Pith Number

pith:LYBCZOOG

pith:2011:LYBCZOOGNJ36NJRDLJKKE3PMKL

not attested not anchored not stored refs pending

Ambiskew Hopf Algebras

Kenneth A. Brown, Monica Macauley

arxiv:1112.3528 v1 · 2011-12-15 · 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{LYBCZOOGNJ36NJRDLJKKE3PMKL}

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	2026-05-18T04:06:18.382381Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5e022cb9c66a77e6a6235a54a26dec52eb5340c35d11a4e5a06fc80c02b2e2ff

Aliases

arxiv: 1112.3528 · arxiv_version: 1112.3528v1 · doi: 10.48550/arxiv.1112.3528 · pith_short_12: LYBCZOOGNJ36 · pith_short_16: LYBCZOOGNJ36NJRD · pith_short_8: LYBCZOOG

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/LYBCZOOGNJ36NJRDLJKKE3PMKL \
  | 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: 5e022cb9c66a77e6a6235a54a26dec52eb5340c35d11a4e5a06fc80c02b2e2ff

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "166d2ccc62e31ecc536f5de3ae7806b90ad7f7fbe64e8f0875b83fd17b70f8fb",
    "cross_cats_sorted": [
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2011-12-15T14:56:35Z",
    "title_canon_sha256": "ca62f9ac8e4a8d139c56e1899167f49109b29462278a7a2914a22c2414db32d8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.3528",
    "kind": "arxiv",
    "version": 1
  }
}