Pith Number

pith:2XFGKJBC

pith:2011:2XFGKJBCKPEEVFDGA5FJHA7IVE

not attested not anchored not stored refs pending

The bondage number of $(n-3)$-regular graphs of order $n$

Fu-Tao Hu, Jun-Ming Xu

arxiv:1109.3931 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{2XFGKJBCKPEEVFDGA5FJHA7IVE}

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	2026-05-18T04:09:54.383770Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d5ca65242253c84a9466074a9383e8a9361b203df0bf67edc88859883387614c

Aliases

arxiv: 1109.3931 · arxiv_version: 1109.3931v1 · doi: 10.48550/arxiv.1109.3931 · pith_short_12: 2XFGKJBCKPEE · pith_short_16: 2XFGKJBCKPEEVFDG · pith_short_8: 2XFGKJBC

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/2XFGKJBCKPEEVFDGA5FJHA7IVE \
  | 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: d5ca65242253c84a9466074a9383e8a9361b203df0bf67edc88859883387614c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5d0fd433708da881bceaecf6267e2356e3f9ff376c84dc413122bebcec983a14",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-09-19T02:58:13Z",
    "title_canon_sha256": "503b5c2cf9984f8dc433e340b0de163f87f8434f34dc2890fa2e396bad036969"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.3931",
    "kind": "arxiv",
    "version": 1
  }
}