Pith Number

pith:Y64L5JKZ

pith:2012:Y64L5JKZBZOPU66KRLINIC3NXB

not attested not anchored not stored refs pending

On congruence in Z^n and the dimension of a multidimensional circulant

M.A. Fiol

arxiv:1209.4984 v1 · 2012-09-22 · math.CO · math.GR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Y64L5JKZBZOPU66KRLINIC3NXB}

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	2026-05-18T03:44:59.527449Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c7b8bea5590e5cfa7bca8ad0d40b6db875443b26ec5e4a37d85b8d975bf626c2

Aliases

arxiv: 1209.4984 · arxiv_version: 1209.4984v1 · doi: 10.48550/arxiv.1209.4984 · pith_short_12: Y64L5JKZBZOP · pith_short_16: Y64L5JKZBZOPU66K · pith_short_8: Y64L5JKZ

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/Y64L5JKZBZOPU66KRLINIC3NXB \
  | 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: c7b8bea5590e5cfa7bca8ad0d40b6db875443b26ec5e4a37d85b8d975bf626c2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1f1eb7bfb96997b9de32b5167a0f9b6fef835a1e2949a968b85bb13d294894c8",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-09-22T11:21:57Z",
    "title_canon_sha256": "4ad123024041f5da2e699cb968bd8b671ffb6b48a98b0295708b760bf229c85a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.4984",
    "kind": "arxiv",
    "version": 1
  }
}