Pith Number

pith:5QXNWBAE

pith:2025:5QXNWBAEFEFIHNPCI33SLVYLKV

not attested not anchored not stored refs pending

The Fourier extension conjecture for the paraboloid

Cristian Rios, Eric T. Sawyer

The Fourier extension conjecture for the paraboloid holds in every dimension greater than 2.

arxiv:2512.24990 v7 · 2025-12-31 · math.CA

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\usepackage{pith}
\pithnumber{5QXNWBAEFEFIHNPCI33SLVYLKV}

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2 Internet Archive

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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

We give a proof of Fourier extension conjecture on the paraboloid in all dimensions bigger than 2 that begins with a decomposition suggested in Sawyer [Saw8] of writing a smooth Alpert projection as a sum of pieces whose Fourier extensions are localized.

C2weakest assumption

The bilinear inequality, when taken over smooth Alpert projections, only requires an averaging over grids of functions mollified by discrete multipliers which converts a difficult exponential sum into an oscillatory integral with periodic amplitude.

C3one line summary

A proof is given that the Fourier extension conjecture holds for the paraboloid in dimensions d greater than 2.

Cited by

1 paper in Pith

A discussion of two new proofs of Fefferman's Fourier extension theorem in the plane

Receipt and verification

First computed	2026-05-20T00:04:20.160903Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ec2edb0404290a83b5e246f725d70b5574a95136e5f71c38f11d26ec24691dfd

Aliases

arxiv: 2512.24990 · arxiv_version: 2512.24990v7 · doi: 10.48550/arxiv.2512.24990 · pith_short_12: 5QXNWBAEFEFI · pith_short_16: 5QXNWBAEFEFIHNPC · pith_short_8: 5QXNWBAE

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/5QXNWBAEFEFIHNPCI33SLVYLKV \
  | 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: ec2edb0404290a83b5e246f725d70b5574a95136e5f71c38f11d26ec24691dfd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "710144df69bd20c93712f78bb7525b6951aca69e80d83bd50773a359dd037279",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2025-12-31T17:36:38Z",
    "title_canon_sha256": "66e783cfeffdc8ddc60a97dea4b04b23ac16dc29d591fb1f39f3e6ac22ce98c4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2512.24990",
    "kind": "arxiv",
    "version": 7
  }
}