Pith Number

pith:AZ4GWUZJ

pith:2015:AZ4GWUZJ6KVBJTFMA5KME42MRX

not attested not anchored not stored refs pending

An Ordinary Differential Equation Model for Fish Schooling

Atsushi Yagi, Takeshi Uchitane, Ta Viet Ton

arxiv:1508.05597 v2 · 2015-08-23 · 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{AZ4GWUZJ6KVBJTFMA5KME42MRX}

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	2026-05-18T01:34:41.492494Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

06786b5329f2aa14ccac0754c2734c8de6ee1cf8102d480b0703e8c509a820f9

Aliases

arxiv: 1508.05597 · arxiv_version: 1508.05597v2 · doi: 10.48550/arxiv.1508.05597 · pith_short_12: AZ4GWUZJ6KVB · pith_short_16: AZ4GWUZJ6KVBJTFM · pith_short_8: AZ4GWUZJ

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/AZ4GWUZJ6KVBJTFMA5KME42MRX \
  | 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: 06786b5329f2aa14ccac0754c2734c8de6ee1cf8102d480b0703e8c509a820f9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8dcb6cc7b4ed963bcfa437e0247aebcb5188e3689ed12942b0fa1399cc26652e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-08-23T11:38:37Z",
    "title_canon_sha256": "a86e49e7e4299b5be94b30775b76d389c3be446850a478e00a9809609dd2d069"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.05597",
    "kind": "arxiv",
    "version": 2
  }
}