Pith Number

pith:GZWUZ2WB

pith:2010:GZWUZ2WBISVQ4RCKNPS5FP6XDX

not attested not anchored not stored refs pending

Discontinuity of the Lyapunov Exponent

Helge Krueger, Zheng Gan

arxiv:1005.0181 v1 · 2010-05-03 · math.SP · math-ph · math.MP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GZWUZ2WBISVQ4RCKNPS5FP6XDX}

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	2026-05-18T02:24:09.308640Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

366d4ceac144ab0e444a6be5d2bfd71dc45202daf97cb34378019df1d4153f65

Aliases

arxiv: 1005.0181 · arxiv_version: 1005.0181v1 · doi: 10.48550/arxiv.1005.0181 · pith_short_12: GZWUZ2WBISVQ · pith_short_16: GZWUZ2WBISVQ4RCK · pith_short_8: GZWUZ2WB

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/GZWUZ2WBISVQ4RCKNPS5FP6XDX \
  | 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: 366d4ceac144ab0e444a6be5d2bfd71dc45202daf97cb34378019df1d4153f65

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "191b69bcdbfe0a93fcf610b76c67b0ac226ee740092fbf9842e69e770ba5fa10",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2010-05-03T03:51:26Z",
    "title_canon_sha256": "8f4c3cf5fe4940ca127a5e0e9b60f6d98253cafc2c3f8ae085e58bc6bcb432cd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1005.0181",
    "kind": "arxiv",
    "version": 1
  }
}