Pith Number

pith:GNZUT5QW

pith:2015:GNZUT5QW5NUIHG5FAWDWXAQDOP

not attested not anchored not stored refs pending

Kirchberg's Factorization Property for Discrete Quantum Groups

Angshuman Bhattacharya, Shuzhou Wang

arxiv:1512.08737 v2 · 2015-12-29 · math.OA · 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{GNZUT5QW5NUIHG5FAWDWXAQDOP}

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	2026-05-18T00:15:59.607407Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

337349f616eb68839ba505876b820373dffa398ddb3760692b2a0b520d609715

Aliases

arxiv: 1512.08737 · arxiv_version: 1512.08737v2 · doi: 10.48550/arxiv.1512.08737 · pith_short_12: GNZUT5QW5NUI · pith_short_16: GNZUT5QW5NUIHG5F · pith_short_8: GNZUT5QW

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/GNZUT5QW5NUIHG5FAWDWXAQDOP \
  | 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: 337349f616eb68839ba505876b820373dffa398ddb3760692b2a0b520d609715

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5e657fa08607be28c2469d9c78976fed37fb27cc1352acd0cafface2d240cccc",
    "cross_cats_sorted": [
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2015-12-29T17:41:45Z",
    "title_canon_sha256": "ff3dd181e515fd4d2f7f5ff43ef9d773cdc12b3ffa446f1bba80b4d545ba50c3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.08737",
    "kind": "arxiv",
    "version": 2
  }
}