Pith Number

pith:6MGZAUCE

pith:2012:6MGZAUCEWNIIRM2NSRFGFNWXL2

not attested not anchored not stored refs pending

Sharp Bounds for the Signless Laplacian Spectral Radius in Terms of Clique Number

Bian He, Xiao-Dong Zhang, Ya-Lei Jin

arxiv:1209.3214 v1 · 2012-09-14 · 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{6MGZAUCEWNIIRM2NSRFGFNWXL2}

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	2026-05-18T03:45:32.493625Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f30d905044b35088b34d944a62b6d75eb0f960476901401e4cbff03a59f2b627

Aliases

arxiv: 1209.3214 · arxiv_version: 1209.3214v1 · doi: 10.48550/arxiv.1209.3214 · pith_short_12: 6MGZAUCEWNII · pith_short_16: 6MGZAUCEWNIIRM2N · pith_short_8: 6MGZAUCE

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/6MGZAUCEWNIIRM2NSRFGFNWXL2 \
  | 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: f30d905044b35088b34d944a62b6d75eb0f960476901401e4cbff03a59f2b627

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2f576e0287613e9e4b2318ab67be7ed4339d64209aaf8ac8665a62331fba98fa",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-09-14T15:04:42Z",
    "title_canon_sha256": "94d3a4405fdeff880619680d6bb3627d16e28a819530d9643114cfc879c502ce"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.3214",
    "kind": "arxiv",
    "version": 1
  }
}