Pith Number

pith:N3TW67P7

pith:2012:N3TW67P7YRWJPC4HTILSZPP7WL

not attested not anchored not stored refs pending

The Reciprocal of $\sum_{n\geq 0}a^nb^n$ for non-commuting $a$ and $b$, Catalan numbers and non-commutative quadratic equations

Arkady Berenstein, Christophe Reutenauer, Doron Zeilberger, Vladimir Retakh

arxiv:1206.4225 v2 · 2012-06-19 · math.CO · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{N3TW67P7YRWJPC4HTILSZPP7WL}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

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	2026-05-18T03:32:20.033631Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6ee76f7dffc46c978b879a172cbdffb2e26ad96ab7402ee3b432008c2c0e7d98

Aliases

arxiv: 1206.4225 · arxiv_version: 1206.4225v2 · doi: 10.48550/arxiv.1206.4225 · pith_short_12: N3TW67P7YRWJ · pith_short_16: N3TW67P7YRWJPC4H · pith_short_8: N3TW67P7

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/N3TW67P7YRWJPC4HTILSZPP7WL \
  | 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: 6ee76f7dffc46c978b879a172cbdffb2e26ad96ab7402ee3b432008c2c0e7d98

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "47656febcaa6796e576ff915b1d5caf28604d9cff97264d7b7c6023b98153935",
    "cross_cats_sorted": [
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-06-19T14:34:54Z",
    "title_canon_sha256": "5a748ade58b7fe0035122901a78db1e9145a8dccfb801825676c90c2d9948283"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.4225",
    "kind": "arxiv",
    "version": 2
  }
}