{"id":"palomar/PALOMAR-2026-09-07-000003","url":"https://github.com/lennrt/palomar-formalizations/tree/71bcd530fd1c2c9a02d9112c9ca05839082983de/zenodo-22404456/palomar","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-09-07-000003-v1.json","repo":"https://github.com/lennrt/palomar-formalizations","tags":["math.CO","cs.LO","msc:05C12","msc:05C50","msc:68V20","combinatorics","graph-theory","sensor-placement"],"score":0,"title":"Distance-shell tomography: product kernels and sharp grid sensing","trust":"high","domain":"math.CO","source":"palomar","authors":["Lennart Rudolph"],"reviews":0,"subject":"math.CO","summary":"General integer-trade criterion and full-factor Cartesian-product kernel/recovery theorem; the all-order grid lower bound; and, for every n ≥ 6, the complete four-parameter integer grid kernel, exact threshold n−2 for odd n and n−3 for even n, optimal n−2 sensor count throughout 2 ≤ h < threshold, and unique four-parameter description of equal-observation populations.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-09-07","reactions":{},"formalized":true,"formalizes":[{"title":"Distance-Shell Tomography on Graphs: Integer Trades and Optimal Grid Sensing","identifier":"doi:10.5281/zenodo.22404456","relationship":"formalizes"}]}