Pith Number

pith:5KSNP5UT

pith:2019:5KSNP5UTYNK4E2K2FMUBPDUB6S

not attested not anchored not stored refs pending

On odd deficient-perfect numbers with four distinct prime divisors

Cui-Fang Sun, Zhao-Cheng He

arxiv:1908.04932 v1 · 2019-08-14 · 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{5KSNP5UTYNK4E2K2FMUBPDUB6S}

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	2026-07-04T23:55:58.353760Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eaa4d7f693c355c2695a2b28178e81f48a51b74e386a38da0b2889efaebf5d62

Aliases

arxiv: 1908.04932 · arxiv_version: 1908.04932v1 · doi: 10.48550/arxiv.1908.04932 · pith_short_12: 5KSNP5UTYNK4 · pith_short_16: 5KSNP5UTYNK4E2K2 · pith_short_8: 5KSNP5UT

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/5KSNP5UTYNK4E2K2FMUBPDUB6S \
  | 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: eaa4d7f693c355c2695a2b28178e81f48a51b74e386a38da0b2889efaebf5d62

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "55446c5bb4a3beb525a9e3e3319c1325769f0243ef9089c26fa7ade2b2257bc5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2019-08-14T02:41:51Z",
    "title_canon_sha256": "1dc8a73fe6f981c7d8cde4d6c491491815e58f338113d28439625add4919b3b4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.04932",
    "kind": "arxiv",
    "version": 1
  }
}