Pith Number

pith:LTZHS6ZT

pith:2013:LTZHS6ZTAJ7O55O4FEHY2UIJNS

not attested not anchored not stored refs pending

The Ergodicity of the Collatz Process in Positive Integer Field

Bojin Zheng, Hongrun Wu, Li Kuang, Yangqian Su

arxiv:1311.5690 v1 · 2013-11-22 · cs.CC

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LTZHS6ZTAJ7O55O4FEHY2UIJNS}

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	2026-05-18T03:06:23.490979Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5cf2797b33027eeef5dc290f8d51096c8ffaac7a91a3c657d58187f9a5319892

Aliases

arxiv: 1311.5690 · arxiv_version: 1311.5690v1 · doi: 10.48550/arxiv.1311.5690 · pith_short_12: LTZHS6ZTAJ7O · pith_short_16: LTZHS6ZTAJ7O55O4 · pith_short_8: LTZHS6ZT

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/LTZHS6ZTAJ7O55O4FEHY2UIJNS \
  | 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: 5cf2797b33027eeef5dc290f8d51096c8ffaac7a91a3c657d58187f9a5319892

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bcd867c30a8b3bcbc6131fa53213358f66f794da559c91b24fbd29e6f2a9c472",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CC",
    "submitted_at": "2013-11-22T09:59:26Z",
    "title_canon_sha256": "93b02bdb64cad193cec42d3f6faf9c68113f549c37133973f1d49bfd93348cf2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.5690",
    "kind": "arxiv",
    "version": 1
  }
}