Pith Number

pith:FXQG7PJL

pith:2012:FXQG7PJL4MITVFIU6SFBPEDVBR

not attested not anchored not stored refs pending

Divisibility Relations for the Dimensions and Hilbert series of Nichols Algebras of Non-Abelian Group Type

Andreas Lochmann

arxiv:1206.6607 v1 · 2012-06-28 · 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{FXQG7PJL4MITVFIU6SFBPEDVBR}

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	2026-05-18T03:52:25.490969Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2de06fbd2be3113a9514f48a1790750c45ad67e98efb22ecbf803acbb16b55ed

Aliases

arxiv: 1206.6607 · arxiv_version: 1206.6607v1 · doi: 10.48550/arxiv.1206.6607 · pith_short_12: FXQG7PJL4MIT · pith_short_16: FXQG7PJL4MITVFIU · pith_short_8: FXQG7PJL

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/FXQG7PJL4MITVFIU6SFBPEDVBR \
  | 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: 2de06fbd2be3113a9514f48a1790750c45ad67e98efb22ecbf803acbb16b55ed

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9a4506532e161b78bf57558ecbe4bd5078a662ff0cf2769572dfb3d54ce5ec28",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2012-06-28T09:48:21Z",
    "title_canon_sha256": "8567f1915853dbd47b8044093d733235c97444849f2d8732b4ab2160e539419b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.6607",
    "kind": "arxiv",
    "version": 1
  }
}