Pith Number

pith:5WE2L5CB

pith:2015:5WE2L5CBCWEBPVACHP4NJUNX5H

not attested not anchored not stored refs pending

Propagation of moments and uniqueness of weak solutions to the Vlasov-Poisson-Fokker-Planck system

Lifeng Zhao, Ze Li

arxiv:1503.04425 v3 · 2015-03-15 · 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{5WE2L5CBCWEBPVACHP4NJUNX5H}

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	2026-05-18T00:32:36.656648Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ed89a5f441158817d4023bf8d4d1b7e9cf8540ecd27296ae7f03ae06458b8a22

Aliases

arxiv: 1503.04425 · arxiv_version: 1503.04425v3 · doi: 10.48550/arxiv.1503.04425 · pith_short_12: 5WE2L5CBCWEB · pith_short_16: 5WE2L5CBCWEBPVAC · pith_short_8: 5WE2L5CB

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/5WE2L5CBCWEBPVACHP4NJUNX5H \
  | 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: ed89a5f441158817d4023bf8d4d1b7e9cf8540ecd27296ae7f03ae06458b8a22

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d26305fd4644621e7002c462602ee51e75923d86f088cc5c316fe33a0ca2e45f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-03-15T13:42:10Z",
    "title_canon_sha256": "fea969041c2d89161a37e836485a0c79f3f872cb7a6c2379d4785ef3a458a969"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.04425",
    "kind": "arxiv",
    "version": 3
  }
}