Pith Number

pith:VLYKARY2

pith:2010:VLYKARY2LAJGPWX5WH33YSY5HQ

not attested not anchored not stored refs pending

Upper and lower bounds for normal derivatives of spectral clusters of Dirichlet Laplacian

Xiangjin Xu

arxiv:1004.2517 v4 · 2010-04-14 · math.AP · 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{VLYKARY2LAJGPWX5WH33YSY5HQ}

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	2026-05-18T04:19:53.496401Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aaf0a0471a581267dafdb1f7bc4b1d3c1299958d8048c44c7859ca9dbbd9d337

Aliases

arxiv: 1004.2517 · arxiv_version: 1004.2517v4 · doi: 10.48550/arxiv.1004.2517 · pith_short_12: VLYKARY2LAJG · pith_short_16: VLYKARY2LAJGPWX5 · pith_short_8: VLYKARY2

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/VLYKARY2LAJGPWX5WH33YSY5HQ \
  | 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: aaf0a0471a581267dafdb1f7bc4b1d3c1299958d8048c44c7859ca9dbbd9d337

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dc9f64a90c58597101070dc8ef2015e982ac228a81ae1bbb2e84a9d7020cab1a",
    "cross_cats_sorted": [
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2010-04-14T22:18:08Z",
    "title_canon_sha256": "576639eef3ece53f2c46a72f166c9b023e54c09f70c92aed52464833058f29de"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.2517",
    "kind": "arxiv",
    "version": 4
  }
}