Pith Number

pith:BZAKU3PY

pith:2012:BZAKU3PYPAQI3S62OTQYL74WJH

not attested not anchored not stored refs pending

On weak product recurrence and synchronization of return times

Guo Hua Zhang, Piotr Oprocha

arxiv:1205.2280 v2 · 2012-05-10 · 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{BZAKU3PYPAQI3S62OTQYL74WJH}

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	2026-05-18T03:20:32.877381Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0e40aa6df878208dcbda74e185ff9649c181984f003fabac80c0c0f746d2fa81

Aliases

arxiv: 1205.2280 · arxiv_version: 1205.2280v2 · doi: 10.48550/arxiv.1205.2280 · pith_short_12: BZAKU3PYPAQI · pith_short_16: BZAKU3PYPAQI3S62 · pith_short_8: BZAKU3PY

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/BZAKU3PYPAQI3S62OTQYL74WJH \
  | 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: 0e40aa6df878208dcbda74e185ff9649c181984f003fabac80c0c0f746d2fa81

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ae28db3814988497482cc7a60c3b0a482e6b0ccaf32e591365fb5dc0efc996a3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-05-10T14:44:00Z",
    "title_canon_sha256": "ded2d9646153943d0342931e5b17412d98475154b29ee4966e64eb883b687474"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.2280",
    "kind": "arxiv",
    "version": 2
  }
}