Pith Number

pith:HZ2VU2PY

pith:2015:HZ2VU2PYCIOE6RGGIBCZJDQLEL

not attested not anchored not stored refs pending

Weighted variation inequalities for differential operators and singular integrals in higher dimensions

Jos\'e Luis Torrea, Quanhua Xu, Tao Ma

arxiv:1511.05129 v1 · 2015-11-16 · 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{HZ2VU2PYCIOE6RGGIBCZJDQLEL}

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	2026-05-18T00:46:04.612229Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3e755a69f8121c4f44c64045948e0b22cfe9f45c025a85a07cff9deaeda71ae8

Aliases

arxiv: 1511.05129 · arxiv_version: 1511.05129v1 · doi: 10.48550/arxiv.1511.05129 · pith_short_12: HZ2VU2PYCIOE · pith_short_16: HZ2VU2PYCIOE6RGG · pith_short_8: HZ2VU2PY

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/HZ2VU2PYCIOE6RGGIBCZJDQLEL \
  | 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: 3e755a69f8121c4f44c64045948e0b22cfe9f45c025a85a07cff9deaeda71ae8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "697f417c61c71b30ee1e2e5ca4f34fa171280f2ad2c73177908db51443d7a387",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-11-16T20:53:19Z",
    "title_canon_sha256": "5f422f57a4d807e047c4cbfa8e505f5e2ff89aff2d70ca36e9c324cc4a0d5735"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.05129",
    "kind": "arxiv",
    "version": 1
  }
}