Pith Number

pith:NZHPVFE5

pith:2024:NZHPVFE5W335T3GURIME66TTN2

not attested not anchored not stored refs pending

On Certain Bounds for Multiset Dimensions of Zero-Divisor Graphs Associated with Rings

Hafiz Muhammad Afzal Siddiqui, Muhammad Imran Qureshi, Nasir Ali

arxiv:2405.06180 v2 · 2024-05-10 · 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{NZHPVFE5W335T3GURIME66TTN2}

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	2026-07-05T08:35:02.643898Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6e4efa949db6f7d9ecd48a184f7a736e93beea6fb28659d7fff386a5ec43483b

Aliases

arxiv: 2405.06180 · arxiv_version: 2405.06180v2 · doi: 10.48550/arxiv.2405.06180 · pith_short_12: NZHPVFE5W335 · pith_short_16: NZHPVFE5W335T3GU · pith_short_8: NZHPVFE5

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/NZHPVFE5W335T3GURIME66TTN2 \
  | 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: 6e4efa949db6f7d9ecd48a184f7a736e93beea6fb28659d7fff386a5ec43483b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e8b7306681e2a752de7ce62c8f247ae981a599dcfa4b8334f7791e14c7d6dcc6",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2024-05-10T01:50:21Z",
    "title_canon_sha256": "5605346e78da61b3fb6f5f30e62daeee1e18eee582f6fb67f15a90fff041dc8a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2405.06180",
    "kind": "arxiv",
    "version": 2
  }
}