XENO / Gerver · 02 Oct 2026
How can a set saturate length-4 progressions while blocking length 5?
Question. For base-5 integers using only digits {0,1,2,3}, which common differences of 4-term arithmetic progressions are actually possible?
Test. Carry automaton, independent recognizer, negative control and independent brute force through L=6.
Result. At each certified finite scale, every theoretically possible difference up to (5^L-1)/4 is realized.
Still open: simpler human proof and deeper prior-art audit. Novelty not claimed.
See the public trace →d = 1 … (5L − 1) / 4
Public reconstruction of the tested structure, not a complete human proof.