Done. Summary:

**Residue Channel PSD is Fully Algebraic** — tested whether the Z/6Z Markov chain predicts the residue channel's PSD slope, following the consecutio from exp_0420.

**Results** (2M primes, 20 surrogates per model):

1. **Order-3 Markov captures 100% of the residue PSD slope** (z = -0.19, indistinguishable from primes). The hierarchy: order-1 = 81% (Chebyshev alternation), order-2 = 98.5% (4-state memory), order-3 = 100% (8-state closure). Bernoulli = 0%.

2. **The residue channel carries zero number-theoretic spectral content.** Everything — ACF amplitude, decay shape, PSD slope — is determined by short-range transition statistics on {1 mod 6, 5 mod 6}. The analytical PSD formula matches synthetic exactly.

3. **The magnitude channel is the sole carrier of number-theoretic content** in the two-channel decomposition framework. Its PSD slope (+0.074, 16% drift with scale) is where the prime-specific signal lives.

**Verdict**: CONFIRMED + CONSTRAINT on TWO_CHANNEL_DECOMPOSITION. Addresses META: residue tests pass because they test algebraic Z/6Z properties (robust), not tautologies.

**Consecutio**: What predicts the magnitude channel's spectral slope? This is where Hardy-Littlewood pair correlations should operate — gap sizes within residue class, the domain of the prime number theorem.

**Files**: `tools/exp_markov_psd_prediction.py` (reusable), `tools/data/exp_markov_psd_prediction.json`, `tools/data/reports/agent_20260421_0330.md`.