Pith Number

pith:4FFXJ4TX

pith:2019:4FFXJ4TX35AS7IISHTHKSUO7TP

not attested not anchored not stored refs pending

Horseshoes and Lyapunov exponents for Banach cocycles over nonuniformly hyperbolic systems

Rui Zou, Yongluo Cao

arxiv:1902.05768 v1 · 2019-02-15 · 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{4FFXJ4TX35AS7IISHTHKSUO7TP}

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	2026-05-17T23:53:56.217363Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e14b74f277df412fa1123ccea951df9bf0c7bd574552554eec2d874c052705c5

Aliases

arxiv: 1902.05768 · arxiv_version: 1902.05768v1 · doi: 10.48550/arxiv.1902.05768 · pith_short_12: 4FFXJ4TX35AS · pith_short_16: 4FFXJ4TX35AS7IIS · pith_short_8: 4FFXJ4TX

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/4FFXJ4TX35AS7IISHTHKSUO7TP \
  | 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: e14b74f277df412fa1123ccea951df9bf0c7bd574552554eec2d874c052705c5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4abfd5afc556e061d42f1cb0aa23cda07b6bf9638a950d9353c9193c1871f1bc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2019-02-15T11:04:13Z",
    "title_canon_sha256": "32efd4b79faeafbd0bef867c9c56b045dae3321b986433727ca61c743a3c5792"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1902.05768",
    "kind": "arxiv",
    "version": 1
  }
}