Pith Number

pith:NGW3ZPOY

pith:2019:NGW3ZPOY2ZJ372IZOCBCTVETOZ

not attested not anchored not stored refs pending

Minimal graphs with disjoint dominating and paired-dominating sets

Jerzy Topp, Michael A. Henning

arxiv:1908.04189 v1 · 2019-08-12 · 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{NGW3ZPOY2ZJ372IZOCBCTVETOZ}

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	2026-07-05T02:20:12.391521Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

69adbcbdd8d653bfe919708229d493766e5ef89ef4c99ac387681eb45f5cf91c

Aliases

arxiv: 1908.04189 · arxiv_version: 1908.04189v1 · doi: 10.48550/arxiv.1908.04189 · pith_short_12: NGW3ZPOY2ZJ3 · pith_short_16: NGW3ZPOY2ZJ372IZ · pith_short_8: NGW3ZPOY

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/NGW3ZPOY2ZJ372IZOCBCTVETOZ \
  | 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: 69adbcbdd8d653bfe919708229d493766e5ef89ef4c99ac387681eb45f5cf91c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3ab777d0cbd0efce53c8f23ca0433412864c98c7daaf8a0988c949137cc90614",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2019-08-12T15:11:27Z",
    "title_canon_sha256": "cd8aad1b72ffb09eb23bc755c6f41db7e7f3779b02190fc4d106b9e3bde8b4c7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.04189",
    "kind": "arxiv",
    "version": 1
  }
}