Pith Number

pith:BI3MZBRT

pith:2026:BI3MZBRTPE3FPZSDRYMU5Y5DRJ

not attested not anchored not stored refs pending

A unified geometric perspective on Zygmund's conjecture for maximal functions associated with vector fields

Lingxiao Zhang

Refining Bourgain's argument identifies a weaker condition for boundedness of maximal functions associated with planar vector fields.

arxiv:2605.04394 v2 · 2026-05-06 · math.CA

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\usepackage{pith}
\pithnumber{BI3MZBRTPE3FPZSDRYMU5Y5DRJ}

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Record completeness

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4 Citations open

5 Replications open

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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.

Claims

C1strongest claim

By refining Bourgain's argument for maximal functions associated with planar vector fields, we identify a condition ensuring boundedness that is weaker than previously known.

C2weakest assumption

The refinement assumes the vector fields satisfy the (unspecified in abstract) weaker condition identified by the refined argument; without the full paper the exact form and verification of this condition cannot be assessed.

C3one line summary

Refines Bourgain's method to establish boundedness of maximal functions under a weaker condition than previously known, strengthening an implicit Lacey-Li result.

Receipt and verification

First computed	2026-05-26T01:02:34.888869Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0a36cc8633793657e6438e194ee3a38a79b69c5ab914160d3b68496a3b68d36d

Aliases

arxiv: 2605.04394 · arxiv_version: 2605.04394v2 · doi: 10.48550/arxiv.2605.04394 · pith_short_12: BI3MZBRTPE3F · pith_short_16: BI3MZBRTPE3FPZSD · pith_short_8: BI3MZBRT

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/BI3MZBRTPE3FPZSDRYMU5Y5DRJ \
  | 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: 0a36cc8633793657e6438e194ee3a38a79b69c5ab914160d3b68496a3b68d36d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3f9968ee95dd7b45f43536c32a71205e08a26dc4851cf0504ee7683d7f3536c5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2026-05-06T01:34:44Z",
    "title_canon_sha256": "44f4e2d3e536623dd46544a48b98aef1e46a237eb3c03e68a7810ed5d77ee208"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.04394",
    "kind": "arxiv",
    "version": 2
  }
}