Pith Number

pith:GRY24JD6

pith:2011:GRY24JD64XBRYCLUIW5QQWV73L

not attested not anchored not stored refs pending

On cross product Hopf algebras

B. Torrecillas, D. Bulacu, S. Caenepeel

arxiv:1109.1947 v1 · 2011-09-09 · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GRY24JD64XBRYCLUIW5QQWV73L}

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	2026-05-18T04:13:46.450371Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3471ae247ee5c31c097445bb085abfdaca3c7e4714920f816c2ad668cf0bc507

Aliases

arxiv: 1109.1947 · arxiv_version: 1109.1947v1 · doi: 10.48550/arxiv.1109.1947 · pith_short_12: GRY24JD64XBR · pith_short_16: GRY24JD64XBRYCLU · pith_short_8: GRY24JD6

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/GRY24JD64XBRYCLUIW5QQWV73L \
  | 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: 3471ae247ee5c31c097445bb085abfdaca3c7e4714920f816c2ad668cf0bc507

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "30f98de055fd6ee8fa43c2918a1928f2d2fa9596fbb5982d55331af03ba5bf29",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2011-09-09T09:30:02Z",
    "title_canon_sha256": "12b7ef9fd3023d0ddf04c9322f475a74447438f8f2e3efb8adca842bc0ff7556"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.1947",
    "kind": "arxiv",
    "version": 1
  }
}