Pith Number

pith:W2FXIYFJ

pith:2012:W2FXIYFJZ4PUDFIWTXZGJZJJGI

not attested not anchored not stored refs pending

Metric Dimension and Zero Forcing Number of Two Families of Line Graphs

Cong X. Kang, Eunjeong Yi, Linda Eroh

arxiv:1207.6127 v2 · 2012-07-25 · 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{W2FXIYFJZ4PUDFIWTXZGJZJJGI}

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	2026-05-18T02:31:38.541603Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b68b7460a9cf1f4195169df264e5293222f58452d0295fc79e45d4ad10b58803

Aliases

arxiv: 1207.6127 · arxiv_version: 1207.6127v2 · doi: 10.48550/arxiv.1207.6127 · pith_short_12: W2FXIYFJZ4PU · pith_short_16: W2FXIYFJZ4PUDFIW · pith_short_8: W2FXIYFJ

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/W2FXIYFJZ4PUDFIWTXZGJZJJGI \
  | 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: b68b7460a9cf1f4195169df264e5293222f58452d0295fc79e45d4ad10b58803

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9323334277fd24da399da0f272219da4fba1863fd71c49615d7aef9ecd874d2a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-07-25T20:51:33Z",
    "title_canon_sha256": "652c73355d42d13d8d07233d906b19b4cb8e0547b38698da8ee33ef79a720c6a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.6127",
    "kind": "arxiv",
    "version": 2
  }
}