Pith Number

pith:ZDJA442L

pith:2010:ZDJA442LDH7OXG6Z4QLTT5J3KM

not attested not anchored not stored refs pending

Two remarks on the Collatz cycle conjecture

Masayoshi Kaneda

arxiv:1010.6206 v3 · 2010-10-29 · 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{ZDJA442LDH7OXG6Z4QLTT5J3KM}

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	2026-05-18T02:42:15.459081Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c8d20e734b19feeb9bd9e41739f53b5304ef98ec65da259ec2b69317b2fc9268

Aliases

arxiv: 1010.6206 · arxiv_version: 1010.6206v3 · doi: 10.48550/arxiv.1010.6206 · pith_short_12: ZDJA442LDH7O · pith_short_16: ZDJA442LDH7OXG6Z · pith_short_8: ZDJA442L

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/ZDJA442LDH7OXG6Z4QLTT5J3KM \
  | 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: c8d20e734b19feeb9bd9e41739f53b5304ef98ec65da259ec2b69317b2fc9268

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5119b6f21319de05e13a1e1670af3fd208b8abd1c7c0969f68e4f5ba430f6e70",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2010-10-29T13:48:50Z",
    "title_canon_sha256": "a8a4643c65c72c9657485d7f44d2a2258953be84ae118428038960772e4f112f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.6206",
    "kind": "arxiv",
    "version": 3
  }
}