Pith Number

pith:ILJYVRRW

pith:2012:ILJYVRRWVBVAGC62YV6XCMYF3Z

not attested not anchored not stored refs pending

Groupoids and Faa di Bruno formulae for Green functions in bialgebras of trees

Andrew Tonks, Imma Galvez-Carrillo, Joachim Kock

arxiv:1207.6404 v2 · 2012-07-26 · math.QA · math-ph · math.CT · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ILJYVRRWVBVAGC62YV6XCMYF3Z}

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	2026-05-18T02:52:56.323377Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

42d38ac636a86a030bdac57d713305de6a0428434da880a31561f6b9ca19d965

Aliases

arxiv: 1207.6404 · arxiv_version: 1207.6404v2 · doi: 10.48550/arxiv.1207.6404 · pith_short_12: ILJYVRRWVBVA · pith_short_16: ILJYVRRWVBVAGC62 · pith_short_8: ILJYVRRW

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/ILJYVRRWVBVAGC62YV6XCMYF3Z \
  | 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: 42d38ac636a86a030bdac57d713305de6a0428434da880a31561f6b9ca19d965

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fd158b3d756438625b9c61d227b564215f2b3768e4701c0e2614421c540f825d",
    "cross_cats_sorted": [
      "math-ph",
      "math.CT",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2012-07-26T20:08:16Z",
    "title_canon_sha256": "7c0b43abb8b1648107acd1789f625dc05ef38ca65aa29d6b8bfa50fbf8d7f529"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.6404",
    "kind": "arxiv",
    "version": 2
  }
}