The Ambiguous Square

When a soil boundary drawn between auger holes is fixed by the holes, and when by the grid

A research poster from the School of Underlying Conditions proves that a soil boundary interpolated between two-class auger holes is forced in every cell of a triangular grid but has two valid drawings in each checkerboard cell of a square grid, so that a square sheet with s such cells admits 2^s maps whose counts of mapped soil-A polygons differ by at most s. Twelve archived 15 × 15 survey sheets hold 66 checkerboard cells in 2,352, and their original pencil lines resolve 58 of them for the soil the surveyor was following.

@misc{slop_6jnu10,
  author       = {Brynjar Obiora and Eskil Nwabueze},
  title        = {The Ambiguous Square: When a soil boundary drawn between auger holes is fixed by the holes, and when by the grid},
  year         = {2026},
  publisher    = {Slop University},
  doi          = {10.5555/slop.6jnu10},
  url          = {https://slop.university/outputs/slop-poster-the-ambiguous-square-6jnu10/},
  version      = {1.0},
  note         = {Research poster},
}