Pith Number

pith:BQFAQKVL

pith:2011:BQFAQKVLDZFVNAZHWBODUWYXUQ

not attested not anchored not stored refs pending

Inclusion relations of hyperbolic type metric balls II

Matti Vuorinen, Riku Kl\'en

arxiv:1105.1231 v3 · 2011-05-06 · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BQFAQKVLDZFVNAZHWBODUWYXUQ}

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	2026-05-18T03:12:58.221807Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0c0a082aab1e4b568327b05c3a5b17a43e0df4fbd1081e1318c7cdd8ca2a9d42

Aliases

arxiv: 1105.1231 · arxiv_version: 1105.1231v3 · doi: 10.48550/arxiv.1105.1231 · pith_short_12: BQFAQKVLDZFV · pith_short_16: BQFAQKVLDZFVNAZH · pith_short_8: BQFAQKVL

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/BQFAQKVLDZFVNAZHWBODUWYXUQ \
  | 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: 0c0a082aab1e4b568327b05c3a5b17a43e0df4fbd1081e1318c7cdd8ca2a9d42

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6c1f3a6a6e3c878483e8afd06d8e4c4cff9946e2bef46f719be1474c94b6dd11",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2011-05-06T06:40:07Z",
    "title_canon_sha256": "7837af1092e2c5fcc144ea12f8dcb4ba6b4ed05b185600ff13c9a53e1b1b52a8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.1231",
    "kind": "arxiv",
    "version": 3
  }
}