The Toccata Invariant: A Structural Fingerprint of the Prime-Zero Duality

We introduce a new observable on Riemann zeta zeros: the lag-2 autocorrelation of the zero-counting deviation S (t) under sequential removal of prime voice contributions Vₚ (t) = − (1/π√p) sin (t log p). The resulting profile — a characteristic descent when the lowest-frequency voice is removed, followed by a floor and recovery — is designated the Toccata Invariant. The core properties are audited on 3, 212 zeta blocks (13, 835, 800 zeros, T ≤ 6. 7 × 10⁶) and extended to 37 datasets reaching T = 3. 06 × 10¹⁰ (191, 944 zeros), with zero violations in 69 tests (p < 0. 001). Deep peeling at T = 30. 6 billion (669 primes) shows AC₂ = 0. 250 and still climbing. The profile is absent in all controls (Poisson, GUE, shuffled, arithmetic). An exact scaffold of five proved propositions — including the conservation law Δθ/π + ΔS = 1, a truncation bound, and a mean-value bridge to gaps — justifies the observable. Perturbation analysis reveals that the first-step descent is driven by the lag-2 autocovariance numerator, identifying a specific algebraic target for future proof. A finite-difference identity exactly links the S-based and gap-based observables before peeling, explaining an observed mirror symmetry with a constant axis near −2/π². The upload includes the paper (v13), replication data (peeling traces at four heights, summary statistics for all 37 datasets), and a README with step-by-step reproduction instructions. All zeta zeros are from David Platt's LMFDB tables. The paper was developed with AI assistance (Claude, GPT, Gemini) under full disclosure.