Pith Number

pith:VBZO7YHD

pith:2011:VBZO7YHDTHSGPQN3ZFLKUOFKYX

not attested not anchored not stored refs pending

Urysohn's metrization theorem for higher cardinals

Joonas Ilmavirta

arxiv:1105.4463 v1 · 2011-05-23 · math.GN

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VBZO7YHDTHSGPQN3ZFLKUOFKYX}

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	2026-05-18T04:21:29.234617Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a872efe0e399e467c1bbc956aa38aac5e3e16e1b70f6d93bbb7ddbdfd0eb2919

Aliases

arxiv: 1105.4463 · arxiv_version: 1105.4463v1 · doi: 10.48550/arxiv.1105.4463 · pith_short_12: VBZO7YHDTHSG · pith_short_16: VBZO7YHDTHSGPQN3 · pith_short_8: VBZO7YHD

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/VBZO7YHDTHSGPQN3ZFLKUOFKYX \
  | 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: a872efe0e399e467c1bbc956aa38aac5e3e16e1b70f6d93bbb7ddbdfd0eb2919

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cf3096818d4fbb1f730cebb334fec23c68b31455f5b21812348f001162c589a7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GN",
    "submitted_at": "2011-05-23T10:45:42Z",
    "title_canon_sha256": "b41667d2ed4ba719cca8517e488c7ccf70d12e3e62456136c5e00d5d227fb1f9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.4463",
    "kind": "arxiv",
    "version": 1
  }
}