Pith Number

pith:OMJP7IYP

pith:2010:OMJP7IYP5SMSYRRWDBBFG2CZV5

not attested not anchored not stored refs pending

A New Lower Bound on the Density of Vertex Identifying Codes for the Infinite Hexagonal Grid

Daniel W. Cranston, Gexin Yu

arxiv:1006.3779 v1 · 2010-06-18 · math.CO · cs.DS

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OMJP7IYP5SMSYRRWDBBFG2CZV5}

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.

Cited by

1 paper in Pith

Finding codes on infinite grids automatically

Receipt and verification

First computed	2026-05-18T04:11:18.027817Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7312ffa30fec992c46361842536859af4b2fbc0411b7763be7a975ce595e12a8

Aliases

arxiv: 1006.3779 · arxiv_version: 1006.3779v1 · doi: 10.48550/arxiv.1006.3779 · pith_short_12: OMJP7IYP5SMS · pith_short_16: OMJP7IYP5SMSYRRW · pith_short_8: OMJP7IYP

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/OMJP7IYP5SMSYRRWDBBFG2CZV5 \
  | 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: 7312ffa30fec992c46361842536859af4b2fbc0411b7763be7a975ce595e12a8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fbe901c03d3f6d2c8b3371371700b499ab14dd51f30afa688b7537636eecbc31",
    "cross_cats_sorted": [
      "cs.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-06-18T19:26:36Z",
    "title_canon_sha256": "c0b444374d46d2911bdd92b54421d40607a81e052e6d7adb38c6fbfed17f0872"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1006.3779",
    "kind": "arxiv",
    "version": 1
  }
}