Pith Number

pith:7IWQ5SCM

pith:2016:7IWQ5SCM53CFBJZEWPXTCW5GVD

not attested not anchored not stored refs pending

The $k$-proper index of complete bipartite and complete multipartite graphs

Jingshu Zhang, Wenjing Li, Xueliang Li

arxiv:1608.00105 v3 · 2016-07-30 · 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{7IWQ5SCM53CFBJZEWPXTCW5GVD}

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	2026-05-18T00:55:51.836188Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fa2d0ec84ceec450a724b3ef315ba6a8de9b404cc5f2e8d44e97d5e1f69af4c0

Aliases

arxiv: 1608.00105 · arxiv_version: 1608.00105v3 · doi: 10.48550/arxiv.1608.00105 · pith_short_12: 7IWQ5SCM53CF · pith_short_16: 7IWQ5SCM53CFBJZE · pith_short_8: 7IWQ5SCM

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/7IWQ5SCM53CFBJZEWPXTCW5GVD \
  | 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: fa2d0ec84ceec450a724b3ef315ba6a8de9b404cc5f2e8d44e97d5e1f69af4c0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "53851c240b485f5367d0285abcd8f1f10fd779d5dc97b8339433d008147bc67f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-07-30T11:53:08Z",
    "title_canon_sha256": "018c3f11ebaaff529adec9a811360f4aeba61235b4b0cdea479219b51a687592"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.00105",
    "kind": "arxiv",
    "version": 3
  }
}