Pith Number

pith:56LRP4ZD

pith:2016:56LRP4ZDMS3ERQNN2QE2JGEWY3

not attested not anchored not stored refs pending

Mean Field Model for Collective Motion Bistability

George Papanicolaou, Josselin Garnier, Tzu-Wei Yang

arxiv:1611.02194 v2 · 2016-11-07 · 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{56LRP4ZDMS3ERQNN2QE2JGEWY3}

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	2026-05-18T00:21:41.323673Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ef9717f32364b648c1add409a49896c6cc355c67e3bd14f5ecfaa77650f59054

Aliases

arxiv: 1611.02194 · arxiv_version: 1611.02194v2 · doi: 10.48550/arxiv.1611.02194 · pith_short_12: 56LRP4ZDMS3E · pith_short_16: 56LRP4ZDMS3ERQNN · pith_short_8: 56LRP4ZD

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/56LRP4ZDMS3ERQNN2QE2JGEWY3 \
  | 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: ef9717f32364b648c1add409a49896c6cc355c67e3bd14f5ecfaa77650f59054

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "48562bcbd7f362fd17f1ade475da5e212e6f211f655e4f21491a070c16dec187",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-11-07T18:07:42Z",
    "title_canon_sha256": "57c784d97865506c87fc4d81bdb0d8174c7fea2ad46b239b2ce32f4e104fa781"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.02194",
    "kind": "arxiv",
    "version": 2
  }
}