Pith Number

pith:BXNLOY3Q

pith:2011:BXNLOY3QMHD45R7B464RQPCGO6

not attested not anchored not stored refs pending

A Conjecture on the Collatz-Kakutani Path Length for the Mersenne Primes

Hiroshi Watanabe, Toru Ohira

arxiv:1104.2804 v3 · 2011-04-13 · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BXNLOY3QMHD45R7B464RQPCGO6}

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	2026-05-18T03:49:32.978513Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0ddab7637061c7cec7e1e7b9183c46778fb237526766e1cc6cbea82a42fa1125

Aliases

arxiv: 1104.2804 · arxiv_version: 1104.2804v3 · doi: 10.48550/arxiv.1104.2804 · pith_short_12: BXNLOY3QMHD4 · pith_short_16: BXNLOY3QMHD45R7B · pith_short_8: BXNLOY3Q

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/BXNLOY3QMHD45R7B464RQPCGO6 \
  | 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: 0ddab7637061c7cec7e1e7b9183c46778fb237526766e1cc6cbea82a42fa1125

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7e551410e1971390dc4e7565363f8b9bdf9cd8e77bf7f6a148b7719db12ade84",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-04-13T13:53:28Z",
    "title_canon_sha256": "f06a3ea3c925b60b8afdbf1161c43d8c36e0768fc206ccab5e1121ef7a6f2012"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1104.2804",
    "kind": "arxiv",
    "version": 3
  }
}