Pith Number

pith:VWQDFVJU

pith:2014:VWQDFVJULU42ZCEH2K3G6N4FI4

not attested not anchored not stored refs pending

A lower bound for the sum of the two largest signless Laplacian eigenvalues

Carla Oliveira, Leonardo de Lima

arxiv:1412.0323 v1 · 2014-12-01 · math.SP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VWQDFVJULU42ZCEH2K3G6N4FI4}

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	2026-05-18T02:32:28.081689Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ada032d5345d39ac8887d2b66f378547086bcf60d7ffd422fb96aa07c0ffea32

Aliases

arxiv: 1412.0323 · arxiv_version: 1412.0323v1 · doi: 10.48550/arxiv.1412.0323 · pith_short_12: VWQDFVJULU42 · pith_short_16: VWQDFVJULU42ZCEH · pith_short_8: VWQDFVJU

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/VWQDFVJULU42ZCEH2K3G6N4FI4 \
  | 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: ada032d5345d39ac8887d2b66f378547086bcf60d7ffd422fb96aa07c0ffea32

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c186311f666f197f6c413ac28a421cf6399ca40749e8f3961169892b3099d0be",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2014-12-01T01:23:02Z",
    "title_canon_sha256": "a3d8139c416252dab6f1e8c1eb82fec2aaa309a0af6b7a7716d2d87fe48a0506"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1412.0323",
    "kind": "arxiv",
    "version": 1
  }
}