Pith Number

pith:5UOCVFSQ

pith:2025:5UOCVFSQBR2MKWM3UUIM62D2VK

not attested not anchored not stored refs pending

Convergence of Time-Averaged Mean Field Gradient Descent Dynamics for Continuous Multi-Player Zero-Sum Games

Pierre Monmarch\'e, Yulong Lu

arxiv:2505.07642 v1 · 2025-05-12 · math.OC · cs.LG · math.AP · math.PR · 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{5UOCVFSQBR2MKWM3UUIM62D2VK}

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	2026-07-05T11:01:51.226780Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ed1c2a96500c74c5599ba510cf687aaa85ab50fc6473c0d889baf31dd826e76a

Aliases

arxiv: 2505.07642 · arxiv_version: 2505.07642v1 · doi: 10.48550/arxiv.2505.07642 · pith_short_12: 5UOCVFSQBR2M · pith_short_16: 5UOCVFSQBR2MKWM3 · pith_short_8: 5UOCVFSQ

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/5UOCVFSQBR2MKWM3UUIM62D2VK \
  | 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: ed1c2a96500c74c5599ba510cf687aaa85ab50fc6473c0d889baf31dd826e76a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a8196331d2868197f15365bd29a66fec013b3429c9655d98746359a7536435cf",
    "cross_cats_sorted": [
      "cs.LG",
      "math.AP",
      "math.PR",
      "stat.ML"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2025-05-12T15:12:27Z",
    "title_canon_sha256": "71b500f5f3962a8001f31a7d88bf5b675cbf52bf45f52a0b8bdc392dd71da563"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2505.07642",
    "kind": "arxiv",
    "version": 1
  }
}