Pith Number

pith:7S265JZ4

pith:2011:7S265JZ4MXP6C7QKJLBCUE3ZCT

not attested not anchored not stored refs pending

On the number of limit cycles which appear by perturbation of two-saddle cycles of planar vector fields

Lubomir Gavrilov

arxiv:1106.0857 v3 · 2011-06-04 · 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{7S265JZ4MXP6C7QKJLBCUE3ZCT}

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	2026-05-18T03:38:43.980624Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fcb5eea73c65dfe17e0a4ac22a137914f3eaf437db9793bbd0d951ec76575523

Aliases

arxiv: 1106.0857 · arxiv_version: 1106.0857v3 · doi: 10.48550/arxiv.1106.0857 · pith_short_12: 7S265JZ4MXP6 · pith_short_16: 7S265JZ4MXP6C7QK · pith_short_8: 7S265JZ4

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/7S265JZ4MXP6C7QKJLBCUE3ZCT \
  | 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: fcb5eea73c65dfe17e0a4ac22a137914f3eaf437db9793bbd0d951ec76575523

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5e75b375f7dc290162aa904ca8fc78b7f41b6429398b0ba08fa4e067084ae19a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2011-06-04T20:45:40Z",
    "title_canon_sha256": "e3095b680f4aa93a8f26207178b0fdc11eafc6dc50ecd21acfafe5508e15f7dd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.0857",
    "kind": "arxiv",
    "version": 3
  }
}