Pith Number

pith:WML4DAAJ

pith:2024:WML4DAAJQ2XNZTQICQ55MDK2EG

not attested not anchored not stored refs pending

Invariant graphs in Julia sets and decompositions of rational maps

Guizhen Cui, Jinsong Zeng, Yan Gao

arxiv:2408.12371 v2 · 2024-08-22 · 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{WML4DAAJQ2XNZTQICQ55MDK2EG}

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.

Cited by

1 paper in Pith

Rigidity of McMullen Julia sets

Receipt and verification

First computed	2026-07-05T09:39:26.102206Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b317c1800986aedcce08143bd60d5a219e8b514a56e621ec3db53ca9f10cd750

Aliases

arxiv: 2408.12371 · arxiv_version: 2408.12371v2 · doi: 10.48550/arxiv.2408.12371 · pith_short_12: WML4DAAJQ2XN · pith_short_16: WML4DAAJQ2XNZTQI · pith_short_8: WML4DAAJ

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/WML4DAAJQ2XNZTQICQ55MDK2EG \
  | 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: b317c1800986aedcce08143bd60d5a219e8b514a56e621ec3db53ca9f10cd750

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f210c163380c2ae7b03f487afff58bfc8638519dbe425cc7f4b1c76fa694ef66",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2024-08-22T13:14:49Z",
    "title_canon_sha256": "e647f3756d17875f77a3e2a0aa4704e9170e5f015b3c2ef86587d203e2cbb4ba"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2408.12371",
    "kind": "arxiv",
    "version": 2
  }
}