{"id":"palomar/PALOMAR-2026-10-08-000004","url":"https://github.com/egor-bakaev/planks-lean/tree/b2fab1d9af2fe6ca3ef93a167fea9ba6a83b671a","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-08-000004-v1.json","repo":"https://github.com/egor-bakaev/planks-lean","tags":["math.MG","math.CO","msc:52C10","msc:52A10","msc:52A38","discrete-geometry","covering","lean-formalization"],"score":0,"title":"Area stability of planar plank covers and Bezdek's annulus theorem","trust":"high","domain":"math.MG","source":"palomar","authors":["Arseniy Akopyan"],"reviews":0,"subject":"math.MG","summary":"A complete Lean 4 formalization of Bezdek's annulus theorem and the quantitative area stability of planar plank covers based on the paper \"Area stability of plank covers\" by Egor Bakaev and Amir Yehudayoff (arXiv:2609.30409). The formalization proves that there exists an explicit positive radius r > 0 such that if finitely many planar planks cover the closed annulus r <= ||x|| <= 1, their total width is at least 2. The core theorem established is the quantitative overlap theorem, which bounds the excess overlap cost on the unit disk from below by a positive constant times the hole area…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-08","reactions":{},"formalized":true,"formalizes":[{"title":"Area stability of plank covers","identifier":"arXiv:2609.30409","relationship":"formalizes"}]}