Pith Number

pith:6AJU6LMU

pith:2013:6AJU6LMUTQ7I6YDC22LGGNWPT5

not attested not anchored not stored refs pending

A probabilistic weak formulation of mean field games and applications

Daniel Lacker, Rene Carmona

arxiv:1307.1152 v2 · 2013-07-03 · 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{6AJU6LMUTQ7I6YDC22LGGNWPT5}

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	2026-05-18T02:19:25.864340Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f0134f2d949c3e8f6062d6966336cf9f419ef304b1dd05e6ac0667ac84f8719c

Aliases

arxiv: 1307.1152 · arxiv_version: 1307.1152v2 · doi: 10.48550/arxiv.1307.1152 · pith_short_12: 6AJU6LMUTQ7I · pith_short_16: 6AJU6LMUTQ7I6YDC · pith_short_8: 6AJU6LMU

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/6AJU6LMUTQ7I6YDC22LGGNWPT5 \
  | 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: f0134f2d949c3e8f6062d6966336cf9f419ef304b1dd05e6ac0667ac84f8719c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d80568bd1b24a082b916b2715501947ef4b83d2c4f6a2e12efb7d4adb357c4ca",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-07-03T20:32:02Z",
    "title_canon_sha256": "8352e9be3c28345e265e079a6af7edfd131eba0307d29266f790c36eda92dbf7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.1152",
    "kind": "arxiv",
    "version": 2
  }
}