Pith Number

pith:KYXQXKEG

pith:2018:KYXQXKEGDERU32CHMCWSYSJYFX

not attested not anchored not stored refs pending

Sharp Hardy-Leray and Rellich-Leray inequalities for curl-free vector fields

Futoshi Takahashi, Naoki Hamamoto

arxiv:1808.09614 v1 · 2018-08-29 · 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{KYXQXKEGDERU32CHMCWSYSJYFX}

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	2026-05-18T00:06:55.010107Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

562f0ba88619234de84760ad2c49382dc7cf6cfe594a68b8f024df8a6607b761

Aliases

arxiv: 1808.09614 · arxiv_version: 1808.09614v1 · doi: 10.48550/arxiv.1808.09614 · pith_short_12: KYXQXKEGDERU · pith_short_16: KYXQXKEGDERU32CH · pith_short_8: KYXQXKEG

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/KYXQXKEGDERU32CHMCWSYSJYFX \
  | 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: 562f0ba88619234de84760ad2c49382dc7cf6cfe594a68b8f024df8a6607b761

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ede9ede62ae0fc8fb36cdd1b9e418c1cd5a1aea8ccd74e9d52d9b15f76592b13",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2018-08-29T02:53:26Z",
    "title_canon_sha256": "37f551d22c130996a09e73c5b09911c813ed9dbaa2aec07508419d782f172e51"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1808.09614",
    "kind": "arxiv",
    "version": 1
  }
}