Pith Number

pith:64DS4FDP

pith:2025:64DS4FDPVRHZ4IBQTGAKZB5TIO

not attested not anchored not stored refs pending

Improved Berezin-Li-Yau inequality and Kr\"oger inequality and consequences

Fanghua Lin, Renjin Jiang, Zaihui Gan

arxiv:2507.20330 v2 · 2025-07-27 · math.SP · math-ph · math.AP · math.CA · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{64DS4FDPVRHZ4IBQTGAKZB5TIO}

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.

Cited by

1 paper in Pith

Improved lower bounds for Dirichlet eigenvalues of the Laplacian and poly-Laplacian on bounded Euclidean domains

Receipt and verification

First computed	2026-07-05T11:48:27.823794Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f7072e146fac4f9e20309980ac87b343be43c23f56e4b821c66449f11d9e3f46

Aliases

arxiv: 2507.20330 · arxiv_version: 2507.20330v2 · doi: 10.48550/arxiv.2507.20330 · pith_short_12: 64DS4FDPVRHZ · pith_short_16: 64DS4FDPVRHZ4IBQ · pith_short_8: 64DS4FDP

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/64DS4FDPVRHZ4IBQTGAKZB5TIO \
  | 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: f7072e146fac4f9e20309980ac87b343be43c23f56e4b821c66449f11d9e3f46

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "29c835d9970d9c3e6a1d91ede2ae28bf3e2b73fae86881828cf59998d50996e9",
    "cross_cats_sorted": [
      "math-ph",
      "math.AP",
      "math.CA",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2025-07-27T15:48:39Z",
    "title_canon_sha256": "f08ffb3a62d7dd4d6d40427e839b446f8fc3d7d5a9994439f21e2b37e95d7613"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.20330",
    "kind": "arxiv",
    "version": 2
  }
}