Pith Number

pith:26J4VXC4

pith:2010:26J4VXC4BSUWCN4A23ZSESOSWO

not attested not anchored not stored refs pending

Limit sets and commensurability of Kleinian groups

Wen-yuan Yang, Yue-ping Jiang

arxiv:1004.1751 v1 · 2010-04-10 · math.GT · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{26J4VXC4BSUWCN4A23ZSESOSWO}

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	2026-05-18T04:40:55.954936Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d793cadc5c0ca9613780d6f32249d2b3bbe0fffd325ce29732d2886f7727403a

Aliases

arxiv: 1004.1751 · arxiv_version: 1004.1751v1 · doi: 10.48550/arxiv.1004.1751 · pith_short_12: 26J4VXC4BSUW · pith_short_16: 26J4VXC4BSUWCN4A · pith_short_8: 26J4VXC4

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/26J4VXC4BSUWCN4A23ZSESOSWO \
  | 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: d793cadc5c0ca9613780d6f32249d2b3bbe0fffd325ce29732d2886f7727403a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6c2837f26b4cf4ac4205fef0e2941a75f8a10e1bda0fe23096cb94eca8631dab",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2010-04-10T23:14:17Z",
    "title_canon_sha256": "18ff2fa44ad3d73a74be50d897ae0bebdb8195690975e6ca61e03969fdc2cd99"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.1751",
    "kind": "arxiv",
    "version": 1
  }
}