bibkey: pemmasani2026blackouts authors: Arjun Pemmasani year: 2026 title: “Blackouts Preserving Rectangle Identifiability on Grid Points: A partial solution to Problem 001 of Kagey’s Open Problem Collection” doi: null url: https://github.com/apemm/Kagey-Problems/blob/b9567e4dc1c7cf1e5034569571a9479b1b83dc57/kagey-problems/problem001/paper/main.tex claim: “The Three-Row conjecture asserts that the maximum valid blackout in a three-row grid with m columns is m+2 for every m>=3, where every lattice rectangle, including tilted rectangles, must remain identifiable from its visible corner set.” strata_touched:

• D5/S0/FiniteGeometry/RectangleIdentifiability/ThreeRowBlackoutMaximum license: “citation-only; no license located for upstream Lean code, which is not copied; OEIS governed by https://oeis.org/LICENSE” triage: anchor

The Three-Row blackout conjecture

Pemmasani’s preliminary note studies Peter Kagey’s Problem 001: delete as many grid points as possible while every rectangle remains identifiable from its visible vertices. The note’s section “Conventions and the presentation map” fixes unordered corner sets, all nondegenerate Euclidean rectangles, including squares and tilted rectangles, and permits the empty presentation. Its “Refuted and live conjectures” section, label conj:threerow, gives the exact target:

T(3,m) = m+2 for all m >= 3.

The corresponding COMMENTS line in OEIS A397315 repeats this conjecture. The entry is by Arjun Pemmasani, September 2, 2026. Its additional claim of verification through width ten is a source claim, not proof evidence used by the formal theorem.

The note’s difference-set/hitting-set criterion and two-row Strip Theorem are known background. In particular, for at least three columns, two columns cannot both have the same two rows entirely blacked out: comparing each with a third column produces equal presentations of different rectangles. The three-row proof credits this obstruction and proves its needed finite-set form locally. The exact three-row upper bound also uses a collision across different row pairs. The two-row theorem by itself does not give the full three-row target.

Verified locator

• https://github.com/apemm/Kagey-Problems/blob/b9567e4dc1c7cf1e5034569571a9479b1b83dc57/kagey-problems/problem001/paper/main.tex
• Preliminary-note Git revision: b9567e4dc1c7cf1e5034569571a9479b1b83dc57, dated 2026-09-09T06:25:25Z. The complete 18,960-byte TeX has SHA-256 a5768b49f620c70e681cacf1ddf12a6771583e1247656ea62f5c08a921892074. The document uses a generated current-date command, so the citation does not infer an independently printed publication date.
• https://oeis.org/A397315 and its complete official text at https://oeis.org/search?q=id:A397315&fmt=text, revision 38, September 12, 2026, 22:10:01; 4,810 bytes, SHA-256 14370cb2594daee56b3efcb29387b2ede84684ca73ea32f0e579ef4982d84983.
• Original general question: https://peterkagey.com/problems/001/. This older problem is not described as a newly posed question.

The complete note and OEIS entry were read. The note’s blanket numerical cross-verification wording conflicts with some “engine only” labels; its older four-row overview and later table also differ. Its five-by-five diagram legend has a polarity conflict with the OEIS marked positions. None of these numerical tables or diagrams is used as a certified witness. The exact named Three-Row conjecture agrees between the inspected sources.

The upstream Lean file uses different pins, and no license was located. No upstream Lean source is copied or imported. The local proof uses only pinned Mathlib and credits known mathematical background. Citation of this source and bounded searches do not establish global priority or exhaustive absence of a prior settlement.