Pith Number

pith:MZR4CKHF

pith:2012:MZR4CKHF6TKJPTCBILH6LEDWZA

not attested not anchored not stored refs pending

\epsilon-Nash Mean Field Game Theory for Nonlinear Stochastic Dynamical Systems with Major and Minor Agents

Mojtaba Nourian, Peter E. Caines

arxiv:1209.5684 v3 · 2012-09-25 · 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{MZR4CKHF6TKJPTCBILH6LEDWZA}

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	2026-05-18T03:21:43.604927Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6663c128e5f4d497cc4142cfe59076c811644e2a96b8e0fbcc6e7edf3d8126de

Aliases

arxiv: 1209.5684 · arxiv_version: 1209.5684v3 · doi: 10.48550/arxiv.1209.5684 · pith_short_12: MZR4CKHF6TKJ · pith_short_16: MZR4CKHF6TKJPTCB · pith_short_8: MZR4CKHF

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/MZR4CKHF6TKJPTCBILH6LEDWZA \
  | 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: 6663c128e5f4d497cc4142cfe59076c811644e2a96b8e0fbcc6e7edf3d8126de

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b1e9785c9c782d09e0cb6c2391bbd7bc887642c72b28a9b9cbba9310ecbf2c46",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2012-09-25T17:04:22Z",
    "title_canon_sha256": "f6ea3e72315a464d1b70d86e5e171956db75ab6991b4f83c22f14a496324ba49"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.5684",
    "kind": "arxiv",
    "version": 3
  }
}