Pith Number

pith:CKOZD52Z

pith:2016:CKOZD52Z5BVXRWTPT5WYIV3LI5

not attested not anchored not stored refs pending

On the parity of the multiplicative order of certain products of integers related to Gauss factorials

Timothy Foo

arxiv:1603.02473 v3 · 2016-03-08 · 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{CKOZD52Z5BVXRWTPT5WYIV3LI5}

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	2026-05-18T01:19:04.999590Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

129d91f759e86b78da6f9f6d84576b476c5fd7e1d9460c22284813aed96a0bae

Aliases

arxiv: 1603.02473 · arxiv_version: 1603.02473v3 · doi: 10.48550/arxiv.1603.02473 · pith_short_12: CKOZD52Z5BVX · pith_short_16: CKOZD52Z5BVXRWTP · pith_short_8: CKOZD52Z

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/CKOZD52Z5BVXRWTPT5WYIV3LI5 \
  | 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: 129d91f759e86b78da6f9f6d84576b476c5fd7e1d9460c22284813aed96a0bae

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3f79202537966e0e5c2ac03a101170d60f1785cf2d6437005318ec24cf726616",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-03-08T10:46:27Z",
    "title_canon_sha256": "3e3d4290e4b57587f64122c2e458f7a978101b4303f00a1c19e970dec257ce69"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.02473",
    "kind": "arxiv",
    "version": 3
  }
}