Pith Number

pith:VPMOYRZM

pith:2015:VPMOYRZM2PO4KXMVSQ6KY6SAIP

not attested not anchored not stored refs pending

Spectral inequality and resolvent estimate for the bi-Laplace operator

IUF), J\'er\^ome Le Rousseau (LAGA, Luc Robbiano (LMV)

arxiv:1509.02098 v5 · 2015-09-07 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VPMOYRZM2PO4KXMVSQ6KY6SAIP}

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	2026-05-18T00:29:15.812676Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

abd8ec472cd3ddc55d95943cac7a4043d7790eac71949062f12bc15a513abe0e

Aliases

arxiv: 1509.02098 · arxiv_version: 1509.02098v5 · doi: 10.48550/arxiv.1509.02098 · pith_short_12: VPMOYRZM2PO4 · pith_short_16: VPMOYRZM2PO4KXMV · pith_short_8: VPMOYRZM

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/VPMOYRZM2PO4KXMVSQ6KY6SAIP \
  | 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: abd8ec472cd3ddc55d95943cac7a4043d7790eac71949062f12bc15a513abe0e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2b720b4b2f9ba48c91f25be70c46a56302602e9985df9ab3340b354174ac4e93",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-09-07T15:55:42Z",
    "title_canon_sha256": "c73a4fa81ca8121dc714e0897bda11109acf1a22726a2b2c409f6f466a2ba6db"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.02098",
    "kind": "arxiv",
    "version": 5
  }
}