Pith Number

pith:DYTNPZZQ

pith:2017:DYTNPZZQG7QZDKGMH2CAD7FTK5

not attested not anchored not stored refs pending

Mixed weak estimates of Sawyer type for commutators of singular integrals and related operators

Fabio Berra, Gladis Pradolini, Marilina Carena

arxiv:1704.04953 v1 · 2017-04-17 · 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{DYTNPZZQG7QZDKGMH2CAD7FTK5}

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	2026-05-18T00:46:17.379184Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1e26d7e73037e191a8cc3e8401fcb3575e990a5a7984b9c73279bf5e575c6dfa

Aliases

arxiv: 1704.04953 · arxiv_version: 1704.04953v1 · doi: 10.48550/arxiv.1704.04953 · pith_short_12: DYTNPZZQG7QZ · pith_short_16: DYTNPZZQG7QZDKGM · pith_short_8: DYTNPZZQ

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/DYTNPZZQG7QZDKGMH2CAD7FTK5 \
  | 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: 1e26d7e73037e191a8cc3e8401fcb3575e990a5a7984b9c73279bf5e575c6dfa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "25dc73b2db033f42e84c672d8c9f355b7273cb1bd53f2f167391683e2c0abb21",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2017-04-17T13:10:57Z",
    "title_canon_sha256": "a322b2a3a17ccb8c8ff80706bd71271af3e6e66ab1f497c440f0b819a484158c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1704.04953",
    "kind": "arxiv",
    "version": 1
  }
}