Pith Number

pith:7AYXPLQL

pith:2011:7AYXPLQLUTP6GHYZPDZH6HQNOP

not attested not anchored not stored refs pending

Bounds for Odd $k$-Perfect Numbers

Hao Luo, Shi-Chao Chen

arxiv:1102.4397 v1 · 2011-02-22 · 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{7AYXPLQLUTP6GHYZPDZH6HQNOP}

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	2026-05-18T04:28:09.049778Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f83177ae0ba4dfe31f1978f27f1e0d73e610b6e88308f85a085392b59a800a99

Aliases

arxiv: 1102.4397 · arxiv_version: 1102.4397v1 · doi: 10.48550/arxiv.1102.4397 · pith_short_12: 7AYXPLQLUTP6 · pith_short_16: 7AYXPLQLUTP6GHYZ · pith_short_8: 7AYXPLQL

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/7AYXPLQLUTP6GHYZPDZH6HQNOP \
  | 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: f83177ae0ba4dfe31f1978f27f1e0d73e610b6e88308f85a085392b59a800a99

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d2993fbe9ca7364e57db31ead1950e3458f7ceb0d41c77462ba4ff92faa4c379",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-02-22T03:41:21Z",
    "title_canon_sha256": "c0a916ca387143d43e416d933fe341c6c1507134d0f6a921166c8388eb1d4c5e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.4397",
    "kind": "arxiv",
    "version": 1
  }
}