Pith Number

pith:WPL33N5R

pith:2015:WPL33N5RXTXZCBTLMDX2J4UVOJ

not attested not anchored not stored refs pending

Existence of positive solutions for an approximation of stationary mean-field games

Andreia Chapouto, Andr\'e Rodrigues, Avetik Karagulyan, Chuliang Song, Daniela Jord\~ao, David Evangelista Junior, Diogo Gomes, Elena Bachini, Giorgia Pagliar, Hector Velasco-Perez, Jo\~ao Reis, Juan Monasterio, Kengo Terai, Levon Nurbekyan, Marco Piccirilli, Mariana Prazeres, Maria Sargsyan, Nojood Almayouf, Orlando Romero, Rita Ferreira, Ryota Tomisaki, Sagar Pratapsi, Tommaso Seneci, Vardan Voskanyan, Xianjin Yang

arxiv:1511.06999 v2 · 2015-11-22 · 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{WPL33N5RXTXZCBTLMDX2J4UVOJ}

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	2026-05-18T00:53:26.281528Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b3d7bdb7b1bcef91066b60efa4f295724eb340265e08ff6cfc4c654ee5a2cb4c

Aliases

arxiv: 1511.06999 · arxiv_version: 1511.06999v2 · doi: 10.48550/arxiv.1511.06999 · pith_short_12: WPL33N5RXTXZ · pith_short_16: WPL33N5RXTXZCBTL · pith_short_8: WPL33N5R

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/WPL33N5RXTXZCBTLMDX2J4UVOJ \
  | 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: b3d7bdb7b1bcef91066b60efa4f295724eb340265e08ff6cfc4c654ee5a2cb4c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b1d4c5e1f87e026986a5ad34193675990d6828e1e6b4c539ee93729c303575a9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-11-22T12:01:09Z",
    "title_canon_sha256": "88c8794a33f039bd6fffdc3490fbbfaa9d0a7558bca7093a62406c963e8dc0a6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.06999",
    "kind": "arxiv",
    "version": 2
  }
}