Pith Number

pith:TI5JCMEH

pith:2026:TI5JCMEH7EGPLDJQVVS6ZIKW2V

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$\ell^{p}$ improving estimates for multilinear forms motivated by distance graphs

Eyvindur Palsson, Jennifer Smucker

ℓ^p improving estimates for distance graph forms depend only on vertex count in many cases

arxiv:2605.12439 v2 · 2026-05-12 · math.CA · math.NT

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4 Citations open

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Claims

C1strongest claim

We obtain ℓ^p improving estimates for the collection of forms based on all graphs with 2, 3, and 4 vertices, as well as chains and simplexes of any size in Z^d. Surprisingly, certain mapping properties only seem to depend on the number of vertices in the graph, not its structure.

C2weakest assumption

The distance graphs are defined in Z^d with the standard Euclidean distances, and the multilinear forms satisfy the usual translation-invariance and Fourier multiplier properties assumed in prior spherical averaging work.

C3one line summary

ℓ^p improving estimates are derived for multilinear forms from all distance graphs with 2, 3, or 4 vertices and from chains and simplexes of arbitrary size in Z^d, with some bounds depending only on vertex count rather than graph structure.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-06-19T16:12:54.894628Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9a3a913087f90cf58d30ad65eca156d547309771d70a9e607a54b5edc7ace3f8

Aliases

arxiv: 2605.12439 · arxiv_version: 2605.12439v2 · doi: 10.48550/arxiv.2605.12439 · pith_short_12: TI5JCMEH7EGP · pith_short_16: TI5JCMEH7EGPLDJQ · pith_short_8: TI5JCMEH

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/TI5JCMEH7EGPLDJQVVS6ZIKW2V \
  | 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: 9a3a913087f90cf58d30ad65eca156d547309771d70a9e607a54b5edc7ace3f8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "15fb28d8772bf66d2e56ebea78e3211e4490108a67d41b9f3905f4c9dbbf60a0",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2026-05-12T17:34:40Z",
    "title_canon_sha256": "19b7544bfcdd2f9a73589c294b9a66afd5246cfbb61def0c992ced2445b67cf3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12439",
    "kind": "arxiv",
    "version": 2
  }
}