Pith Number

pith:27XFG4DJ

pith:2017:27XFG4DJC6N77LVBRG3GW6GAQU

not attested not anchored not stored refs pending

Lyapunov exponents for products of matrices

Chiu-Hong Lo, De-Jun Feng, Shuang Shen

arxiv:1702.07251 v1 · 2017-02-23 · 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{27XFG4DJC6N77LVBRG3GW6GAQU}

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	2026-05-18T00:50:07.707164Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d7ee537069179bffaea189b66b78c0852a6f7aca91dc9fdeadfc388b6762751d

Aliases

arxiv: 1702.07251 · arxiv_version: 1702.07251v1 · doi: 10.48550/arxiv.1702.07251 · pith_short_12: 27XFG4DJC6N7 · pith_short_16: 27XFG4DJC6N77LVB · pith_short_8: 27XFG4DJ

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/27XFG4DJC6N77LVBRG3GW6GAQU \
  | 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: d7ee537069179bffaea189b66b78c0852a6f7aca91dc9fdeadfc388b6762751d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0dba645714f9e615dcabb9b30a0d97967d53957af4701646583c6e744ec46c64",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2017-02-23T15:07:49Z",
    "title_canon_sha256": "f26f26e97855bb95db4a87a6b260b782bfc88112e4f281fdfcebbff6a09b2e63"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1702.07251",
    "kind": "arxiv",
    "version": 1
  }
}