BASE + 1 · which witness is unforgeable

A register of base N uses symbols 0…N−1; the witness sits at the +1 exterior position. The witness is unforgeable iff N+1 is prime (then Z/(N+1)ℤ is a field — no zero-divisors, so no two register elements can multiply to a counterfeit null). The grid is the mod-(N+1) multiplication table; red cells are products that hit 0 from non-zero inputs — forged nulls. A clean field has none. This is Lemma 257 §4, generalized.