Pith Number

pith:CUMVSEVI

pith:2017:CUMVSEVITHDGOTFTS4PNXETNUW

not attested not anchored not stored refs pending

The Calkin algebra is $\aleph_1$-universal

Alessandro Vignati, Ilan Hirshberg, Ilijas Farah

arxiv:1707.01782 v4 · 2017-07-06 · math.OA · math.LO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CUMVSEVITHDGOTFTS4PNXETNUW}

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	2026-05-18T00:03:19.626195Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

15195912a899c6674cb3971edb926da58b920b4a2d4c9262776ef52b78e7ed5a

Aliases

arxiv: 1707.01782 · arxiv_version: 1707.01782v4 · doi: 10.48550/arxiv.1707.01782 · pith_short_12: CUMVSEVITHDG · pith_short_16: CUMVSEVITHDGOTFT · pith_short_8: CUMVSEVI

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/CUMVSEVITHDGOTFTS4PNXETNUW \
  | 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: 15195912a899c6674cb3971edb926da58b920b4a2d4c9262776ef52b78e7ed5a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7d3540034cfaee80641e67be04d01e637a414991ec7efbda988a1b4a0f5f3a6c",
    "cross_cats_sorted": [
      "math.LO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2017-07-06T13:39:17Z",
    "title_canon_sha256": "a3a7ae3af10db23c30558e355fcd33f694e1f6c5fa5fa0c548c7f2d7184fdbcd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1707.01782",
    "kind": "arxiv",
    "version": 4
  }
}