Pith Number

pith:24RS6Y5E

pith:2025:24RS6Y5EAXRO75WFJMSWMC2MEL

not attested not anchored not stored refs pending

The discontinuous planar piecewise linear system with two nodes has at most two limit cycles

Changjian Liu, Lu Chen

arxiv:2506.07716 v1 · 2025-06-09 · math.DS · 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{24RS6Y5EAXRO75WFJMSWMC2MEL}

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	2026-07-05T11:18:31.993218Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d7232f63a405e2eff6c54b25660b4c22d2c8c6e61c6f7b56682741c7dde30316

Aliases

arxiv: 2506.07716 · arxiv_version: 2506.07716v1 · doi: 10.48550/arxiv.2506.07716 · pith_short_12: 24RS6Y5EAXRO · pith_short_16: 24RS6Y5EAXRO75WF · pith_short_8: 24RS6Y5E

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/24RS6Y5EAXRO75WFJMSWMC2MEL \
  | 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: d7232f63a405e2eff6c54b25660b4c22d2c8c6e61c6f7b56682741c7dde30316

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a21294417a003212d3323c74a08790e6cfbd579b599c58b81da970e41b996003",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2025-06-09T12:58:51Z",
    "title_canon_sha256": "4bf552156df7c5a4d240077180955fab222227c83f744bf93ab02841067337b2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.07716",
    "kind": "arxiv",
    "version": 1
  }
}