Pith Number

pith:OCC7X3AO

pith:2003:OCC7X3AOYOJ7YAJ34YYZXY2L7W

not attested not anchored not stored refs pending

The 3x+1 problem: An annotated bibliography (1963--1999) (sorted by author)

Jeffrey C. Lagarias

arxiv:math/0309224 v13 · 2003-09-13 · math.NT · 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{OCC7X3AOYOJ7YAJ34YYZXY2L7W}

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.

Cited by

2 papers in Pith

Exploring Collatz Dynamics with Human-LLM Collaboration

Parity vectors and paradoxical sequences in the accelerated Collatz map

Receipt and verification

First computed	2026-05-18T04:31:50.715510Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7085fbec0ec393fc013be6319be34bfd929bb2f8116afa9658e0207445e54e00

Aliases

arxiv: math/0309224 · arxiv_version: math/0309224v13 · doi: 10.48550/arxiv.math/0309224 · pith_short_12: OCC7X3AOYOJ7 · pith_short_16: OCC7X3AOYOJ7YAJ3 · pith_short_8: OCC7X3AO

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/OCC7X3AOYOJ7YAJ34YYZXY2L7W \
  | 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: 7085fbec0ec393fc013be6319be34bfd929bb2f8116afa9658e0207445e54e00

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f8a3653dd3ac25f395cfff9ec34f7d9a79f955464f6d3d1fd841307158d495dd",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2003-09-13T20:48:54Z",
    "title_canon_sha256": "43ae9e32531518f0f5b0857591b761b7a4791cb658a7bfb5806dd3b6a9f34d95"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0309224",
    "kind": "arxiv",
    "version": 13
  }
}