Pith Number

pith:HAPIDW56

pith:2025:HAPIDW566QKYXEDBLETYCIQMYW

not attested not anchored not stored refs pending

Wilson's theorem modulo higher prime powers I: Fermat and Wilson quotients

Bernd C. Kellner

arxiv:2509.05235 v1 · 2025-09-05 · 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{HAPIDW566QKYXEDBLETYCIQMYW}

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	2026-07-05T12:05:38.145457Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

381e81dbbef4158b9061592781220cc5bf9f733ebb7b9f9203c12928b180ec10

Aliases

arxiv: 2509.05235 · arxiv_version: 2509.05235v1 · doi: 10.48550/arxiv.2509.05235 · pith_short_12: HAPIDW566QKY · pith_short_16: HAPIDW566QKYXEDB · pith_short_8: HAPIDW56

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/HAPIDW566QKYXEDBLETYCIQMYW \
  | 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: 381e81dbbef4158b9061592781220cc5bf9f733ebb7b9f9203c12928b180ec10

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "96cf01923868958a8114375deb78f4a50325e385fc7591507811c46042bb72c0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2025-09-05T16:50:06Z",
    "title_canon_sha256": "1bc35889d194d8d77c6e5f5920eb1c2e285e0e246ee93a3ef8a6349dede2b13f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.05235",
    "kind": "arxiv",
    "version": 1
  }
}