Pith Number

pith:2YOMLPC3

pith:2015:2YOMLPC3DHO3KAGSUISFVJED7H

not attested not anchored not stored refs pending

The master equation and the convergence problem in mean field games

Fran\c{c}ois Delarue, Jean-Michel Lasry, Pierre Cardaliaguet, Pierre-Louis Lions

arxiv:1509.02505 v1 · 2015-09-08 · 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{2YOMLPC3DHO3KAGSUISFVJED7H}

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.

Cited by

1 paper in Pith

Relative Arbitrage Opportunities with Interactions among $N$ Investors

Receipt and verification

First computed	2026-05-18T01:33:40.758798Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d61cc5bc5b19ddb500d2a2245aa483f9cc2a51b9a8ee5589015e766e8078a72b

Aliases

arxiv: 1509.02505 · arxiv_version: 1509.02505v1 · doi: 10.48550/arxiv.1509.02505 · pith_short_12: 2YOMLPC3DHO3 · pith_short_16: 2YOMLPC3DHO3KAGS · pith_short_8: 2YOMLPC3

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/2YOMLPC3DHO3KAGSUISFVJED7H \
  | 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: d61cc5bc5b19ddb500d2a2245aa483f9cc2a51b9a8ee5589015e766e8078a72b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7d6efe40e04fcbb0be352fa35b179fd7b29aaed63a7fa09226219ab008e46aeb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-09-08T19:24:27Z",
    "title_canon_sha256": "7c5d68d3a42058bf635c678bb7032af6636eb9edbd90dd4660ceeb70e21c1848"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.02505",
    "kind": "arxiv",
    "version": 1
  }
}