Pith Number

pith:HMMX3K76

pith:2012:HMMX3K76PUSO6NKVXRGVMDDH4B

not attested not anchored not stored refs pending

The 2-Domination and 2-Bondage Numbers of Grid Graphs

Jun-Ming Xu, You Lu

arxiv:1204.4514 v1 · 2012-04-20 · 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{HMMX3K76PUSO6NKVXRGVMDDH4B}

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	2026-05-18T03:57:27.125866Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3b197dabfe7d24ef3555bc4d560c67e0674f9aaaf6760291df86f1dcd1031687

Aliases

arxiv: 1204.4514 · arxiv_version: 1204.4514v1 · doi: 10.48550/arxiv.1204.4514 · pith_short_12: HMMX3K76PUSO · pith_short_16: HMMX3K76PUSO6NKV · pith_short_8: HMMX3K76

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/HMMX3K76PUSO6NKVXRGVMDDH4B \
  | 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: 3b197dabfe7d24ef3555bc4d560c67e0674f9aaaf6760291df86f1dcd1031687

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dba9e409886fc05ca8c98957b6ca3e8840351a107aa5cecc9c5334c8f9dfcb1b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-04-20T01:50:58Z",
    "title_canon_sha256": "09c63566b719b4b2c839ce553b8233194b3785eae1e1ff7197ff367671486243"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.4514",
    "kind": "arxiv",
    "version": 1
  }
}