Pith Number

pith:ULDJ5D7F

pith:2018:ULDJ5D7FFG6GZBQEHGNR5WNE2R

not attested not anchored not stored refs pending

On the number of total prime factors of an odd perfect number

Joshua Zelinsky

arxiv:1810.13063 v3 · 2018-10-31 · 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{ULDJ5D7FFG6GZBQEHGNR5WNE2R}

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	2026-07-05T00:13:12.652588Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a2c69e8fe529bc6c8604399b1ed9a4d47766c81f78b77e02e7bff247f50cd6ce

Aliases

arxiv: 1810.13063 · arxiv_version: 1810.13063v3 · doi: 10.48550/arxiv.1810.13063 · pith_short_12: ULDJ5D7FFG6G · pith_short_16: ULDJ5D7FFG6GZBQE · pith_short_8: ULDJ5D7F

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/ULDJ5D7FFG6GZBQEHGNR5WNE2R \
  | 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: a2c69e8fe529bc6c8604399b1ed9a4d47766c81f78b77e02e7bff247f50cd6ce

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8bf085ba299862f6ec7cb988df004caec8f5df4c47785972572085f51caf42e7",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2018-10-31T01:39:30Z",
    "title_canon_sha256": "eacd5fe6e6105ca7d8bbdcdea53936674eba832e580fc1cc07a625c2f1fa7233"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1810.13063",
    "kind": "arxiv",
    "version": 3
  }
}