The Subject-Authentic Interface: A Mathematical Foundation for Neuroprosthetics and BCI Based on Titov's Subject-Centred Model

Modern brain-computer interfaces (BCIs) and neuroprosthetics have achieved remarkable engineering successes in decoding motor intentions from neural activity. Yet the field confronts a fundamental theoretical barrier: current systems are pattern classifiers that can detect *what* a user intends but not *why* an action is intended, *how strongly* it is desired, or *whether* the user experiences the prosthetic as part of themselves. We argue that this barrier stems from the absence of a *model of the subject* in the design loop. We present a mathematical framework based on Titov's subject-centred model (2023) that fills this gap. The subject is described as the dynamic interaction of two subsystems — the *intentional* (I, memory and meanings) and the *intending* (D, drives and motives) — whose coupling through a *reentry loop* generates emotions, significance, and the sense of "I." We define a *subject-authentic interface* as one for which the integrated information Φ(S ∪ J) > Φ(S), i.e., the interface becomes part of the subject. We derive the operator formalism in detail, propose a concrete neural-network architecture (with full PyTorch specifications) for a BCI with artificial reentry, provide the computable Φ_G-criterion of Barrett & Seth (2011) as the training objective, and formulate three falsifiable experimental predictions. A Lean 4 proof sketch establishes that reentry implies Φ > 0 under the Gaussian approximation.