Pith Number

pith:GMWET4SU

pith:2012:GMWET4SUO33RWRTEDH563A635W

not attested not anchored not stored refs pending

The Collatz conjecture and De Bruijn graphs

Benne de Weger, Thijs Laarhoven

arxiv:1209.3495 v1 · 2012-09-16 · math.NT · cs.DM · 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{GMWET4SUO33RWRTEDH563A635W}

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	2026-05-18T03:07:43.204472Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

332c49f25476f71b466419fbed83dbed9cfaa01bc190e2466cd504019d508a40

Aliases

arxiv: 1209.3495 · arxiv_version: 1209.3495v1 · doi: 10.48550/arxiv.1209.3495 · pith_short_12: GMWET4SUO33R · pith_short_16: GMWET4SUO33RWRTE · pith_short_8: GMWET4SU

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/GMWET4SUO33RWRTEDH563A635W \
  | 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: 332c49f25476f71b466419fbed83dbed9cfaa01bc190e2466cd504019d508a40

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4c8094ec13d1a6e21b8f03c9ff0f2ed7f5843876c7aca776cca90e20f853c8f8",
    "cross_cats_sorted": [
      "cs.DM",
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-09-16T15:37:48Z",
    "title_canon_sha256": "91368b22e32d058fac1f2328e1fb3996ac6664ef46cc19c921fe41133c6fea46"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.3495",
    "kind": "arxiv",
    "version": 1
  }
}