Pith Number

pith:65BX626U

pith:2012:65BX626UUF246TTZNEGRHGUL2C

not attested not anchored not stored refs pending

Principal Lyapunov exponents and principal Floquet spaces of positive random dynamical systems. I. General theory

Janusz Mierczy\'nski, Wenxian Shen

arxiv:1209.3475 v3 · 2012-09-16 · math.DS · math.AP · 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{65BX626UUF246TTZNEGRHGUL2C}

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	2026-05-18T02:38:37.552510Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f7437f6bd4a175cf4e79690d139a8bd08288156efe6ec0b33c17eb11e3788c0a

Aliases

arxiv: 1209.3475 · arxiv_version: 1209.3475v3 · doi: 10.48550/arxiv.1209.3475 · pith_short_12: 65BX626UUF24 · pith_short_16: 65BX626UUF246TTZ · pith_short_8: 65BX626U

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/65BX626UUF246TTZNEGRHGUL2C \
  | 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: f7437f6bd4a175cf4e79690d139a8bd08288156efe6ec0b33c17eb11e3788c0a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ea0147b1f132f2744c3b6ba5dbca93626a218e79e0ac86587b0898cccb1bc89f",
    "cross_cats_sorted": [
      "math.AP",
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-09-16T11:42:08Z",
    "title_canon_sha256": "72a35afddde7ed3977ee5a78b74cad1ed49b6b172710a26b41ff94ce55abe89e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.3475",
    "kind": "arxiv",
    "version": 3
  }
}