Pith Number

pith:QJIRGRR3

pith:2008:QJIRGRR37FP76KOTPS2Q2LTRIA

not attested not anchored not stored refs pending

Measures and dimensions of Julia sets of semi-hyperbolic rational semigroups

Hiroki Sumi, Mariusz Urbanski

arxiv:0811.1809 v7 · 2008-11-12 · math.DS · math.CV · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QJIRGRR37FP76KOTPS2Q2LTRIA}

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	2026-05-18T04:28:45.864458Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

825113463bf95fff29d37cb50d2e71402e4c800b081e554f325eb3bfd8ecf8a8

Aliases

arxiv: 0811.1809 · arxiv_version: 0811.1809v7 · doi: 10.48550/arxiv.0811.1809 · pith_short_12: QJIRGRR37FP7 · pith_short_16: QJIRGRR37FP76KOT · pith_short_8: QJIRGRR3

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/QJIRGRR37FP76KOTPS2Q2LTRIA \
  | 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: 825113463bf95fff29d37cb50d2e71402e4c800b081e554f325eb3bfd8ecf8a8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "da11a7251a99ba487272634d5856262ba4e2b407c8fe7474fcc7dab420903d0a",
    "cross_cats_sorted": [
      "math.CV",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2008-11-12T03:06:25Z",
    "title_canon_sha256": "064157a993b78195e455537bb5a055af79363c0098d731c814435ef572895a5f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0811.1809",
    "kind": "arxiv",
    "version": 7
  }
}