Pith Number

pith:7K4NP66Q

pith:2011:7K4NP66QIC6CTBROAC6MVY32UQ

not attested not anchored not stored refs pending

Equality in a Linear Vizing-Like Relation that Relates the Size and Total Domination Number of a Graph

Ernst J. Joubert, Michael A. Henning

arxiv:1108.5949 v1 · 2011-08-30 · 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{7K4NP66QIC6CTBROAC6MVY32UQ}

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	2026-05-18T04:14:28.187215Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fab8d7fbd040bc29862e00bccae37aa4038372fabe398e77e3061d2986b54d02

Aliases

arxiv: 1108.5949 · arxiv_version: 1108.5949v1 · doi: 10.48550/arxiv.1108.5949 · pith_short_12: 7K4NP66QIC6C · pith_short_16: 7K4NP66QIC6CTBRO · pith_short_8: 7K4NP66Q

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/7K4NP66QIC6CTBROAC6MVY32UQ \
  | 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: fab8d7fbd040bc29862e00bccae37aa4038372fabe398e77e3061d2986b54d02

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "566a30eb8b343bc32b19d87a5901d4f2ddc0fa582bd3e6c2c0c4a7e552708b9c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-08-30T12:54:07Z",
    "title_canon_sha256": "125634e37635fbf74ce201f873e68a542f6a628dfb8807e3017c5fa28dbae58d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.5949",
    "kind": "arxiv",
    "version": 1
  }
}