Pith Number

pith:4W4HF7J5

pith:2009:4W4HF7J5UM26OAMBI346V7E7BA

not attested not anchored not stored refs pending

Regularity versus complexity in the binary representation of 3^n

Eric S. Rowland

arxiv:0902.3257 v2 · 2009-02-18 · 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{4W4HF7J5UM26OAMBI346V7E7BA}

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	2026-05-18T02:24:56.363518Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e5b872fd3da335e7018146f9eafc9f080a8a9328034dbc5d2e47952367d4ad30

Aliases

arxiv: 0902.3257 · arxiv_version: 0902.3257v2 · doi: 10.48550/arxiv.0902.3257 · pith_short_12: 4W4HF7J5UM26 · pith_short_16: 4W4HF7J5UM26OAMB · pith_short_8: 4W4HF7J5

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/4W4HF7J5UM26OAMBI346V7E7BA \
  | 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: e5b872fd3da335e7018146f9eafc9f080a8a9328034dbc5d2e47952367d4ad30

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "97220457d61d46ad145608476efa84037b164f8a81e9b5e30b6d1995d03abbd6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2009-02-18T21:48:15Z",
    "title_canon_sha256": "33743896554712b1c45d71790bf3d2e9cf5da28e4788c184a60e12430697951e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0902.3257",
    "kind": "arxiv",
    "version": 2
  }
}