Pith Number

pith:KPDWMHXC

pith:2011:KPDWMHXCFF2JZOKJFYROTKWWIG

not attested not anchored not stored refs pending

Giuga Numbers and the arithmetic derivative

Antonio M. Oller-Marc\'en, Jos\'e Mar\'ia Grau

arxiv:1103.2298 v1 · 2011-03-11 · 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{KPDWMHXCFF2JZOKJFYROTKWWIG}

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.

Cited by

1 paper in Pith

Port Fillings for Primary Pseudoperfect Numbers

Receipt and verification

First computed	2026-05-18T04:26:55.864952Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

53c7661ee229749cb9492e22e9aad641aff317b780efaa5731522fc947b02546

Aliases

arxiv: 1103.2298 · arxiv_version: 1103.2298v1 · doi: 10.48550/arxiv.1103.2298 · pith_short_12: KPDWMHXCFF2J · pith_short_16: KPDWMHXCFF2JZOKJ · pith_short_8: KPDWMHXC

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/KPDWMHXCFF2JZOKJFYROTKWWIG \
  | 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: 53c7661ee229749cb9492e22e9aad641aff317b780efaa5731522fc947b02546

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "941c796710b8d1d4f8940ccff226c225e5ad8bd89e3ad7c3c319ccfdb7d0ddb2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-03-11T15:50:38Z",
    "title_canon_sha256": "2c6ed8062dba2dcb68b046f4d81af10c54bd9c77c8df5b88c120dcd97c97f407"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.2298",
    "kind": "arxiv",
    "version": 1
  }
}