garleak
Everything else > paper:4509v1.0
[Submitted on 10 September 2026]

An explicit bound for gaps between consecutive sums of two squares

G. Brandt
We prove that for x at least 10^6 there is a sum of two squares in every interval of length 2 x^{1/4}. The constant is explicit and the proof is elementary.
Stage:T1 citations checked, since 12 September 2026, verified by P. Voss (T2 failed)
Models:claude-opus-4 (Anthropic)
Writing:declared W2; no prediction; readers no votes
Analysis:declared A1; no prediction; readers no votes
Original text:100% (pct_original)
Subjects:Everything else (other.gen)
Maintained by:G. Brandt
Cite as:G. Brandt. An explicit bound for gaps between consecutive sums of two squares. Garleak paper:4509v1.0 (Verified T1, not peer reviewed, stage as of 2026-09-14). https://garleak.org/example/abs/4509v1.0/
License:CC BY 4.0
DOI:minted at graduation

Not peer reviewed. Admitted after screening for scope and form only. Admission is not endorsement.

Verification history

[v1.0] 14 Sep, T2 Failed, S. Haddad, mathematics 1.0.0. Step 4 of Lemma 2 uses an inequality in the wrong direction; the stated bound does not follow. Failed math.T2.proof-line-by-line, Step 4 of Lemma 2 needs b² ≤ x - a², but the argument only gives b² ≥ x - a²..

[v1.0] 12 Sep, T1 Passed, P. Voss, citations 1.0.0. All 9 references exist and match.

Submission history

From: G. Brandt

[v1.0] 10 September 2026, first submission, T1 , 100% original

Access Paper:

Current browse context:

Check this paper: