Pith Number

pith:VQFSAVRY

pith:2011:VQFSAVRYNIOOAOANIA24Z3WM2Q

not attested not anchored not stored refs pending

The critical exponent, the Hausdorff dimension of the limit set and the convex core entropy of a Kleinian group

Katsuhiko Matsuzaki, Kurt Falk

arxiv:1106.4409 v3 · 2011-06-22 · math.CV · 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{VQFSAVRYNIOOAOANIA24Z3WM2Q}

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	2026-05-18T03:58:14.110081Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ac0b2056386a1ce0380d4035cceeccd4388c08da2bcf559ef4877418aa376c1a

Aliases

arxiv: 1106.4409 · arxiv_version: 1106.4409v3 · doi: 10.48550/arxiv.1106.4409 · pith_short_12: VQFSAVRYNIOO · pith_short_16: VQFSAVRYNIOOAOAN · pith_short_8: VQFSAVRY

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/VQFSAVRYNIOOAOANIA24Z3WM2Q \
  | 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: ac0b2056386a1ce0380d4035cceeccd4388c08da2bcf559ef4877418aa376c1a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "42cbb6c4e46741f629ad72a7f0a779a18f07890ad9298ab361c5174076c8e2c4",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2011-06-22T10:02:14Z",
    "title_canon_sha256": "4287b52795d01b00f21248fd73be864a7d84af67cb25f5b7f83dcb30ece3e64b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.4409",
    "kind": "arxiv",
    "version": 3
  }
}