Pith Number

pith:YN4BQCFT

pith:2010:YN4BQCFT6A2SGZB4SO4FCXGZNL

not attested not anchored not stored refs pending

On the Sum and Product of Distinct Prime Factors of an Odd Perfect Number

Anirudh Prabhu

arxiv:1008.1114 v1 · 2010-08-06 · 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{YN4BQCFT6A2SGZB4SO4FCXGZNL}

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	2026-05-18T04:42:34.107552Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c3781808b3f03523643c93b8515cd96ada5b73e3aa9b4eabf2f1f2930767efa2

Aliases

arxiv: 1008.1114 · arxiv_version: 1008.1114v1 · doi: 10.48550/arxiv.1008.1114 · pith_short_12: YN4BQCFT6A2S · pith_short_16: YN4BQCFT6A2SGZB4 · pith_short_8: YN4BQCFT

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/YN4BQCFT6A2SGZB4SO4FCXGZNL \
  | 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: c3781808b3f03523643c93b8515cd96ada5b73e3aa9b4eabf2f1f2930767efa2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "08ac9995109187f6bf617112403cc1f94ad606ebbd1a8762d57134a93794c28d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2010-08-06T05:10:27Z",
    "title_canon_sha256": "5997da2702ecd9b83082586d80155d274a9c43b721e3c0117720fc76c8e14ebf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1008.1114",
    "kind": "arxiv",
    "version": 1
  }
}