Pith Number

pith:A2LDCF5Z

pith:2004:A2LDCF5Z2DE72ZGJRLOKA4NGCS

not attested not anchored not stored refs pending

Kleinian groups and the rank problem

Ilya Kapovich, Richard Weidmann

arxiv:math/0407438 v3 · 2004-07-26 · 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{A2LDCF5Z2DE72ZGJRLOKA4NGCS}

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	2026-05-18T02:38:00.000557Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

06963117b9d0c9fd64c98adca071a614856b75266b33637f0d124644a436f19c

Aliases

arxiv: math/0407438 · arxiv_version: math/0407438v3 · doi: 10.48550/arxiv.math/0407438 · pith_short_12: A2LDCF5Z2DE7 · pith_short_16: A2LDCF5Z2DE72ZGJ · pith_short_8: A2LDCF5Z

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/A2LDCF5Z2DE72ZGJRLOKA4NGCS \
  | 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: 06963117b9d0c9fd64c98adca071a614856b75266b33637f0d124644a436f19c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f59f4f08e115f9fa6ecd24b66040388b0c331b5e8930b14778fd33f86d38ef58",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2004-07-26T14:32:35Z",
    "title_canon_sha256": "5598ea76307a4bd9735d414c70f41c2bb5a26961c2d36a9b7aa858e75a9fc24f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0407438",
    "kind": "arxiv",
    "version": 3
  }
}