Pith Number

pith:CBY4K5CA

pith:2012:CBY4K5CAQ2W4E7N6ZKOHJZVHTN

not attested not anchored not stored refs pending

A Combinatorial Interpretation of the Joint Cumulant

Connor Ahlbach, Jeremy Usatine, Nicholas Pippenger

arxiv:1211.0652 v1 · 2012-11-03 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CBY4K5CAQ2W4E7N6ZKOHJZVHTN}

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	2026-05-18T03:41:32.916016Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1071c5744086adc27dbeca9c74e6a79b5af3ccd203589007ab30bdffbe46434e

Aliases

arxiv: 1211.0652 · arxiv_version: 1211.0652v1 · doi: 10.48550/arxiv.1211.0652 · pith_short_12: CBY4K5CAQ2W4 · pith_short_16: CBY4K5CAQ2W4E7N6 · pith_short_8: CBY4K5CA

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/CBY4K5CAQ2W4E7N6ZKOHJZVHTN \
  | 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: 1071c5744086adc27dbeca9c74e6a79b5af3ccd203589007ab30bdffbe46434e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "59db45094418cef3a675a24ff331dfa77b379032e71001e16b2c2d54ac6da55f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-11-03T23:59:38Z",
    "title_canon_sha256": "625bdc55523f95831fb966bcfd63e7fdb71493449a9492840409465fa0183f80"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.0652",
    "kind": "arxiv",
    "version": 1
  }
}