Pith Number

pith:NUXLUFBC

pith:2015:NUXLUFBCUB6VN65N5SQENLNZTD

not attested not anchored not stored refs pending

On the Hopf (co)center of a Hopf algebra

Alexandru Chirvasitu, Pawe{\l} Kasprzak

arxiv:1512.03749 v4 · 2015-12-11 · math.QA · math.CT · 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{NUXLUFBCUB6VN65N5SQENLNZTD}

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	2026-05-18T01:11:21.617860Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6d2eba1422a07d56fbadeca046adb998db5e2fd26be0f2c4814a7b30d5f85a26

Aliases

arxiv: 1512.03749 · arxiv_version: 1512.03749v4 · doi: 10.48550/arxiv.1512.03749 · pith_short_12: NUXLUFBCUB6V · pith_short_16: NUXLUFBCUB6VN65N · pith_short_8: NUXLUFBC

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/NUXLUFBCUB6VN65N5SQENLNZTD \
  | 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: 6d2eba1422a07d56fbadeca046adb998db5e2fd26be0f2c4814a7b30d5f85a26

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "42f19b2f89b6467e2dc6420453ee4299d26f14d517b1d7f77e066d300f22680c",
    "cross_cats_sorted": [
      "math.CT",
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2015-12-11T18:13:48Z",
    "title_canon_sha256": "d3d8e094ad530736137a0ece87dba8d6c55a4469189c6a5d3a9a9143574c25ca"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.03749",
    "kind": "arxiv",
    "version": 4
  }
}