Pith Number

pith:VLNJCBCL

pith:2016:VLNJCBCL3T3ZDNMS4VCKAJDSUZ

not attested not anchored not stored refs pending

The local metric dimension of the lexicographic product of graphs

A. Estrada-Moreno, G. A. Barrag\'an-Ram\'irez, J. A. Rodr\'iguez-Vel\'azquez, Y. Ram\'irez-Cruz

arxiv:1602.07537 v3 · 2016-02-24 · 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{VLNJCBCL3T3ZDNMS4VCKAJDSUZ}

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	2026-05-18T01:12:43.170168Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aada91044bdcf791b592e544a02472a67464e413920b57f171834308f7add598

Aliases

arxiv: 1602.07537 · arxiv_version: 1602.07537v3 · doi: 10.48550/arxiv.1602.07537 · pith_short_12: VLNJCBCL3T3Z · pith_short_16: VLNJCBCL3T3ZDNMS · pith_short_8: VLNJCBCL

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/VLNJCBCL3T3ZDNMS4VCKAJDSUZ \
  | 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: aada91044bdcf791b592e544a02472a67464e413920b57f171834308f7add598

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "efacdfcabdb311dcc8be6e0698369b75991a2fb4e8ced0ecf8db189418a4a7e5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-02-24T14:54:22Z",
    "title_canon_sha256": "d1fda745903884a4ba677bf123c0068834a63759e4716dda6eb3fd6ec359b1a4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1602.07537",
    "kind": "arxiv",
    "version": 3
  }
}