Pith Number

pith:GN3IDN43

pith:2010:GN3IDN43T4LWTXMXZZ5TVY23CJ

not attested not anchored not stored refs pending

Apollonian circles and hyperbolic geometry

Matti Vuorinen, Riku Kl\'en

arxiv:1010.2630 v4 · 2010-10-13 · 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{GN3IDN43T4LWTXMXZZ5TVY23CJ}

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	2026-05-18T03:36:46.860706Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

337681b79b9f1769dd97ce7b3ae35b1259a1f27cc0c34b7deba238ccfd16fc1e

Aliases

arxiv: 1010.2630 · arxiv_version: 1010.2630v4 · doi: 10.48550/arxiv.1010.2630 · pith_short_12: GN3IDN43T4LW · pith_short_16: GN3IDN43T4LWTXMX · pith_short_8: GN3IDN43

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/GN3IDN43T4LWTXMXZZ5TVY23CJ \
  | 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: 337681b79b9f1769dd97ce7b3ae35b1259a1f27cc0c34b7deba238ccfd16fc1e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "74876f0c6bc8725fb25764688fc8a95f373f2656bc46ae0deab09716d1201d89",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2010-10-13T11:19:23Z",
    "title_canon_sha256": "056b2a8dc5d946a2b216a67374b5b15c9f1680c6b41ccf385854a69b83531b16"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.2630",
    "kind": "arxiv",
    "version": 4
  }
}