Pith Number

pith:KGL7N46B

pith:2011:KGL7N46BE6CHCIQUDDKVFSBPIN

not attested not anchored not stored refs pending

Lower Bounds for Laplacian and Fractional Laplacian Eigenvalues

Guoxin Wei, He-Jun Sun, Lingzhong Zeng

arxiv:1112.4571 v2 · 2011-12-20 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KGL7N46BE6CHCIQUDDKVFSBPIN}

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	2026-05-18T02:51:25.647625Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5197f6f3c1278471221418d552c82f43421b93d76d533ee681814efdf6642a16

Aliases

arxiv: 1112.4571 · arxiv_version: 1112.4571v2 · doi: 10.48550/arxiv.1112.4571 · pith_short_12: KGL7N46BE6CH · pith_short_16: KGL7N46BE6CHCIQU · pith_short_8: KGL7N46B

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/KGL7N46BE6CHCIQUDDKVFSBPIN \
  | 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: 5197f6f3c1278471221418d552c82f43421b93d76d533ee681814efdf6642a16

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dcfd31ec50819e15542cc43f0492efc6a56442f18a2081524075a8cc413d7171",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2011-12-20T04:56:25Z",
    "title_canon_sha256": "1a50be70a472c61c0ad232254bcf024b9ae2bdb96adf904cd3623fb4524019b7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.4571",
    "kind": "arxiv",
    "version": 2
  }
}