Pith Number

pith:W6COOEZQ

pith:2009:W6COOEZQ3AJJQNQHBYGSUQZAT6

not attested not anchored not stored refs pending

Expansion of the propagation of chaos for Bird and Nanbu systems

Sylvain Rubenthaler (JAD)

arxiv:0901.3476 v10 · 2009-01-22 · 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{W6COOEZQ3AJJQNQHBYGSUQZAT6}

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	2026-05-18T01:02:05.526633Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b784e71330d8129836070e0d2a43209fb8be4bbddba253c8d4320478fe7038fd

Aliases

arxiv: 0901.3476 · arxiv_version: 0901.3476v10 · doi: 10.48550/arxiv.0901.3476 · pith_short_12: W6COOEZQ3AJJ · pith_short_16: W6COOEZQ3AJJQNQH · pith_short_8: W6COOEZQ

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/W6COOEZQ3AJJQNQHBYGSUQZAT6 \
  | 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: b784e71330d8129836070e0d2a43209fb8be4bbddba253c8d4320478fe7038fd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a7bb122d4ba1a2e23731851370b5b732152f37de4291250203547938735f9281",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2009-01-22T13:13:26Z",
    "title_canon_sha256": "5fef1334fdfa616afa619c9749828943fefdd799cec99ace0ce6a318a13e29eb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0901.3476",
    "kind": "arxiv",
    "version": 10
  }
}