Pith Number

pith:X5DG22Z4

pith:2012:X5DG22Z4S4PVJWCQY6P46NQSPM

not attested not anchored not stored refs pending

Probabilistic Analysis of Mean-Field Games

Francois Delarue, Rene Carmona

arxiv:1210.5780 v1 · 2012-10-21 · 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{X5DG22Z4S4PVJWCQY6P46NQSPM}

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	2026-05-18T03:42:43.041963Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bf466d6b3c971f54d850c79fcf36127b14d21dd35f4bbe0358d03bc2ff057786

Aliases

arxiv: 1210.5780 · arxiv_version: 1210.5780v1 · doi: 10.48550/arxiv.1210.5780 · pith_short_12: X5DG22Z4S4PV · pith_short_16: X5DG22Z4S4PVJWCQ · pith_short_8: X5DG22Z4

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/X5DG22Z4S4PVJWCQY6P46NQSPM \
  | 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: bf466d6b3c971f54d850c79fcf36127b14d21dd35f4bbe0358d03bc2ff057786

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2791206b345cd2c23309208d2f71805c4987ffeee8a457edb9688a058bb858a7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-10-21T23:31:42Z",
    "title_canon_sha256": "d41cabd9fdbc5bf24ced7d1572e97933b81785b40c2dd58385cbc2760de9a26d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.5780",
    "kind": "arxiv",
    "version": 1
  }
}