Pith Number

pith:KUVJPZ3B

pith:2018:KUVJPZ3BHNG64MY7EHHQXIVWOD

not attested not anchored not stored refs pending

A simple proof of the Wirsching-Goodwin representation of integers connected to 1 in the $3x+1$ problem

Jean-Jacques Daudin, Laurent Pierre

arxiv:1801.07678 v3 · 2018-01-23 · 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{KUVJPZ3BHNG64MY7EHHQXIVWOD}

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	2026-05-18T00:14:34.069870Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

552a97e7613b4dee331f21cf0ba2b670e2727484046218843307df6ac1d2a487

Aliases

arxiv: 1801.07678 · arxiv_version: 1801.07678v3 · doi: 10.48550/arxiv.1801.07678 · pith_short_12: KUVJPZ3BHNG6 · pith_short_16: KUVJPZ3BHNG64MY7 · pith_short_8: KUVJPZ3B

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/KUVJPZ3BHNG64MY7EHHQXIVWOD \
  | 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: 552a97e7613b4dee331f21cf0ba2b670e2727484046218843307df6ac1d2a487

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8ec12067c806c8fc1f02cc887eae51f1994f3d68b47de27d27cae09dd0156786",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2018-01-23T17:59:20Z",
    "title_canon_sha256": "a0e4e93f1090e54036fd54872e4bf36143d73dae94fffa7420120a224344b173"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1801.07678",
    "kind": "arxiv",
    "version": 3
  }
}