Pith Number

pith:YYZRF7GQ

pith:2005:YYZRF7GQUTEGXGXP2CQLIZKR65

not attested not anchored not stored refs pending

Benford's law for the $3x+1$ function

Jeffrey C. Lagarias, K. Soundararajan

arxiv:math/0509175 v2 · 2005-09-07 · math.NT · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YYZRF7GQUTEGXGXP2CQLIZKR65}

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	2026-07-04T14:59:41.137399Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c63312fcd0a4c86b9aefd0a0b46551f77de630a7aa994ff92872e8f6f2880326

Aliases

arxiv: math/0509175 · arxiv_version: math/0509175v2 · doi: 10.48550/arxiv.math/0509175 · pith_short_12: YYZRF7GQUTEG · pith_short_16: YYZRF7GQUTEGXGXP · pith_short_8: YYZRF7GQ

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/YYZRF7GQUTEGXGXP2CQLIZKR65 \
  | 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: c63312fcd0a4c86b9aefd0a0b46551f77de630a7aa994ff92872e8f6f2880326

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1a92f50b3fa8adb91f7ff7a2b6718b39a35e91fc65779bebb08f95f68d93147c",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2005-09-07T23:47:36Z",
    "title_canon_sha256": "59cad7e58611ba67dac76c0cead83a601edf0f4baf55feb2ef42dbd5cf483248"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0509175",
    "kind": "arxiv",
    "version": 2
  }
}