Pith Number

pith:3NSUGGP7

pith:2021:3NSUGGP72RJMLWJN7XHR7CQRRF

not attested not anchored not stored refs pending

Empirical Policy Optimization for $n$-Player Markov Games

Dongbin Zhao, Dong Li, Mengchen Zhao, Yuanheng Zhu

arxiv:2110.08979 v1 · 2021-10-18 · cs.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3NSUGGP72RJMLWJN7XHR7CQRRF}

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	2026-07-05T03:23:22.560103Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

db654319ffd452c5d92dfdcf1f8a118957c42cff2e1752ae8154bf0adb3b5573

Aliases

arxiv: 2110.08979 · arxiv_version: 2110.08979v1 · doi: 10.48550/arxiv.2110.08979 · pith_short_12: 3NSUGGP72RJM · pith_short_16: 3NSUGGP72RJMLWJN · pith_short_8: 3NSUGGP7

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/3NSUGGP72RJMLWJN7XHR7CQRRF \
  | 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: db654319ffd452c5d92dfdcf1f8a118957c42cff2e1752ae8154bf0adb3b5573

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fb6e17f91e76ce430b0e537a93126f7a36d78ca7b9971fe95ae7f6c481c85494",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "cs.GT",
    "submitted_at": "2021-10-18T02:14:57Z",
    "title_canon_sha256": "3fbed4d208b07303620c76192b49cd886459bf686e2f151639b7745193985609"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2110.08979",
    "kind": "arxiv",
    "version": 1
  }
}