Pith Number

pith:GTAR45GQ

pith:2016:GTAR45GQKTRSELKORGVMMGMR7N

not attested not anchored not stored refs pending

A Fractional Micro-Macro Model for Crowds of Pedestrians based on Fractional Mean Field Games

Dan Stuart, Ke-cai Cao, YangQuan Chen

arxiv:1602.01211 v1 · 2016-02-03 · nlin.AO · physics.soc-ph

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GTAR45GQKTRSELKORGVMMGMR7N}

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	2026-05-18T01:21:20.799061Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

34c11e74d054e3222d4e89aac61991fb4f9648411b977dfa2d4ea0495eb6df6b

Aliases

arxiv: 1602.01211 · arxiv_version: 1602.01211v1 · doi: 10.48550/arxiv.1602.01211 · pith_short_12: GTAR45GQKTRS · pith_short_16: GTAR45GQKTRSELKO · pith_short_8: GTAR45GQ

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/GTAR45GQKTRSELKORGVMMGMR7N \
  | 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: 34c11e74d054e3222d4e89aac61991fb4f9648411b977dfa2d4ea0495eb6df6b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ecdca76a251ebfe2eaafa66edba8662201e32edcaf8c01c2f724916f26635068",
    "cross_cats_sorted": [
      "physics.soc-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "nlin.AO",
    "submitted_at": "2016-02-03T07:05:17Z",
    "title_canon_sha256": "b9bc15ad23ad8599d89ac870e921d20a0add697450824437fb5cca9045bb00f3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1602.01211",
    "kind": "arxiv",
    "version": 1
  }
}