Pith Number

pith:RFVN3EKL

pith:2015:RFVN3EKLO2Q524JR72WWK6BAFP

not attested not anchored not stored refs pending

Convergence of Stochastic Interacting Particle Systems in Probability under a Sobolev Norm

Jian-Guo Liu, Yuan Zhang

arxiv:1511.07014 v2 · 2015-11-22 · 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{RFVN3EKLO2Q524JR72WWK6BAFP}

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	2026-05-18T01:25:33.230615Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

896add914b76a1dd7131fead6578202be3dc9edf2c96f6262f2cc95e8f242fe2

Aliases

arxiv: 1511.07014 · arxiv_version: 1511.07014v2 · doi: 10.48550/arxiv.1511.07014 · pith_short_12: RFVN3EKLO2Q5 · pith_short_16: RFVN3EKLO2Q524JR · pith_short_8: RFVN3EKL

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/RFVN3EKLO2Q524JR72WWK6BAFP \
  | 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: 896add914b76a1dd7131fead6578202be3dc9edf2c96f6262f2cc95e8f242fe2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8c4ddc90e65b9bd804f92faf73687ebe5dc852f3f296c898ecbdc98f59c4c7b7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-11-22T14:15:53Z",
    "title_canon_sha256": "57d3dba590826f0cab29e4005ec30d040b89ae6a4d4b51c4cd952879693719a6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.07014",
    "kind": "arxiv",
    "version": 2
  }
}