Pith Number

pith:CQC6JS7G

pith:2024:CQC6JS7GYOU3H2XKO7FMXSTVRO

not attested not anchored not stored refs pending

Learning Koopman-based Stability Certificates for Unknown Nonlinear Systems

Jun Liu, Ruikun Zhou, Yiming Meng, Zhexuan Zeng

arxiv:2412.02807 v2 · 2024-12-03 · eess.SY · cs.LG · cs.SY · 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{CQC6JS7GYOU3H2XKO7FMXSTVRO}

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	2026-07-05T10:43:03.519992Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1405e4cbe6c3a9b3eaea77cacbca758ba0651b2934b7af10c2bcc5fe72f04b23

Aliases

arxiv: 2412.02807 · arxiv_version: 2412.02807v2 · doi: 10.48550/arxiv.2412.02807 · pith_short_12: CQC6JS7GYOU3 · pith_short_16: CQC6JS7GYOU3H2XK · pith_short_8: CQC6JS7G

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/CQC6JS7GYOU3H2XKO7FMXSTVRO \
  | 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: 1405e4cbe6c3a9b3eaea77cacbca758ba0651b2934b7af10c2bcc5fe72f04b23

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3c457ac4076964df2e224f050e99cbf728374c8b4608f6a27e53a58d7a131eb9",
    "cross_cats_sorted": [
      "cs.LG",
      "cs.SY",
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "eess.SY",
    "submitted_at": "2024-12-03T20:18:24Z",
    "title_canon_sha256": "663ce64dca752bb23174d518d79040fee56bcf2e6ca3366c598e5cb946199f0a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.02807",
    "kind": "arxiv",
    "version": 2
  }
}