Pith Number

pith:HIBQPKWS

pith:2018:HIBQPKWS7RWYM6OZCSNWG7XPY5

not attested not anchored not stored refs pending

Lower bounds for Laplacian spread and relations with invariant parameters revisited

Enide Andrade, Jonnathan Rodr\'iguez, Maria Aguieiras A. de Freitas, Mar\'ia Robbiano

arxiv:1805.12250 v1 · 2018-05-30 · math.SP · 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{HIBQPKWS7RWYM6OZCSNWG7XPY5}

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	2026-05-18T00:14:30.937168Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3a0307aad2fc6d8679d9149b637eefc75790ac65a89251b31b4d02ec7dd54740

Aliases

arxiv: 1805.12250 · arxiv_version: 1805.12250v1 · doi: 10.48550/arxiv.1805.12250 · pith_short_12: HIBQPKWS7RWY · pith_short_16: HIBQPKWS7RWYM6OZ · pith_short_8: HIBQPKWS

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/HIBQPKWS7RWYM6OZCSNWG7XPY5 \
  | 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: 3a0307aad2fc6d8679d9149b637eefc75790ac65a89251b31b4d02ec7dd54740

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b513f357b7dc11539ea2d619032855c876130f7a463ab1131550aa848d3d81a6",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2018-05-30T22:34:49Z",
    "title_canon_sha256": "6354c313950b75fe9840b35adc3b3c92e77c83d013ea05cc1f4484abeb9c14fb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1805.12250",
    "kind": "arxiv",
    "version": 1
  }
}