Pith Number

pith:4D45D2NH

pith:2023:4D45D2NH4QNDZRZ73HVS76JZBA

not attested not anchored not stored refs pending

Hardness of Independent Learning and Sparse Equilibrium Computation in Markov Games

Dylan J. Foster, Noah Golowich, Sham M. Kakade

arxiv:2303.12287 v1 · 2023-03-22 · cs.LG · cs.AI · cs.GT · stat.ML

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4D45D2NH4QNDZRZ73HVS76JZBA}

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	2026-07-05T05:53:39.385257Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e0f9d1e9a7e41a3cc73fd9eb2ff939082e4b954094dfb6bc0e075ad7ffd739fc

Aliases

arxiv: 2303.12287 · arxiv_version: 2303.12287v1 · doi: 10.48550/arxiv.2303.12287 · pith_short_12: 4D45D2NH4QND · pith_short_16: 4D45D2NH4QNDZRZ7 · pith_short_8: 4D45D2NH

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/4D45D2NH4QNDZRZ73HVS76JZBA \
  | 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: e0f9d1e9a7e41a3cc73fd9eb2ff939082e4b954094dfb6bc0e075ad7ffd739fc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7e56f333dce5fe65a4a0b2f610166013ee0c56ff62e21d081d990a8c88eb7e39",
    "cross_cats_sorted": [
      "cs.AI",
      "cs.GT",
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2023-03-22T03:28:12Z",
    "title_canon_sha256": "89446bd4a4885262a81d68a1612276aa6cb447a4c952b0d0caacd686cac1b3f9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2303.12287",
    "kind": "arxiv",
    "version": 1
  }
}