Pith Number

pith:HJBPO47P

pith:2012:HJBPO47PORNNXNI7T3NILNRA3J

not attested not anchored not stored refs pending

Principal Lyapunov exponents and principal Floquet spaces of positive random dynamical systems. II. Finite-dimensional systems

Janusz Mierczy\'nski, Wenxian Shen

arxiv:1209.3381 v3 · 2012-09-15 · 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{HJBPO47PORNNXNI7T3NILNRA3J}

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	2026-05-18T02:38:37.559829Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3a42f773ef745adbb51f9eda85b620da68ade750e9f33741e6ec666cfaa34752

Aliases

arxiv: 1209.3381 · arxiv_version: 1209.3381v3 · doi: 10.48550/arxiv.1209.3381 · pith_short_12: HJBPO47PORNN · pith_short_16: HJBPO47PORNNXNI7 · pith_short_8: HJBPO47P

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/HJBPO47PORNNXNI7T3NILNRA3J \
  | 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: 3a42f773ef745adbb51f9eda85b620da68ade750e9f33741e6ec666cfaa34752

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "078bcb6515d27bae86953713615d579f819ca3b3e1c6cfa62fe9e1761f726a6d",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-09-15T09:26:49Z",
    "title_canon_sha256": "bb40cd88734b023db49690c3b52287c9fca0e7b20944d556aaf79b0f0ba5fd5e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.3381",
    "kind": "arxiv",
    "version": 3
  }
}