Pith Number

pith:L4NN345O

pith:2016:L4NN345OYWCYUDT673Q4AFJ4LX

not attested not anchored not stored refs pending

Some upper bounds for the signless Laplacian spectral radius of digraphs

Ligong Wang, Weige Xi

arxiv:1610.07888 v1 · 2016-10-25 · 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{L4NN345OYWCYUDT673Q4AFJ4LX}

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	2026-05-18T01:01:17.287408Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5f1addf3aec5858a0e7efee1c0153c5dc2a1830beb3b85efd3bbc777dd8e6c02

Aliases

arxiv: 1610.07888 · arxiv_version: 1610.07888v1 · doi: 10.48550/arxiv.1610.07888 · pith_short_12: L4NN345OYWCY · pith_short_16: L4NN345OYWCYUDT6 · pith_short_8: L4NN345O

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/L4NN345OYWCYUDT673Q4AFJ4LX \
  | 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: 5f1addf3aec5858a0e7efee1c0153c5dc2a1830beb3b85efd3bbc777dd8e6c02

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8e1356ca038f9abefe95691e69e1f8315c3f5d1ec881028bfbace8cc3fb360aa",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-10-25T14:20:30Z",
    "title_canon_sha256": "bf18475a15a6db0a1f7c2385c5ad5c4a88dcb493555e245dc1ed008ae8c4c75b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.07888",
    "kind": "arxiv",
    "version": 1
  }
}