Pith Number

pith:O2YOMLAJ

pith:2012:O2YOMLAJWS5HQKKR6CIR3ASKBG

not attested not anchored not stored refs pending

Free group $C^*$-algebras associated with $\ell_p$

Rui Okayasu

arxiv:1203.0800 v3 · 2012-03-05 · 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{O2YOMLAJWS5HQKKR6CIR3ASKBG}

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	2026-05-18T03:51:14.149351Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

76b0e62c09b4ba782951f0911d824a09be45945f886acdac13525cb9cdc628fc

Aliases

arxiv: 1203.0800 · arxiv_version: 1203.0800v3 · doi: 10.48550/arxiv.1203.0800 · pith_short_12: O2YOMLAJWS5H · pith_short_16: O2YOMLAJWS5HQKKR · pith_short_8: O2YOMLAJ

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/O2YOMLAJWS5HQKKR6CIR3ASKBG \
  | 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: 76b0e62c09b4ba782951f0911d824a09be45945f886acdac13525cb9cdc628fc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "915572de89aae8c30e4995252c7ec00e59892e858480a6d6b8a6111068e2af1c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2012-03-05T01:56:04Z",
    "title_canon_sha256": "f6b91ab26a44f7f02dcee0d58be73dc050db83bfb0a6eaece6159c8e40f29c89"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.0800",
    "kind": "arxiv",
    "version": 3
  }
}