Pith Number

pith:KR5K7CS4

pith:2004:KR5K7CS4TTUH7E2AACAMCECQO5

not attested not anchored not stored refs pending

Representations of matched pairs of groupoids and applications to weak Hopf algebras

Marcelo Aguiar, Nicolas Andruskiewitsch

arxiv:math/0402118 v1 · 2004-02-07 · math.QA · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KR5K7CS4TTUH7E2AACAMCECQO5}

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	2026-05-18T01:05:26.596302Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

547aaf8a5c9ce87f93400080c11050775627781e6348c1e83b6988f026fefd22

Aliases

arxiv: math/0402118 · arxiv_version: math/0402118v1 · doi: 10.48550/arxiv.math/0402118 · pith_short_12: KR5K7CS4TTUH · pith_short_16: KR5K7CS4TTUH7E2A · pith_short_8: KR5K7CS4

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/KR5K7CS4TTUH7E2AACAMCECQO5 \
  | 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: 547aaf8a5c9ce87f93400080c11050775627781e6348c1e83b6988f026fefd22

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "63114d1be11005cdfd83c603bdd35f6f087d69519a03f0cc960cb2efd95e5119",
    "cross_cats_sorted": [
      "math.RA"
    ],
    "license": "",
    "primary_cat": "math.QA",
    "submitted_at": "2004-02-07T23:57:21Z",
    "title_canon_sha256": "420c22628574539be70ce22ea3c6500ed65f176e0d5a15c9e12f5577a6032105"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0402118",
    "kind": "arxiv",
    "version": 1
  }
}