Pith Number

pith:DZC76CUW

pith:2005:DZC76CUWSFXS7MTYRTJJZDTY65

not attested not anchored not stored refs pending

On the Metric Dimension of Cartesian Products of Graphs

Carlos Seara, Carmen Hernando, David R. Wood, Ignacio M. Pelayo, Jos\'e C\'aceres, Mar\'ia L. Puertas, Merc\'e Mora

arxiv:math/0507527 v3 · 2005-07-26 · 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{DZC76CUWSFXS7MTYRTJJZDTY65}

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	2026-07-04T15:01:58.394232Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1e45ff0a96916f2fb2788cd29c8e78f771d6837b7111227e35df38962db217a6

Aliases

arxiv: math/0507527 · arxiv_version: math/0507527v3 · doi: 10.48550/arxiv.math/0507527 · pith_short_12: DZC76CUWSFXS · pith_short_16: DZC76CUWSFXS7MTY · pith_short_8: DZC76CUW

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/DZC76CUWSFXS7MTYRTJJZDTY65 \
  | 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: 1e45ff0a96916f2fb2788cd29c8e78f771d6837b7111227e35df38962db217a6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d6cf534079f2e2c8752a84182d2815d20de61f83c194911ace1f9d24f92ad28c",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "2005-07-26T09:30:57Z",
    "title_canon_sha256": "7d66ddd7edda5b65c3731b8a5a04ce70b0ca7eec72692ba0dba5ff492a3d5527"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0507527",
    "kind": "arxiv",
    "version": 3
  }
}