Pith Number

pith:QS4EM7RB

pith:2013:QS4EM7RBLSFRJEHDGPKQGY3VQO

not attested not anchored not stored refs pending

Lower estimates of top Lyapunov exponent for cooperative random systems of linear ODEs

Janusz Mierczy\'nski

arxiv:1305.6198 v2 · 2013-05-27 · 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{QS4EM7RBLSFRJEHDGPKQGY3VQO}

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	2026-05-18T00:37:53.064055Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

84b8467e215c8b1490e333d503637583a4e8beb05f718dc4232a00e649dd9255

Aliases

arxiv: 1305.6198 · arxiv_version: 1305.6198v2 · doi: 10.48550/arxiv.1305.6198 · pith_short_12: QS4EM7RBLSFR · pith_short_16: QS4EM7RBLSFRJEHD · pith_short_8: QS4EM7RB

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/QS4EM7RBLSFRJEHDGPKQGY3VQO \
  | 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: 84b8467e215c8b1490e333d503637583a4e8beb05f718dc4232a00e649dd9255

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e10346507f9ef9e7ef0adddaa53a7e676836a28ac5a8e9a799c74364a7868e34",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2013-05-27T12:45:12Z",
    "title_canon_sha256": "4c051a85cff2f9c8c9d1006a22cf717c62eda77de87379f68cc913a908764b8b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1305.6198",
    "kind": "arxiv",
    "version": 2
  }
}