Paper T: N-Bonacci Quasiperiodic Coherence: Spectral Modes, Time Quasicrystals, and the Adelic Limit

Abstract. This paper identifies a precise connection between the n-bonacci spectral mode hierarchy of the MNZI programme (Paper P [5]) and the physics of quasiperiodically driven quantum systems, also known as time quasicrystals. The n-bonacci criticality equation Σ(k = 1 to n) x^k = 1 (Lean-verified as MNZI.reciprocal_identity) characterises the unique stable threshold of the n-step memory branching process. Its solution r*n = 1 / Cn, where Cn is the n-bonacci constant, satisfies r*n > ½ for all finite n, and r*n → ½ monotonically at rate O(2^(−n)) (Lean-verified as MNZI.rn_decreasing and MNZI.rn_gt_half). The paper proposes the Criticality–Coherence Correspondence (Conjecture 3.1): for an n-bonacci quasiperiodic driving protocol, the quantum coherence enhancement over periodic driving is governed by r*n, the criticality threshold of the n-step memory system. Specifically: (i) The Fibonacci case (n = 2) The Fibonacci protocol achieves the largest deviation from the binary limit: r*2 = φ^(−1) ≈ 0.618, consistent with the reported approximately 3.7× coherence enhancement observed in 10-qubit time quasicrystal experiments. (ii) Higher-order protocols Higher-order protocols (n = 3, 4, ...) produce progressively smaller deviations: r*n → 1/2, corresponding to diminishing marginal coherence enhancement. (iii) The adelic limit The adelic limit r*∞ = ½ (maximum entropy, pure binary driving) represents the theoretical maximum coherence achievable by quasiperiodic means alone. This limit is approached, but never reached, for any finite n. The Buchanan Coil Invariant π²/12 > ln(2) (Lean-verified as MNZI.coil_exceeds_landauer) connects the spectral stiffness of the Riemann zero distribution to the Landauer erasure bound, suggesting a universal information-theoretic lower bound for coherence enhancement. Three testable predictions are formally registered. All mathematical results from the MNZI programme are machine-verified in Lean 4. All physical interpretations and conjectures are explicitly labelled as conjectural.