A Matrix Realization of the Chinese Remainder Theorem on the 6k ±1 Candidate Axis

The ordered 6k ±1 candidate axis A6 = {n ≥5 : n ≡±1 (mod 6)} can be used as the horizontal coordinate of a factor-incidence matrix. Its vertical rows correspond to prime factors p ≥5; an entry at position (p, n) means p |n. This note shows that, together with its numerical candidate axis, the matrix admits a natural extension to residue coordinates. On composite candidate columns, a factor hit p |n is simultaneously a visible zero of the residue class n mod p; the primary zero n = p is carried separately by the prime row in the sparse visualization used here. Starting from a zero anchor, the remaining residue values can be propagated along the 6k ±1 axis through its alternating step sizes 2 and 4. This produces a complete residue-class view. For the number 29 and the moduli 5, 7, 11, the vertical mat