Pith Number

pith:H5TK4Q6U

pith:2013:H5TK4Q6U2ME7EFFCWTSZUA37XJ

not attested not anchored not stored refs pending

An Interlacing Approach for Bounding the Sum of Laplacian Eigenvalues of Graphs

A. Abiad, G. Perarnau, M.A. Fiol, W.H. Haemers

arxiv:1307.4670 v2 · 2013-07-17 · 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{H5TK4Q6U2ME7EFFCWTSZUA37XJ}

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	2026-05-18T03:06:44.461805Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3f66ae43d4d309f214a2b4e59a037fba5d516161379ce75f4714d23866a3ef41

Aliases

arxiv: 1307.4670 · arxiv_version: 1307.4670v2 · doi: 10.48550/arxiv.1307.4670 · pith_short_12: H5TK4Q6U2ME7 · pith_short_16: H5TK4Q6U2ME7EFFC · pith_short_8: H5TK4Q6U

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/H5TK4Q6U2ME7EFFCWTSZUA37XJ \
  | 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: 3f66ae43d4d309f214a2b4e59a037fba5d516161379ce75f4714d23866a3ef41

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fd31602d4c20d90a6ca1878725325e109b273a3789dcf9084752ae98d09fdb91",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2013-07-17T15:19:33Z",
    "title_canon_sha256": "23ea756c3f3f03c7e792bd4a53f8a6896faca88c7b0870176736a413c6da0c1a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.4670",
    "kind": "arxiv",
    "version": 2
  }
}