The theorem appears as a spectral scroll written in bone-white ink that glows with amber light. After each round, the calculations rewrite themselves, updating the bearer's standing in the Deadlands' mathematical hierarchy. The scroll is cold to the touch and cannot be destroyed by conventional means. When displayed, other competitors can sense the precise calculations written upon it, recognizing the bearer as one who has proven their worth through the frontier's deadly equations.

The Tumblebone Theorem serves as the Deadlands' system of record - it calculates who survives and who falls, proving mathematically that the strong deserve remembrance while the weak deserve oblivion. It is the fundamental law that transforms the culling from random fate into inevitable mathematical certainty.