Pith Number

pith:4BLD6CAY

pith:2025:4BLD6CAY7EXEZV45U2GWYFY5BR

not attested not anchored not stored refs pending

Domination and Total Domination Numbers in Zero-divisor Graphs of Commutative Rings

Brenda Kroschel, Joe Stickles, Mike Axtell, Sarah Anderson

arxiv:2506.02953 v1 · 2025-06-03 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4BLD6CAY7EXEZV45U2GWYFY5BR}

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	2026-07-05T11:15:12.407372Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e0563f0818f92e4cd79da68d6c171d0c46e43758456544b4a7cf54d3ad5f57b4

Aliases

arxiv: 2506.02953 · arxiv_version: 2506.02953v1 · doi: 10.48550/arxiv.2506.02953 · pith_short_12: 4BLD6CAY7EXE · pith_short_16: 4BLD6CAY7EXEZV45 · pith_short_8: 4BLD6CAY

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/4BLD6CAY7EXEZV45U2GWYFY5BR \
  | 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: e0563f0818f92e4cd79da68d6c171d0c46e43758456544b4a7cf54d3ad5f57b4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2d60a4eeab49a24490e47411ef552524fbe644a0b18b9748f43e19d0908267f5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-06-03T14:46:53Z",
    "title_canon_sha256": "7dc1134d7c047d63b5428f2883ed3ae27244f630e9fc495758f869bf319cfc4a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.02953",
    "kind": "arxiv",
    "version": 1
  }
}