Pith Number

pith:KNIT25Z4

pith:2003:KNIT25Z4KY3YEUNZVLD6M7AAGF

not attested not anchored not stored refs pending

Double categories and quantum groupoids

Nicolas Andruskiewitsch, Sonia Natale

arxiv:math/0308228 v2 · 2003-08-25 · 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{KNIT25Z4KY3YEUNZVLD6M7AAGF}

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	2026-07-04T14:49:29.222514Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

53513d773c56378251b9aac7e67c00317dc0458b1d27d3b96211acdcdfe21ee3

Aliases

arxiv: math/0308228 · arxiv_version: math/0308228v2 · doi: 10.48550/arxiv.math/0308228 · pith_short_12: KNIT25Z4KY3Y · pith_short_16: KNIT25Z4KY3YEUNZ · pith_short_8: KNIT25Z4

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/KNIT25Z4KY3YEUNZVLD6M7AAGF \
  | 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: 53513d773c56378251b9aac7e67c00317dc0458b1d27d3b96211acdcdfe21ee3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b4d69befadec36a94ec46e0d6759913032f5844bbf8cd44d7ed8b550b66fa2f3",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.QA",
    "submitted_at": "2003-08-25T10:30:27Z",
    "title_canon_sha256": "a7599ef805bb31388eb64699683e2e504372877aef1f72e8a18651681736866b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0308228",
    "kind": "arxiv",
    "version": 2
  }
}