Pith Number

pith:67X6WUGA

pith:2013:67X6WUGA222ZK3SO3T3NDW5TC6

not attested not anchored not stored refs pending

Invertibility in groupoid C*-algebras

Ruy Exel

arxiv:1302.1728 v1 · 2013-02-07 · 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{67X6WUGA222ZK3SO3T3NDW5TC6}

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	2026-05-18T03:34:14.809853Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f7efeb50c0d6b5956e4edcf6d1dbb317b79c9f8e10f9ec880aad7b165b0d6fa5

Aliases

arxiv: 1302.1728 · arxiv_version: 1302.1728v1 · doi: 10.48550/arxiv.1302.1728 · pith_short_12: 67X6WUGA222Z · pith_short_16: 67X6WUGA222ZK3SO · pith_short_8: 67X6WUGA

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/67X6WUGA222ZK3SO3T3NDW5TC6 \
  | 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: f7efeb50c0d6b5956e4edcf6d1dbb317b79c9f8e10f9ec880aad7b165b0d6fa5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "72aed5b7853fdc13eec0be0ef3a3e57527aa190ecc031179eac7c98ac515ea4c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2013-02-07T12:30:54Z",
    "title_canon_sha256": "95240010b0aceabcd2656a760279e9b405cee9f24b137b85fa6e7b5f51da02cb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1302.1728",
    "kind": "arxiv",
    "version": 1
  }
}