Pith Number

pith:U6F5LYFZ

pith:2019:U6F5LYFZSKV57NVSOEBIGLW6YS

not attested not anchored not stored refs pending

Mean Field Games for Multi-agent Systems with Multiplicative Noises

Bing-Chang Wang, Huanshui Zhang, Yuan-Hua Ni

arxiv:1906.03177 v1 · 2019-06-07 · 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{U6F5LYFZSKV57NVSOEBIGLW6YS}

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	2026-05-17T23:43:54.767375Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a78bd5e0b992abdfb6b27102832edec4b2838d2cdaac0d963d58744e963edf76

Aliases

arxiv: 1906.03177 · arxiv_version: 1906.03177v1 · doi: 10.48550/arxiv.1906.03177 · pith_short_12: U6F5LYFZSKV5 · pith_short_16: U6F5LYFZSKV57NVS · pith_short_8: U6F5LYFZ

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/U6F5LYFZSKV57NVSOEBIGLW6YS \
  | 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: a78bd5e0b992abdfb6b27102832edec4b2838d2cdaac0d963d58744e963edf76

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dacb22ba8e7f6877bc62ee54dc66c72aa6c4fd26589cd6eeb0a39b5871a212f0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2019-06-07T15:43:58Z",
    "title_canon_sha256": "f532aa41d9da65ceda2627a6fe59a00bde2cef6c3bc38f4b00366f3d1311bc5e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1906.03177",
    "kind": "arxiv",
    "version": 1
  }
}