Pith Number

pith:AOQUNFYZ

pith:2022:AOQUNFYZGSSRLEFQNHQZ75ZPDY

not attested not anchored not stored refs pending

Some Limit Theorems Regarding Products of Random Matrices I: Directional Derivative of the Lyapunov Exponent

Fan Wang

arxiv:2209.07750 v1 · 2022-09-16 · math.PR · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AOQUNFYZGSSRLEFQNHQZ75ZPDY}

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	2026-07-05T04:58:09.433266Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

03a146971934a51590b069e19ff72f1e13efe3d5833f4d8c2091e9a7a1d37681

Aliases

arxiv: 2209.07750 · arxiv_version: 2209.07750v1 · doi: 10.48550/arxiv.2209.07750 · pith_short_12: AOQUNFYZGSSR · pith_short_16: AOQUNFYZGSSRLEFQ · pith_short_8: AOQUNFYZ

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/AOQUNFYZGSSRLEFQNHQZ75ZPDY \
  | 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: 03a146971934a51590b069e19ff72f1e13efe3d5833f4d8c2091e9a7a1d37681

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a38f5d61e495c695ac2ccc26d2a71a45a6c8f5b4267146876256029fe8f619e8",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2022-09-16T07:08:54Z",
    "title_canon_sha256": "63c5434760b8b301d830ccec4c814f9a2b16eef869d5bcbbbe900465a61e4540"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2209.07750",
    "kind": "arxiv",
    "version": 1
  }
}