Pith Number

pith:VLAEP4Y4

pith:2011:VLAEP4Y4YNXBHHQPR6FAXY2OJZ

not attested not anchored not stored refs pending

Bounds for eigenvalue ratios of the Laplacian

Qing-Ming Cheng, Xuerong Qi

arxiv:1104.5298 v2 · 2011-04-28 · 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{VLAEP4Y4YNXBHHQPR6FAXY2OJZ}

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	2026-05-18T04:20:23.053282Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aac047f31cc36e139e0f8f8a0be34e4e608b5ed1eee7166f2e410b9e1182b572

Aliases

arxiv: 1104.5298 · arxiv_version: 1104.5298v2 · doi: 10.48550/arxiv.1104.5298 · pith_short_12: VLAEP4Y4YNXB · pith_short_16: VLAEP4Y4YNXBHHQP · pith_short_8: VLAEP4Y4

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/VLAEP4Y4YNXBHHQPR6FAXY2OJZ \
  | 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: aac047f31cc36e139e0f8f8a0be34e4e608b5ed1eee7166f2e410b9e1182b572

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7532cdc0019dbeadc8cf7b93880dba75cc4704252b8d5582b9dd63fb77e42798",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2011-04-28T05:25:55Z",
    "title_canon_sha256": "f91bc048365d509f23f46d75755eb5da3aa394f9999428d44ee5eddabb7ef2e0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1104.5298",
    "kind": "arxiv",
    "version": 2
  }
}