Pith Number

pith:LK75IX34

pith:2010:LK75IX34WL7KLFG54DLQBHYTZD

not attested not anchored not stored refs pending

The # product in combinatorial Hopf algebras

Jean-Christophe Aval (LaBRI), Jean-Christophe Novelli (IGM-LabInfo), Jean-Yves Thibon (IGM-LabInfo)

arxiv:1007.1901 v2 · 2010-07-12 · 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{LK75IX34WL7KLFG54DLQBHYTZD}

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	2026-05-18T04:12:43.019921Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5abfd45f7cb2fea594dde0d7009f13c8ca7875c78d146366ba312c8a69c02d62

Aliases

arxiv: 1007.1901 · arxiv_version: 1007.1901v2 · doi: 10.48550/arxiv.1007.1901 · pith_short_12: LK75IX34WL7K · pith_short_16: LK75IX34WL7KLFG5 · pith_short_8: LK75IX34

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/LK75IX34WL7KLFG54DLQBHYTZD \
  | 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: 5abfd45f7cb2fea594dde0d7009f13c8ca7875c78d146366ba312c8a69c02d62

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5c549e095d1148a0fa420f4375237bb39162a38f30a843eaa85a079063831287",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-07-12T13:49:58Z",
    "title_canon_sha256": "a5e5d64c3b11d961960c0ab46bffb6bb3e82f6f2cd33526a7ea55741d4f34ad0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1007.1901",
    "kind": "arxiv",
    "version": 2
  }
}