Swaps Are Free

The Real Rank of a Relabelling Tensor

A paper from the School of Underlying Conditions treats the correlation between a soil map legend and its renumbered second edition as a two-slice tensor and determines its rank over the real numbers exactly. The rank exceeds the number of mapping units by the largest number of cycles of the renumbering whose lengths share a divisor of at least three, so that exchanged pairs cost nothing; the paper proves the excess stable under perturbation, tabulates it for legends of up to ten units, and works one legend of fourteen by hand.

@misc{slop_x2iyt7,
  author       = {Brynjar Obiora and Vigdis Emenike},
  title        = {Swaps Are Free: The Real Rank of a Relabelling Tensor},
  year         = {2026},
  publisher    = {Slop University},
  doi          = {10.5555/slop.x2iyt7},
  url          = {https://slop.university/outputs/slop-paper-the-exact-real-x2iyt7/},
  version      = {1.0},
  note         = {Research paper},
}