Pith Number

pith:GD353UAJ

pith:2013:GD353UAJJH32AOZRJHTJL4KSZ6

not attested not anchored not stored refs pending

On the strong metric dimension of Cartesian and direct products of graphs

Dorota Kuziak, Ismael G. Yero, Juan A. Rodr\'iguez-Vel\'azquez, Ortrud R. Oellermann

arxiv:1307.4722 v1 · 2013-07-17 · 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{GD353UAJJH32AOZRJHTJL4KSZ6}

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	2026-05-18T03:18:17.312605Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

30f7ddd00949f7a03b3149e695f152cf976a0a457b3556bb1b257124af933f4a

Aliases

arxiv: 1307.4722 · arxiv_version: 1307.4722v1 · doi: 10.48550/arxiv.1307.4722 · pith_short_12: GD353UAJJH32 · pith_short_16: GD353UAJJH32AOZR · pith_short_8: GD353UAJ

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/GD353UAJJH32AOZRJHTJL4KSZ6 \
  | 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: 30f7ddd00949f7a03b3149e695f152cf976a0a457b3556bb1b257124af933f4a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5663f45c7e67f7139730a0e002889f850984db2a948bdfe4b0d3e88e2082ace0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-07-17T18:41:18Z",
    "title_canon_sha256": "4373c8bdfb3e76df1f5ba480fccc3289d103da7515414daca3857f6280b3f5ec"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.4722",
    "kind": "arxiv",
    "version": 1
  }
}