Pith Number

pith:PX53JUAP

pith:2013:PX53JUAPD4GIHVNE6VZAM6RZY7

not attested not anchored not stored refs pending

On the Cayley graph of a commutative ring with respect to its zero-divisors

Ghodratollah Aalipour, Saieed Akbari

arxiv:1305.0601 v1 · 2013-05-03 · math.CO · math.AC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PX53JUAPD4GIHVNE6VZAM6RZY7}

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	2026-05-18T03:26:33.239437Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7dfbb4d00f1f0c83d5a4f572067a39c7ce5235089f71c7b956d440dc120cacdc

Aliases

arxiv: 1305.0601 · arxiv_version: 1305.0601v1 · doi: 10.48550/arxiv.1305.0601 · pith_short_12: PX53JUAPD4GI · pith_short_16: PX53JUAPD4GIHVNE · pith_short_8: PX53JUAP

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/PX53JUAPD4GIHVNE6VZAM6RZY7 \
  | 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: 7dfbb4d00f1f0c83d5a4f572067a39c7ce5235089f71c7b956d440dc120cacdc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "38e0762a483e87f7c48bc3b67a014d97a15c2104c0cb9f80be1265d661d9e9be",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-05-03T00:25:24Z",
    "title_canon_sha256": "bd55a09b6ced2e1718a8262992ad921b9ba43f21aac57ac3fafdd1e620dce6e0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1305.0601",
    "kind": "arxiv",
    "version": 1
  }
}