Pith Number

pith:WAXUKLQ5

pith:2011:WAXUKLQ5LSOR2VYPMMQQHPGNO5

not attested not anchored not stored refs pending

Note on the minimal size of a graph with generalized connectivity kappa_3= 2

Shasha Li, Xueliang Li, Yongtang Shi

arxiv:1106.4411 v1 · 2011-06-22 · 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{WAXUKLQ5LSOR2VYPMMQQHPGNO5}

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	2026-05-18T04:19:33.028589Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b02f452e1d5c9d1d570f632103bccd777c578745a4d443ffe43839c453b31a73

Aliases

arxiv: 1106.4411 · arxiv_version: 1106.4411v1 · doi: 10.48550/arxiv.1106.4411 · pith_short_12: WAXUKLQ5LSOR · pith_short_16: WAXUKLQ5LSOR2VYP · pith_short_8: WAXUKLQ5

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/WAXUKLQ5LSOR2VYPMMQQHPGNO5 \
  | 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: b02f452e1d5c9d1d570f632103bccd777c578745a4d443ffe43839c453b31a73

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "70c0cce1790f71b43e9b27d385efeb576bcfdfa1e64f851debf82d2db97eaf09",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-06-22T10:34:25Z",
    "title_canon_sha256": "cb3f32247352ba2fd7eca82711e40caf227c1e8ff623db2eed748de9b0aabe3a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.4411",
    "kind": "arxiv",
    "version": 1
  }
}