Pith Number

pith:F5QJ3OWR

pith:2026:F5QJ3OWRAHHNL36FDBRUCCXPY6

not attested not anchored not stored refs pending

On the Complexity of Hop Domination and 2-Step Domination in Graph Classes

Sandip Das, Sk Samim Islam, Sweta Das

arxiv:2605.20970 v1 · 2026-05-20 · cs.DM · 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{F5QJ3OWRAHHNL36FDBRUCCXPY6}

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	2026-05-21T01:05:30.453003Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2f609dbad101ced5efc51863410aefc796a77acd980bd4b5270c80ee2fb0bf40

Aliases

arxiv: 2605.20970 · arxiv_version: 2605.20970v1 · doi: 10.48550/arxiv.2605.20970 · pith_short_12: F5QJ3OWRAHHN · pith_short_16: F5QJ3OWRAHHNL36F · pith_short_8: F5QJ3OWR

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/F5QJ3OWRAHHNL36FDBRUCCXPY6 \
  | 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: 2f609dbad101ced5efc51863410aefc796a77acd980bd4b5270c80ee2fb0bf40

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1834b1c1ad071ff32ca6982c6d117c34cfcdb3b09fc2741265e55ee6f8d01201",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "cs.DM",
    "submitted_at": "2026-05-20T09:57:50Z",
    "title_canon_sha256": "b6a7a1769afc07904beeb0075b18d25da2f2f7ae121517fd373e0b4c99ca0efc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.20970",
    "kind": "arxiv",
    "version": 1
  }
}