Pith Number

pith:FD52ZJZL

pith:2010:FD52ZJZLBXWJHSYMIWDDVEFYW4

not attested not anchored not stored refs pending

Lyapunov exponent of the random frequency oscillator: cumulant expansion approach

C. Anteneodo, R.O. Vallejos

arxiv:1008.4708 v1 · 2010-08-27 · cond-mat.stat-mech · nlin.CD

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FD52ZJZLBXWJHSYMIWDDVEFYW4}

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	2026-05-18T02:05:42.054804Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

28fbaca72b0dec93cb0c45863a90b8b73b1ef64d3384751de84a2018a7bf34dd

Aliases

arxiv: 1008.4708 · arxiv_version: 1008.4708v1 · doi: 10.48550/arxiv.1008.4708 · pith_short_12: FD52ZJZLBXWJ · pith_short_16: FD52ZJZLBXWJHSYM · pith_short_8: FD52ZJZL

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/FD52ZJZLBXWJHSYMIWDDVEFYW4 \
  | 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: 28fbaca72b0dec93cb0c45863a90b8b73b1ef64d3384751de84a2018a7bf34dd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7b59ce9184c872bfafe61e6ac0b677d965a78f67fe428306a6179ddfae7ad7c6",
    "cross_cats_sorted": [
      "nlin.CD"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2010-08-27T12:53:01Z",
    "title_canon_sha256": "0b232a98e8d137f2329922fba503d0fa57e9e4280d710b109b6a8aa55d0b5650"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1008.4708",
    "kind": "arxiv",
    "version": 1
  }
}