Pith Number

pith:AO5ECI5N

pith:2012:AO5ECI5NGD27AZCIUM2WO3MKAQ

not attested not anchored not stored refs pending

A Multiplicative Ergodic Theorem for Discontinuous Random Dynamical Systems and Applications

Huijie Qiao, Jinqiao Duan

arxiv:1204.5050 v5 · 2012-04-23 · 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{AO5ECI5NGD27AZCIUM2WO3MKAQ}

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	2026-05-18T00:26:40.550843Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

03ba4123ad30f5f06448a335676d8a042e7ce0668a9a3e0fd21c8633779b81cf

Aliases

arxiv: 1204.5050 · arxiv_version: 1204.5050v5 · doi: 10.48550/arxiv.1204.5050 · pith_short_12: AO5ECI5NGD27 · pith_short_16: AO5ECI5NGD27AZCI · pith_short_8: AO5ECI5N

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/AO5ECI5NGD27AZCIUM2WO3MKAQ \
  | 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: 03ba4123ad30f5f06448a335676d8a042e7ce0668a9a3e0fd21c8633779b81cf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "040467e5e8193550d92f9e750e29952472b46ab3e228d3233c309a5f9971270b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-04-23T12:59:44Z",
    "title_canon_sha256": "33de59805817aeb348be3dc7f0d9fcd38467309b1d887bd6f2ee962fa2e641ac"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.5050",
    "kind": "arxiv",
    "version": 5
  }
}