PRIMALITY ZOO · FIELD INSTRUMENTS

Residue rows: cells the pattern occupies mod p light cyan. Fill an entire row → a full residue class is forced composite at every position → KILLED (one stray occurrence allowed if the covering prime is itself in the pattern). Escape every row → LIVES, and Hardy–Littlewood predicts the count (amber curve = S·∫dx/ln^kx). Guard: if the white staircase tracks the amber curve, your eyes are seeing real structure.

Cyan band = π(x; q, nonres) − π(x; q, res). Amber dash = ½·π(√x), the prime-power mass secretly parked in the residue class (every odd p² ≡ 1). The race hugs the mass curve: the bias is the ψ→π correction, i.e. the wavelets between staircase steps. Magenta = residual after removing it: pure L-function zero music around 0. Amber ticks mark lead inversions (first at x = 26,861 for mod 4).

Row = residue of prime pₙ, column = residue of pₙ₊₁; cell = row-percentage. Guard: a memoryless fair die reads flat 1/φ(q) everywhere (printed under each cell as Δ). The dark diagonal = primes avoid repeating their residue; mechanism is gap economics (returning home costs a gap ≡ 0 mod q, fresh classes sit at gaps 2, 6, 8…). Invariance knob: switch modulus, and the diagonal stripe survives, so it's residue structure, not a base-10 costume. Watch it fade (glacially) in the upper windows: real, and converging to fair like a coastline erodes. This matrix is the GAPFORMER probe target.