Pith Number

pith:LUBYLY5G

pith:2026:LUBYLY5GJFMF6TPXWFPPWKC62W

not attested not anchored not stored refs pending

Non-Uniqueness for Nonlinear Fokker--Planck Equations and Their Associated Distribution-Dependent SDEs

Huaxiang L\"u

arxiv:2606.31500 v1 · 2026-06-30 · math.PR · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LUBYLY5GJFMF6TPXWFPPWKC62W}

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	2026-07-01T01:18:05.146441Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5d0385e3a649585f4df7b15efb285ed5bb4f506143f16fba712b67fc2457a4fa

Aliases

arxiv: 2606.31500 · arxiv_version: 2606.31500v1 · doi: 10.48550/arxiv.2606.31500 · pith_short_12: LUBYLY5GJFMF · pith_short_16: LUBYLY5GJFMF6TPX · pith_short_8: LUBYLY5G

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/LUBYLY5GJFMF6TPXWFPPWKC62W \
  | 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: 5d0385e3a649585f4df7b15efb285ed5bb4f506143f16fba712b67fc2457a4fa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4d00bc81542202d8fd90748262b99730b3d0cfb280b589bae6c5f97c0620bc18",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-06-30T11:20:46Z",
    "title_canon_sha256": "c6b1bef44a81900e66ef3d50f4b28fad6d03fb2b474339a7ba41a77b6bde3a66"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.31500",
    "kind": "arxiv",
    "version": 1
  }
}