Pith Number

pith:COU6JQQO

pith:2016:COU6JQQOO77IQN6WCNDAP4OHZJ

not attested not anchored not stored refs pending

Singular behavior of the leading Lyapunov exponent of a product of random $2 \times 2$ matrices

Giambattista Giacomin, Giuseppe Genovese, Rafael Leon Greenblatt

arxiv:1602.03633 v2 · 2016-02-11 · math-ph · math.MP · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{COU6JQQOO77IQN6WCNDAP4OHZJ}

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	2026-05-18T00:48:28.487788Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

13a9e4c20e77fe8837d6134607f1c7ca6cba84c61a64c4f5693d0aa4a8afcaa2

Aliases

arxiv: 1602.03633 · arxiv_version: 1602.03633v2 · doi: 10.48550/arxiv.1602.03633 · pith_short_12: COU6JQQOO77I · pith_short_16: COU6JQQOO77IQN6W · pith_short_8: COU6JQQO

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/COU6JQQOO77IQN6WCNDAP4OHZJ \
  | 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: 13a9e4c20e77fe8837d6134607f1c7ca6cba84c61a64c4f5693d0aa4a8afcaa2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e236d42ed98e717e6f137583a23cd5b1b9e83e46e5d6148d5810184450c3e3a6",
    "cross_cats_sorted": [
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2016-02-11T07:53:55Z",
    "title_canon_sha256": "fdd2dc486a13667a0747c8ac76173a755560846df47e350a508f0f963c1809a7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1602.03633",
    "kind": "arxiv",
    "version": 2
  }
}