Pith Number

pith:4KAOGZJX

pith:2016:4KAOGZJXE7QTWQD2HLR7EIHZRL

not attested not anchored not stored refs pending

Proving the existence of numerically detected planar limit cycles

Armengol Gasull, H\'ector Giacomini, Maite Grau

arxiv:1602.00113 v1 · 2016-01-30 · 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{4KAOGZJXE7QTWQD2HLR7EIHZRL}

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	2026-05-18T01:21:36.259905Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e280e3653727e13b407a3ae3f220f98af49121f5e6ac5021a463ef9ae3261083

Aliases

arxiv: 1602.00113 · arxiv_version: 1602.00113v1 · doi: 10.48550/arxiv.1602.00113 · pith_short_12: 4KAOGZJXE7QT · pith_short_16: 4KAOGZJXE7QTWQD2 · pith_short_8: 4KAOGZJX

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/4KAOGZJXE7QTWQD2HLR7EIHZRL \
  | 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: e280e3653727e13b407a3ae3f220f98af49121f5e6ac5021a463ef9ae3261083

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "31e29421b0587832b96b453c70db975c076a93b4617455289ad92257502af57b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2016-01-30T12:18:46Z",
    "title_canon_sha256": "1cc5e83d7839f14f02d648a216d7b72e05ac48a171cd50d0bb58332ddda557b4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1602.00113",
    "kind": "arxiv",
    "version": 1
  }
}