Pith Number

pith:4BMEPR4U

pith:2016:4BMEPR4UJKT5H2NRNAHRJXRPHQ

not attested not anchored not stored refs pending

Weakly mixing, topologically weakly mixing, and sensitivity for non-autonomous discrete systems

Hao Zhu, Hua Shao, Yuming Shi

arxiv:1606.01521 v1 · 2016-06-05 · 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{4BMEPR4UJKT5H2NRNAHRJXRPHQ}

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	2026-05-18T01:12:54.025259Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e05847c7944aa7d3e9b1680f14de2f3c1eb5cf19ed5b895e060626a00d6fc1bc

Aliases

arxiv: 1606.01521 · arxiv_version: 1606.01521v1 · doi: 10.48550/arxiv.1606.01521 · pith_short_12: 4BMEPR4UJKT5 · pith_short_16: 4BMEPR4UJKT5H2NR · pith_short_8: 4BMEPR4U

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/4BMEPR4UJKT5H2NRNAHRJXRPHQ \
  | 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: e05847c7944aa7d3e9b1680f14de2f3c1eb5cf19ed5b895e060626a00d6fc1bc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "53c7ca24e5356a10e50ee361b5d7e88132e7308888b36dfa1668138e27caa584",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2016-06-05T14:52:12Z",
    "title_canon_sha256": "250e381d7f40bf2d3c24579f692df7ad4e38a774789426398748fe9f52fae898"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.01521",
    "kind": "arxiv",
    "version": 1
  }
}