Pith Number

pith:V6GJBAGM

pith:2022:V6GJBAGMDVVWXCX5FBIVRK7C4B

not attested not anchored not stored refs pending

Entropic Fictitious Play for Mean Field Optimization Problem

Fan Chen, Songbo Wang, Zhenjie Ren

arxiv:2202.05841 v2 · 2022-02-11 · math.OC · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{V6GJBAGMDVVWXCX5FBIVRK7C4B}

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	2026-07-05T06:41:43.597385Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

af8c9080cc1d6b6b8afd285158abe2e0705da5b5de863918fc8ea3acfa06f9e3

Aliases

arxiv: 2202.05841 · arxiv_version: 2202.05841v2 · doi: 10.48550/arxiv.2202.05841 · pith_short_12: V6GJBAGMDVVW · pith_short_16: V6GJBAGMDVVWXCX5 · pith_short_8: V6GJBAGM

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/V6GJBAGMDVVWXCX5FBIVRK7C4B \
  | 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: af8c9080cc1d6b6b8afd285158abe2e0705da5b5de863918fc8ea3acfa06f9e3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "711fae4517142e234d8c217b5984edb97b28688d88e15686e338a4706044e81c",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2022-02-11T14:38:00Z",
    "title_canon_sha256": "9f8ef500bf486a514783a1a5414ef7cb8dae67dc6e10250a201ab340d3eb0a11"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2202.05841",
    "kind": "arxiv",
    "version": 2
  }
}