Pith Number

pith:PGRGPNZF

pith:2018:PGRGPNZFL2YROP2TX7WDE7HZ54

not attested not anchored not stored refs pending

On the (in)efficiency of MFG equilibria

Catherine Rainer (LM), Pierre Cardaliaguet (CEREMADE)

arxiv:1802.06637 v1 · 2018-02-19 · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PGRGPNZFL2YROP2TX7WDE7HZ54}

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

An example of multiple mean field limits in ergodic differential games

Receipt and verification

First computed	2026-05-18T00:23:02.698330Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

79a267b7255eb1173f53bfec327cf9ef3968d507c1d1dfeaf667fcc2bee0a28d

Aliases

arxiv: 1802.06637 · arxiv_version: 1802.06637v1 · doi: 10.48550/arxiv.1802.06637 · pith_short_12: PGRGPNZFL2YR · pith_short_16: PGRGPNZFL2YROP2T · pith_short_8: PGRGPNZF

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/PGRGPNZFL2YROP2TX7WDE7HZ54 \
  | 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: 79a267b7255eb1173f53bfec327cf9ef3968d507c1d1dfeaf667fcc2bee0a28d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e09e09baec029fd269119fdbfb04eefe85a620ac7b6c25ad428ff6dd39f968da",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2018-02-19T14:13:49Z",
    "title_canon_sha256": "13ea041f49f7c6353621aa33cdc733d158481ffcd79af75b1baf6e23d7803b4c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1802.06637",
    "kind": "arxiv",
    "version": 1
  }
}