Pith Number

pith:Q7BGTR4Q

pith:2010:Q7BGTR4QJDPYKRB3G2CR4RJGWG

not attested not anchored not stored refs pending

Minimizing Laplacian spectral radius of unicyclic graphs with fixed girth

Binod Kumar Sahoo, Kamal Lochan Patra

arxiv:1012.0888 v2 · 2010-12-04 · 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{Q7BGTR4QJDPYKRB3G2CR4RJGWG}

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	2026-05-18T04:33:03.325567Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

87c269c79048df85443b36851e4526b18a7669ee2d78b0cda1ea0d065c220ed8

Aliases

arxiv: 1012.0888 · arxiv_version: 1012.0888v2 · doi: 10.48550/arxiv.1012.0888 · pith_short_12: Q7BGTR4QJDPY · pith_short_16: Q7BGTR4QJDPYKRB3 · pith_short_8: Q7BGTR4Q

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/Q7BGTR4QJDPYKRB3G2CR4RJGWG \
  | 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: 87c269c79048df85443b36851e4526b18a7669ee2d78b0cda1ea0d065c220ed8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8539958cfabc15f8e88aa29dd3186c53a98dba203d6c7d98193f1bf30c2645b9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-12-04T07:32:45Z",
    "title_canon_sha256": "f92fb34ac0091c2f48da449244d3f716a44daa4f37d063b6f4b6227a44969254"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.0888",
    "kind": "arxiv",
    "version": 2
  }
}