Pith Number

pith:VSCR347B

pith:2002:VSCR347BWDIWNINPZHNWQAEWUC

not attested not anchored not stored refs pending

On the density of geometrically finite Kleinian groups

Jeffrey F. Brock, Kenneth W. Bromberg

arxiv:math/0212189 v1 · 2002-12-13 · math.GT · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VSCR347BWDIWNINPZHNWQAEWUC}

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	2026-07-04T14:36:49.726425Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ac851df3e1b0d166a1afc9db680096a0bca4058fdd8a74c816a866e5bea40fd8

Aliases

arxiv: math/0212189 · arxiv_version: math/0212189v1 · doi: 10.48550/arxiv.math/0212189 · pith_short_12: VSCR347BWDIW · pith_short_16: VSCR347BWDIWNINP · pith_short_8: VSCR347B

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/VSCR347BWDIWNINPZHNWQAEWUC \
  | 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: ac851df3e1b0d166a1afc9db680096a0bca4058fdd8a74c816a866e5bea40fd8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bec2acd300a9dcae5a2fd91f515d02479d62f3c98c0d97bc4627a5f2e2a07f11",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2002-12-13T16:55:35Z",
    "title_canon_sha256": "e1bb07a915f3f1a309a3a36c4506d828431bdd480c47ad8e8b4718e33dc338c6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0212189",
    "kind": "arxiv",
    "version": 1
  }
}