Pith Number

pith:6IAQT67M

pith:2019:6IAQT67MISJNO5GSWU5V5HQQDD

not attested not anchored not stored refs pending

Morrey spaces for Schr\"odinger operators with nonnegative potentials, fractional integral operators and the Adams inequality on the Heisenberg groups

Hua Wang

arxiv:1907.03573 v1 · 2019-07-04 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6IAQT67MISJNO5GSWU5V5HQQDD}

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	2026-05-17T23:41:14.292002Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f20109fbec4492d774d2b53b5e9e1018cf3995b9232f782bc4983948c64e90c2

Aliases

arxiv: 1907.03573 · arxiv_version: 1907.03573v1 · doi: 10.48550/arxiv.1907.03573 · pith_short_12: 6IAQT67MISJN · pith_short_16: 6IAQT67MISJNO5GS · pith_short_8: 6IAQT67M

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/6IAQT67MISJNO5GSWU5V5HQQDD \
  | 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: f20109fbec4492d774d2b53b5e9e1018cf3995b9232f782bc4983948c64e90c2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c3fd83438ff28fec408999ea05e59866480c3fd6013c9bdebdf06f751083ab9e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2019-07-04T03:51:40Z",
    "title_canon_sha256": "4dbf69caaf96743be6cde7e200504bcbe12fe074c50447597179c1444304b75e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1907.03573",
    "kind": "arxiv",
    "version": 1
  }
}