Pith Number

pith:GFRAJ7AP

pith:2012:GFRAJ7APZ3UA4QBIAVW7VC7VR6

not attested not anchored not stored refs pending

The doubles of a braided Hopf algebra

Alain Brugui\`eres, Alexis Virelizier

arxiv:1208.5693 v1 · 2012-08-28 · 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{GFRAJ7APZ3UA4QBIAVW7VC7VR6}

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	2026-05-18T03:46:58.001925Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

316204fc0fcee80e4028056dfa8bf58f983412375f6f7e7ec1ac5419d0d2952b

Aliases

arxiv: 1208.5693 · arxiv_version: 1208.5693v1 · doi: 10.48550/arxiv.1208.5693 · pith_short_12: GFRAJ7APZ3UA · pith_short_16: GFRAJ7APZ3UA4QBI · pith_short_8: GFRAJ7AP

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/GFRAJ7APZ3UA4QBIAVW7VC7VR6 \
  | 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: 316204fc0fcee80e4028056dfa8bf58f983412375f6f7e7ec1ac5419d0d2952b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8f7f28493ee5c5806cf84158b7ac54f7ab7013e7dc71846b20a6d7c1dd7c2870",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2012-08-28T15:48:54Z",
    "title_canon_sha256": "5305c847b9a00b2f87bafa4d707018bd5d565491d312867ba5efa212181fccf7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.5693",
    "kind": "arxiv",
    "version": 1
  }
}