19:48.711417Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9575ab1642ed256b6420227298ea198796ed5eabf99f66b059d699bf397d866b

Aliases

arxiv: 2607.08385 · arxiv_version: 2607.08385v1 · doi: 10.48550/arxiv.2607.08385 · pith_short_12: SV22WFSC5USW · pith_short_16: SV22WFSC5USWWZBA · pith_short_8: SV22WFSC

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/SV22WFSC5USWWZBAEJZJR2QZQ6 \
  | 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: 9575ab1642ed256b6420227298ea198796ed5eabf99f66b059d699bf397d866b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6de3a9c3d075b1b28c99d0e05b21236a977058774c53b1ce135bca1bb57fc780",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-07-09T12:03:44Z",
    "title_canon_sha256": "518b33bd6c3414d2606a11b9ffb33dc9be4c2767034b1a7303597f842cf6783d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.08385",
    "kind": "arxiv",
    "version": 1
  }
}