Pith Number

pith:OS6OIIWX

pith:2020:OS6OIIWXVFT6A63P4ANTJRJFKZ

not attested not anchored not stored refs pending

On Coupling Lemma and Stochastic Properties with Unbounded Observables for 1-d Expanding Maps

Hongkun Zhang, Jianyu Chen, Yiwei Zhang

arxiv:2001.11172 v1 · 2020-01-30 · math.DS · 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{OS6OIIWXVFT6A63P4ANTJRJFKZ}

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	2026-07-05T00:37:21.287809Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

74bce422d7a967e07b6fe01b34c5255659a1edb8850fb7f114f54acdc7d70bb6

Aliases

arxiv: 2001.11172 · arxiv_version: 2001.11172v1 · doi: 10.48550/arxiv.2001.11172 · pith_short_12: OS6OIIWXVFT6 · pith_short_16: OS6OIIWXVFT6A63P · pith_short_8: OS6OIIWX

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/OS6OIIWXVFT6A63P4ANTJRJFKZ \
  | 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: 74bce422d7a967e07b6fe01b34c5255659a1edb8850fb7f114f54acdc7d70bb6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "30dc835e96046ecf1223b88292fe42e3bcd7b32ace48804c5857282246a3be6c",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2020-01-30T04:44:18Z",
    "title_canon_sha256": "28e5b1e199a66c6f9889be506a18d44ca9ffdad78dd1b9f17e40e70259a0a870"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2001.11172",
    "kind": "arxiv",
    "version": 1
  }
}