Pith Number

pith:CJIPGVCA

pith:2011:CJIPGVCAZFRJ6P3UOLSZ355U4E

not attested not anchored not stored refs pending

Size of Union

Boli Wang, Min Yan, Yuanzhong Ou

arxiv:1108.2339 v3 · 2011-08-11 · math.CO · 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{CJIPGVCAZFRJ6P3UOLSZ355U4E}

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	2026-05-18T03:49:10.448214Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1250f35440c9629f3f7472e59df7b4e122cf958dbf5f023bf689ae74fa2599d7

Aliases

arxiv: 1108.2339 · arxiv_version: 1108.2339v3 · doi: 10.48550/arxiv.1108.2339 · pith_short_12: CJIPGVCAZFRJ · pith_short_16: CJIPGVCAZFRJ6P3U · pith_short_8: CJIPGVCA

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/CJIPGVCAZFRJ6P3UOLSZ355U4E \
  | 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: 1250f35440c9629f3f7472e59df7b4e122cf958dbf5f023bf689ae74fa2599d7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "53714e29281d3f53191c4fb59aa7317076f84e7478ac64df3c6760b32374e84f",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-08-11T07:38:49Z",
    "title_canon_sha256": "90c365b5455c87c38307f4a9d53fd393dea4c9b1f4a150593771725abe13052c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.2339",
    "kind": "arxiv",
    "version": 3
  }
}