The Cybernetic Architecture of the Primes: Parity Barriers, Σ∆ Noise-Shaping, and a Thermodynamic Dictionary for the Riemann Hypothesis

This research note develops a DAGI-motivated dictionary for prime cancellation and the Riemann Hypothesis. It is not a proof of RH. Its purpose is to isolate one exact algebraic obstruction, the parity-conjugacy of signed and unsigned Mobius divisor-incidence operators, and then use that obstruction to motivate a phase-sensitive interpretation of prime discrepancy. The central formal result is the identity P_N M_N P_N = A_N, where M_N is the signed Mobius incidence operator, A_N is the unsigned squarefree incidence operator, and P_N is diagonal prime-factor parity. Version v0.4 preserves the v0.3 strengthened obstruction statement and updates the DAGI citation layer with registry-backed DOI links from the project brain. The note develops a signal-processing and control-theoretic dictionary in which smoothed prime discrepancy resembles a shaped residual, the explicit formula behaves like a spectral transfer representation, low-frequency suppression has a Bode/waterbed analogue, and critical-line symmetry suggests a lossless or passive scaling-flow interpretation. These components are presented as evidence, model, dictionary, or conjectural operator anchors, not as completed equivalences.