Pith Number

pith:4UQVFAGY

pith:2016:4UQVFAGYVEEEVNTMNGTPDC4ZHV

not attested not anchored not stored refs pending

Markov-Nash Equilibria in Mean-Field Games with Discounted Cost

Maxim Raginsky, Naci Saldi, Tamer Ba\c{s}ar

arxiv:1612.07878 v2 · 2016-12-23 · cs.SY · 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{4UQVFAGYVEEEVNTMNGTPDC4ZHV}

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	2026-05-18T00:52:49.133147Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e5215280d8a9084ab66c69a6f18b993d6e1fcaf1a9710630c4682222e5ee344a

Aliases

arxiv: 1612.07878 · arxiv_version: 1612.07878v2 · doi: 10.48550/arxiv.1612.07878 · pith_short_12: 4UQVFAGYVEEE · pith_short_16: 4UQVFAGYVEEEVNTM · pith_short_8: 4UQVFAGY

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/4UQVFAGYVEEEVNTMNGTPDC4ZHV \
  | 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: e5215280d8a9084ab66c69a6f18b993d6e1fcaf1a9710630c4682222e5ee344a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "788820e0493884844e795bfad8814a55676baa7e81ee36b3c29c96119681a334",
    "cross_cats_sorted": [
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.SY",
    "submitted_at": "2016-12-23T05:34:28Z",
    "title_canon_sha256": "16e9f43880a072a22bc1d5c75639fdd068d3e69e236e1c3c8a2a5f80fbdea3f0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.07878",
    "kind": "arxiv",
    "version": 2
  }
}