Minimal core of the Quantum Relay Theory: functional duality, active memory, and emergence of a privileged observable

This preprint presents the stabilised minimal core of the Quantum Relay Theory (QRT), developed as a compact theoretical note built on the Geometric Relay Theory (GRT) and connected to Entangled Relativity. The model is based on a six-variable dynamical system involving a strong branch, a weak branch, a resonant two-component memory, and an adaptive controller. The main result is that neither the strong branch alone, nor the weak branch alone, nor their raw sum reaches the entangling regime within the tested framework. The central operator is the memory stage, which acts as a spectral reorganisation mechanism. Across the tested regimes, the memory flux M˙1 emerges as the systematically privileged internal observable. The paper also reports important negative results: no bistability and no hysteresis were detected in the explored model families. The duality is therefore interpreted as functional rather than attractorial. In the open quantum sector, the Gaussian dissipative regime is exactly solvable; the novelty claimed here is not the standard Gaussian solution itself, but the internal closure of the squeezing coefficient κ through the QRT chain. This work is presented as a stabilised minimal core, not as a final theory. It explicitly distinguishes established internal results from open limitations, including the absence of a microscopic derivation of the effective parameters and the absence of a naturally identified physical context at photonic or microwave frequencies.