Pith Number

pith:A2NL56B2

pith:2015:A2NL56B2CK4BYIGKV7IFMVOUCJ

not attested not anchored not stored refs pending

Twisted Topological Graph Algebras Are Twisted Groupoid C*-algebras

Alex Kumjian, Hui Li

arxiv:1507.04449 v3 · 2015-07-16 · math.OA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{A2NL56B2CK4BYIGKV7IFMVOUCJ}

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	2026-05-18T00:52:17.736773Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

069abef83a12b81c20caafd05655d4126345fc57641336f069a157709cf9db57

Aliases

arxiv: 1507.04449 · arxiv_version: 1507.04449v3 · doi: 10.48550/arxiv.1507.04449 · pith_short_12: A2NL56B2CK4B · pith_short_16: A2NL56B2CK4BYIGK · pith_short_8: A2NL56B2

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/A2NL56B2CK4BYIGKV7IFMVOUCJ \
  | 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: 069abef83a12b81c20caafd05655d4126345fc57641336f069a157709cf9db57

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dc3435056eb308e6c601ca8e4d391e0df4faf130ee782820d42eb13fe54115f6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2015-07-16T04:55:39Z",
    "title_canon_sha256": "2c69a2885c636a3f34936b4a15666cdeb51faaac1b5b8f543e9999b35e46323c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.04449",
    "kind": "arxiv",
    "version": 3
  }
}