Pith Number

pith:VW3B6WEQ

pith:2026:VW3B6WEQLACG3GWE74AUXNYMIM

not attested not anchored not stored refs pending

A sharp point-sphere incidence bound for $(u, s)$-Salem sets

Dung The Tran, Steven Senger

For (4,s)-Salem point sets P in F_q^d with |P| much smaller than q to the power d over 4s, the deviation of point-sphere incidences from the average is bounded by q to the d/4 times |P| to the 1-s times |S| to the 3/4.

arxiv:2601.07105 v4 · 2026-01-12 · math.CO

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VW3B6WEQLACG3GWE74AUXNYMIM}

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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.

Claims

C1strongest claim

If P subset F_q^d is a (4,s)-Salem set with s in (1/4, 1/2] and |P| << q^{d/(4s)}, then for any finite family S of spheres, |I(P,S) - |P||S|/q| << q^{d/4} |P|^{1-s} |S|^{3/4}.

C2weakest assumption

The point set P satisfies the (4,s)-Salem condition quantifying its fourth-order additive energy, together with the size restriction |P| << q^{d/(4s)} that enables the lifting argument to succeed.

C3one line summary

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-06-09T01:05:12.583260Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

adb61f589058046d9ac4ff014bb70c4325bea4c95dad1da51a78fd456f6d4640

Aliases

arxiv: 2601.07105 · arxiv_version: 2601.07105v4 · doi: 10.48550/arxiv.2601.07105 · pith_short_12: VW3B6WEQLACG · pith_short_16: VW3B6WEQLACG3GWE · pith_short_8: VW3B6WEQ

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/VW3B6WEQLACG3GWE74AUXNYMIM \
  | 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: adb61f589058046d9ac4ff014bb70c4325bea4c95dad1da51a78fd456f6d4640

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e2697dfb259f785fed7f6e06ba54c3bf3ff8d908eca8dc5c0434f3b7338fc83f",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-01-12T00:05:47Z",
    "title_canon_sha256": "15d71f4b7c14ff779e6e3f4c1844dc903e777b458256b0dfd33dad47e7ce87b4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2601.07105",
    "kind": "arxiv",
    "version": 4
  }
}