Pith Number

pith:CX47SMLA

pith:2004:CX47SMLAYGH2FTMLKJGJEJEH3U

not attested not anchored not stored refs pending

McShane's identity for classical Schottky Groups

Ser Peow Tan, Yan Loi Wong, Ying Zhang

arxiv:math/0411628 v1 · 2004-11-29 · math.GT · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CX47SMLAYGH2FTMLKJGJEJEH3U}

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	2026-07-04T14:39:24.969055Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

15f9f93160c18fa2cd8b524c922487dd177b98b4cc9758202939c8d23aa7b114

Aliases

arxiv: math/0411628 · arxiv_version: math/0411628v1 · doi: 10.48550/arxiv.math/0411628 · pith_short_12: CX47SMLAYGH2 · pith_short_16: CX47SMLAYGH2FTML · pith_short_8: CX47SMLA

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/CX47SMLAYGH2FTMLKJGJEJEH3U \
  | 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: 15f9f93160c18fa2cd8b524c922487dd177b98b4cc9758202939c8d23aa7b114

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "444ac58e1c9de4ac1f7cfe8a60edd726194f77d8aefffc4ee4b1668f35d784f6",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2004-11-29T12:34:11Z",
    "title_canon_sha256": "35854179f7130f8aba4d0018cc3b708d0f8bd95bf52d6ae999fc0f7e1fbba22f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0411628",
    "kind": "arxiv",
    "version": 1
  }
}