Pith Number

pith:N2T7O7CB

pith:2026:N2T7O7CBHSHLUJLPCVNXNUA2PX

not attested not anchored not stored refs pending

On Vu's restricted box estimate in Waring's problem

Christian T\'afula

The restricted box estimate in Waring's problem holds with power-saving error for s at least k squared minus k plus order square root of k, improving on the prior exponential threshold.

arxiv:2605.15067 v1 · 2026-05-14 · math.NT

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\pithnumber{N2T7O7CBHSHLUJLPCVNXNUA2PX}

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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

We show that one may take s ≥ k² - k + O(√k).

C2weakest assumption

The minor-arc estimates or box-restriction handling in the circle method continue to deliver a power-saving error once s reaches the new quadratic threshold; this is not verified from the abstract alone.

C3one line summary

The restricted box estimate in Waring's problem holds with power-saving error for s at least k squared minus k plus order square root of k, improving on the prior exponential threshold.

Receipt and verification

First computed	2026-05-17T21:40:26.054547Z
Last reissued	2026-05-17T21:57:19.355495Z
Builder	pith-number-builder-2026-05-17-v1
Signature	unsigned_v0
Schema	pith-number/v1.0

Canonical hash

6ea7f77c413c8eba256f155b76d01a7dd560374dedbe0e5e43f2519bb23ff7fb

Aliases

arxiv: 2605.15067 · arxiv_version: 2605.15067v1 · pith_short_12: N2T7O7CBHSHL · pith_short_16: N2T7O7CBHSHLUJLP · pith_short_8: N2T7O7CB

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/N2T7O7CBHSHLUJLPCVNXNUA2PX \
  | 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: 6ea7f77c413c8eba256f155b76d01a7dd560374dedbe0e5e43f2519bb23ff7fb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "637879a39ffc08d81760414e8d13cd0a73890e228adc95eb8b4bb68611e88108",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-05-14T16:57:00Z",
    "title_canon_sha256": "7e398b6090f3542d58485a651e196b37c7b098c3870d5893c0d901e14e132b77"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15067",
    "kind": "arxiv",
    "version": 1
  }
}