Pith Number

pith:FSPEDIOK

pith:2019:FSPEDIOKMFOIYP3NSMD2UE4JLG

not attested not anchored not stored refs pending

Morrey spaces for Schr\"odinger operators with certain nonnegative potentials, Littlewood-Paley and Lusin functions on the Heisenberg groups

Hua Wang

arxiv:1907.09398 v1 · 2019-07-16 · math.CA · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FSPEDIOKMFOIYP3NSMD2UE4JLG}

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	2026-05-17T23:39:59.313751Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2c9e41a1ca615c8c3f6d9307aa1389599ee71c80dd4308afc9df2e4a25120184

Aliases

arxiv: 1907.09398 · arxiv_version: 1907.09398v1 · doi: 10.48550/arxiv.1907.09398 · pith_short_12: FSPEDIOKMFOI · pith_short_16: FSPEDIOKMFOIYP3N · pith_short_8: FSPEDIOK

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/FSPEDIOKMFOIYP3NSMD2UE4JLG \
  | 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: 2c9e41a1ca615c8c3f6d9307aa1389599ee71c80dd4308afc9df2e4a25120184

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d1158ba0904145301d392478580f180610563fd323cc15e36c3ba791da9cce7c",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2019-07-16T05:26:02Z",
    "title_canon_sha256": "198c9abdff9dd0d1b3b9737477b6268cc867e700b8cbb2d916c8af56d1adedd6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1907.09398",
    "kind": "arxiv",
    "version": 1
  }
}