Pith Number

pith:BKRTFA74

pith:2017:BKRTFA74QL6UH2Q7I3K3K5RMKO

not attested not anchored not stored refs pending

Sharp upper bounds for multiplicative Zagreb indices of bipartite graphs with given diameter

Chunxiang Wang, Jia-Bao Liu, Shaohui Wang

arxiv:1701.08389 v2 · 2017-01-29 · 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{BKRTFA74QL6UH2Q7I3K3K5RMKO}

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	2026-05-18T00:45:30.081821Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0aa33283fc82fd43ea1f46d5b5762c53b51217ffb8fdf7e2a8efd6ad5f5a4b37

Aliases

arxiv: 1701.08389 · arxiv_version: 1701.08389v2 · doi: 10.48550/arxiv.1701.08389 · pith_short_12: BKRTFA74QL6U · pith_short_16: BKRTFA74QL6UH2Q7 · pith_short_8: BKRTFA74

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/BKRTFA74QL6UH2Q7I3K3K5RMKO \
  | 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: 0aa33283fc82fd43ea1f46d5b5762c53b51217ffb8fdf7e2a8efd6ad5f5a4b37

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0cf5db16079d2d4fab00d0979ddaf86218ea5ddf14720af818509fed02a5b383",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2017-01-29T14:53:48Z",
    "title_canon_sha256": "e1839dc031122c99c038e6900a3af16ca3edf103097f97367e610894a2e29558"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1701.08389",
    "kind": "arxiv",
    "version": 2
  }
}