We study the inter-dyadic prime count Delta (n) = pi (2ⁿ - 1) - pi (2^ (n-1) - 1) through a layered discrete architecture. The first layer is the dyadic prime-number-theorem backbone F (n) = 2^ (n-1) / (n ln 2). The second layer is the normalized ratio R (n) = Delta (n) /F (n), which is well approximated on the computed range by R (n) ≈ 1 + (1 - ln 2) / (n ln 2). The third layer is the scaled residual K (n) = -n² (R (n) - 1 - (1 - ln 2) / (n ln 2) ). Rather than fitting K (n) on arbitrary windows, we organize the analysis in natural dyadic blocks of the index n, namely 2ᵏ, 2^ (k+1) - 1. On the block k = 4 (n = 16,. . . , 31), K (n) exhibits a structured transitional regime, while on the block k = 5 (n = 32,. . . , 50 in the available data) it enters a numerically stabilized tail near -0. 28. In each block, K (n) is modeled empirically by a class-dependent modulation K (n) ≈ Aₖ (r) + Bₖ (r) (-1) ⁿ/n, where r = n mod 4. After subtraction of this blockwise analytic correction, the remaining residual, quantized into bands, is governed by a deterministic finite-state transducer: on the first block it requires two steps of memory, whereas on the second block one-step memory suffices and the residual is almost entirely absorbed into the central band. The result is presented as a computationally observed dyadic state architecture, not as a theorem.
Ricardo Adonis Caraccioli Abrego (Sat,) studied this question.