Pith Number

pith:C6M72GWX

pith:2018:C6M72GWXJMS3XVSYJXQYRGXGJT

not attested not anchored not stored refs pending

The L^p-to-L^q boundedness of commutators with applications to the Jacobian operator

Tuomas P. Hyt\"onen

arxiv:1804.11167 v4 · 2018-04-30 · math.CA · math.AP · math.FA

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{C6M72GWXJMS3XVSYJXQYRGXGJT}

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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.

Cited by

1 paper in Pith

Commutators of Hilbert transforms along monomial curves

Receipt and verification

First computed	2026-07-05T03:20:52.359806Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1799fd1ad74b25bbd6584de1889ae64cf9d7e68cbd37895c567d47daf2398a09

Aliases

arxiv: 1804.11167 · arxiv_version: 1804.11167v4 · doi: 10.48550/arxiv.1804.11167 · pith_short_12: C6M72GWXJMS3 · pith_short_16: C6M72GWXJMS3XVSY · pith_short_8: C6M72GWX

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/C6M72GWXJMS3XVSYJXQYRGXGJT \
  | 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: 1799fd1ad74b25bbd6584de1889ae64cf9d7e68cbd37895c567d47daf2398a09

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4133cc9adacff5946e38a596e2b4b3ce6ef53d81a2123af7d59360f686e3adec",
    "cross_cats_sorted": [
      "math.AP",
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2018-04-30T12:59:39Z",
    "title_canon_sha256": "23412d37492b2794803d0aab539cb21d1adea0368297d8e8dec5eae28b4df50b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1804.11167",
    "kind": "arxiv",
    "version": 4
  }
}