Pith Number

pith:JVA6LUXM

pith:2010:JVA6LUXMORYXLFTAXBX3C62DR7

not attested not anchored not stored refs pending

Counting visible circles on the sphere and Kleinian groups

Hee Oh, Nimish Shah

arxiv:1004.2129 v3 · 2010-04-13 · math.DS · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JVA6LUXMORYXLFTAXBX3C62DR7}

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	2026-05-17T23:58:59.539389Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4d41e5d2ec7471759660b86fb17b438fc2ebc2cccb8026e56e291944e9e0de00

Aliases

arxiv: 1004.2129 · arxiv_version: 1004.2129v3 · doi: 10.48550/arxiv.1004.2129 · pith_short_12: JVA6LUXMORYX · pith_short_16: JVA6LUXMORYXLFTA · pith_short_8: JVA6LUXM

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/JVA6LUXMORYXLFTAXBX3C62DR7 \
  | 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: 4d41e5d2ec7471759660b86fb17b438fc2ebc2cccb8026e56e291944e9e0de00

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3f034f1a4c059d686f9c39e233d831978a50f83876ccbb047514f01b59da5972",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2010-04-13T09:29:51Z",
    "title_canon_sha256": "4529bb59002e05b49afd2812fbbd8e6a47bec5465b82fc928d1f02d966e709e8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.2129",
    "kind": "arxiv",
    "version": 3
  }
}