Pith Number

pith:OF3MLSQ5

pith:2026:OF3MLSQ5EH7VNVTL6YPNOGMR66

not attested not anchored not stored refs pending

Kernel-based potential mean-field games with unbiased random Fourier $U$-statistics

Yumiharu Nakano

arxiv:2605.29371 v1 · 2026-05-28 · math.OC · cs.LG · cs.NA · math.NA · 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{OF3MLSQ5EH7VNVTL6YPNOGMR66}

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	2026-05-29T01:05:35.759474Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7176c5ca1d21ff56d66bf61ed71991f796084b69e75bfd62451ec916f21df273

Aliases

arxiv: 2605.29371 · arxiv_version: 2605.29371v1 · doi: 10.48550/arxiv.2605.29371 · pith_short_12: OF3MLSQ5EH7V · pith_short_16: OF3MLSQ5EH7VNVTL · pith_short_8: OF3MLSQ5

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/OF3MLSQ5EH7VNVTL6YPNOGMR66 \
  | 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: 7176c5ca1d21ff56d66bf61ed71991f796084b69e75bfd62451ec916f21df273

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "585f7f446b325d6007eea20ee3b9de14d13dc7b8229fb015575f4448e9ce2ad3",
    "cross_cats_sorted": [
      "cs.LG",
      "cs.NA",
      "math.NA",
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-05-28T05:15:25Z",
    "title_canon_sha256": "b7d7726198c8174621ae901cb59ec6c3f0ea4f394a836e0f9c6a2911aea5e4ba"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.29371",
    "kind": "arxiv",
    "version": 1
  }
}