Pith Number

pith:YDQ2TZGK

pith:2006:YDQ2TZGKJUTJKZ3BHE2UKU5MY4

not attested not anchored not stored refs pending

Odd Perfect Numbers Have At Least Nine Distinct Prime Factors

Pace P. Nielsen

arxiv:math/0602485 v1 · 2006-02-22 · 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{YDQ2TZGKJUTJKZ3BHE2UKU5MY4}

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	2026-07-04T17:02:08.500471Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c0e1a9e4ca4d2695676139354553acc7129d867dbd10c0ae2932d0e07a4bf0d8

Aliases

arxiv: math/0602485 · arxiv_version: math/0602485v1 · doi: 10.48550/arxiv.math/0602485 · pith_short_12: YDQ2TZGKJUTJ · pith_short_16: YDQ2TZGKJUTJKZ3B · pith_short_8: YDQ2TZGK

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/YDQ2TZGKJUTJKZ3BHE2UKU5MY4 \
  | 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: c0e1a9e4ca4d2695676139354553acc7129d867dbd10c0ae2932d0e07a4bf0d8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "81b7cd82f054926996b36c9a2810a487e4122a0015e51af2e448d84dc6120d32",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2006-02-22T04:17:01Z",
    "title_canon_sha256": "b6fd1613a7d0a5b1fab03d22540ea936a58d679cdfb6447310accbab7cd9cf1f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0602485",
    "kind": "arxiv",
    "version": 1
  }
}