Pith Number

pith:HZRX2R5K

pith:2019:HZRX2R5KCUQSSHZDYR3GMUSSKM

not attested not anchored not stored refs pending

Invariant graphs of rational maps

Guizhen Cui, Jinsong Zeng, Yan Gao

arxiv:1907.02870 v2 · 2019-07-05 · 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{HZRX2R5KCUQSSHZDYR3GMUSSKM}

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

Expansion properties for finite subdivision rules II

Receipt and verification

First computed	2026-07-05T04:15:26.477453Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3e637d47aa1521291f23c476665252533d01e611fbf07595f860309af90514d6

Aliases

arxiv: 1907.02870 · arxiv_version: 1907.02870v2 · doi: 10.48550/arxiv.1907.02870 · pith_short_12: HZRX2R5KCUQS · pith_short_16: HZRX2R5KCUQSSHZD · pith_short_8: HZRX2R5K

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/HZRX2R5KCUQSSHZDYR3GMUSSKM \
  | 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: 3e637d47aa1521291f23c476665252533d01e611fbf07595f860309af90514d6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ac6f7812a1d65b4434c2c22c1d583eac7ea2ad08288a3959d88784e45ee6d6c3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2019-07-05T14:49:13Z",
    "title_canon_sha256": "d0212ec47a6656b8db5effa93fb83d0dbb04ad0c3c885ddf042a5fa15b8d26e1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1907.02870",
    "kind": "arxiv",
    "version": 2
  }
}