Pith Number

pith:D222UKNN

pith:2026:D222UKNNACAPGB77MKBOC4JXPO

not attested not anchored not stored refs pending

Aggregate in the Advantage, Not the Ratio: A Canonical-Form Analysis of Cooperative Multi-Agent Policy Optimization

Sen Li, Zijian Zhao

arxiv:2607.17924 v1 · 2026-07-20 · cs.MA · cs.LG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{D222UKNNACAPGB77MKBOC4JXPO}

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	2026-07-21T02:22:06.866746Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1eb5aa29ad0080f307ff6282e171377b83841a9b50a8a270c6a7c9561f893f9d

Aliases

arxiv: 2607.17924 · arxiv_version: 2607.17924v1 · doi: 10.48550/arxiv.2607.17924 · pith_short_12: D222UKNNACAP · pith_short_16: D222UKNNACAPGB77 · pith_short_8: D222UKNN

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/D222UKNNACAPGB77MKBOC4JXPO \
  | 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: 1eb5aa29ad0080f307ff6282e171377b83841a9b50a8a270c6a7c9561f893f9d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "46c514199523fb7d7f576d89118e2b8e299a636064d6db2b6475396af6cfbee1",
    "cross_cats_sorted": [
      "cs.LG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.MA",
    "submitted_at": "2026-07-20T13:20:29Z",
    "title_canon_sha256": "109890c079e2fc21f98aa66fcdf93d31306d12cf32d8002e10e2b8ac9a5df59d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.17924",
    "kind": "arxiv",
    "version": 1
  }
}