Pith Number

pith:4T2GATBE

pith:2012:4T2GATBERUXYFPRRHLAMX5QMZF

not attested not anchored not stored refs pending

Limit Cycle Bifurcations from Centers of Symmetric Hamiltonian Systems Perturbing by Cubic Polynomials

Bin Gao, Valery G. Romanovski, Zhaoping Hu

arxiv:1201.2709 v1 · 2012-01-12 · 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{4T2GATBERUXYFPRRHLAMX5QMZF}

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	2026-05-18T01:58:51.749840Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e4f4604c248d2f82be313ac0cbf60cc9510b907fc2a3c18fa83ec70ca39db0c6

Aliases

arxiv: 1201.2709 · arxiv_version: 1201.2709v1 · doi: 10.48550/arxiv.1201.2709 · pith_short_12: 4T2GATBERUXY · pith_short_16: 4T2GATBERUXYFPRR · pith_short_8: 4T2GATBE

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/4T2GATBERUXYFPRRHLAMX5QMZF \
  | 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: e4f4604c248d2f82be313ac0cbf60cc9510b907fc2a3c18fa83ec70ca39db0c6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8c42795fc90f9c9515390965943a30ecce8ce2a9d5905973b50ae11571cc77d0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2012-01-12T23:45:44Z",
    "title_canon_sha256": "fe61d61aa22501e55a9fd3d8aad41c8562840f42610d580c7bdd628c1f85ad62"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.2709",
    "kind": "arxiv",
    "version": 1
  }
}