Pith Number

pith:N3XM5AUA

pith:2011:N3XM5AUAWOOCTOJQME5UA7ZV7Y

not attested not anchored not stored refs pending

The maximal number of limit cycles in a family of polynomial systems

Guanghui Xiang, Zhaoping Hu

arxiv:1111.0960 v1 · 2011-11-03 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{N3XM5AUAWOOCTOJQME5UA7ZV7Y}

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	2026-05-18T04:09:36.546096Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6eeece8280b39c29b930613b407f35fe22f3efa41fdc446fef75162559383ae8

Aliases

arxiv: 1111.0960 · arxiv_version: 1111.0960v1 · doi: 10.48550/arxiv.1111.0960 · pith_short_12: N3XM5AUAWOOC · pith_short_16: N3XM5AUAWOOCTOJQ · pith_short_8: N3XM5AUA

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/N3XM5AUAWOOCTOJQME5UA7ZV7Y \
  | 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: 6eeece8280b39c29b930613b407f35fe22f3efa41fdc446fef75162559383ae8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "24f038c07bec58544b4ded5ac152ab6a47912e02543324e034a92a66beb96d7a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2011-11-03T19:51:09Z",
    "title_canon_sha256": "ed4a3646e6bd6565f2e59e1907e8282e1d828a4babf2eecc6ebfa902df321aff"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.0960",
    "kind": "arxiv",
    "version": 1
  }
}