Pith Number

pith:F54CG3U4

pith:2011:F54CG3U4UGPOYRKSH4BQZQSYR5

not attested not anchored not stored refs pending

Total and paired domination numbers of toroidal meshes

Fu-Tao Hu, Jun-Ming Xu

arxiv:1109.3928 v1 · 2011-09-19 · 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{F54CG3U4UGPOYRKSH4BQZQSYR5}

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	2026-05-18T04:12:45.570528Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2f78236e9ca19eec45523f030cc2588f79be78b6fc57ab80a52fa52eb9395082

Aliases

arxiv: 1109.3928 · arxiv_version: 1109.3928v1 · doi: 10.48550/arxiv.1109.3928 · pith_short_12: F54CG3U4UGPO · pith_short_16: F54CG3U4UGPOYRKS · pith_short_8: F54CG3U4

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/F54CG3U4UGPOYRKSH4BQZQSYR5 \
  | 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: 2f78236e9ca19eec45523f030cc2588f79be78b6fc57ab80a52fa52eb9395082

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a94a124676a6bd31bd6ea2e6168f0dfa78c65057165bc5a7dee38a8f4e89457f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-09-19T02:35:41Z",
    "title_canon_sha256": "74a18bdfeab06c1f9f635cdfc895f63b5f34e58923503342954831833c22845b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.3928",
    "kind": "arxiv",
    "version": 1
  }
}