Pith Number

pith:47LXZI5Q

pith:2011:47LXZI5QINHFOBAYSETKKIWSYL

not attested not anchored not stored refs pending

Rank gradient in co-final towers of certain Kleinian groups

Darlan Gir\~ao

arxiv:1102.4281 v1 · 2011-02-21 · 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{47LXZI5QINHFOBAYSETKKIWSYL}

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	2026-05-18T04:28:10.514970Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e7d77ca3b0434e5704189126a522d2c2effda32dc89167570f583f52d57098b7

Aliases

arxiv: 1102.4281 · arxiv_version: 1102.4281v1 · doi: 10.48550/arxiv.1102.4281 · pith_short_12: 47LXZI5QINHF · pith_short_16: 47LXZI5QINHFOBAY · pith_short_8: 47LXZI5Q

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/47LXZI5QINHFOBAYSETKKIWSYL \
  | 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: e7d77ca3b0434e5704189126a522d2c2effda32dc89167570f583f52d57098b7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "19a3be9871166f077c18e8277e98b1c3a58faecbb879f44900913c070ceae05d",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-02-21T17:05:08Z",
    "title_canon_sha256": "983724b606469736a5623153461d7eb215d68c764309461c4475596d141e9db8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.4281",
    "kind": "arxiv",
    "version": 1
  }
}