Pith Number

pith:UUE4ZY7Q

pith:2010:UUE4ZY7QTIMXOMGBRVS4KTT3RF

not attested not anchored not stored refs pending

On complements and the factorization problem for Hopf algebras

Sebastian Burciu

arxiv:1012.2540 v1 · 2010-12-12 · math.RA · 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{UUE4ZY7QTIMXOMGBRVS4KTT3RF}

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	2026-05-18T03:49:22.443358Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a509cce3f09a197730c18d65c54e7b894326f661fbbefccab944d09a5f62b5c0

Aliases

arxiv: 1012.2540 · arxiv_version: 1012.2540v1 · doi: 10.48550/arxiv.1012.2540 · pith_short_12: UUE4ZY7QTIMX · pith_short_16: UUE4ZY7QTIMXOMGB · pith_short_8: UUE4ZY7Q

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/UUE4ZY7QTIMXOMGBRVS4KTT3RF \
  | 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: a509cce3f09a197730c18d65c54e7b894326f661fbbefccab944d09a5f62b5c0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6942e0a0a82633928063e5ed75b5ec2411062e53db7d48a52d219e0f6ed6f882",
    "cross_cats_sorted": [
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2010-12-12T13:27:26Z",
    "title_canon_sha256": "87e7b17518ac8ec291751b37a76e68cf11c0d2023fa77ddc0e882ba2e68237aa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.2540",
    "kind": "arxiv",
    "version": 1
  }
}