Non-transitive Correlation Structure among EEG, Brain Topology, and Quantum Computation: A Time-Series Analysis of Subjectivity Alignment Conditions

This study empirically investigates the structural conditions under which subjective states may influence quantum probability distributions, through the simultaneous measurement of electroencephalography (EEG), brain topological indices (first homology, H1), and quantum computation outcomes. Whereas conventional neuroscientific analyses primarily rely on spectral power of EEG signals as energetic quantities, the present work demonstrates a non-trivial relationship in which energetic (EEG) and structural (topological) variables remain mutually orthogonal, yet become integrated exclusively through quantum computation. Our analyses reveal that the five canonical EEG frequency bands and H1 indices do not exhibit direct significant correlations with each other. In contrast, the probability distribution of quantum computation outcomes shows statistically significant correlations with each of them independently. This pattern suggests that quantum computation does not respond to a single physiological variable, but rather functions as an integrative gate that nonlinearly detects moments in which energetic and geometric structures are simultaneously aligned. To further characterize this alignment, we introduce a composite measure, the \emph{Subjectivity Alignment Index} (SAI), integrating energetic and topological components. The correlation between SAI and quantum probability was found to be substantially stronger than correlations obtained using either component alone. Moreover, a hierarchical temporal propagation was identified, in which subjective alignment in higher-frequency bands (gamma) precedes maximal responses in lower-frequency bands (theta) and quantum probability with a delay of approximately three cycles. Notably, backward lag correlations (lag $-3$), in which past alignment states are inferred from later quantum outcomes, were significantly stronger than forward lag correlations (lag $+3$). This asymmetry indicates that the relationship between subjectivity and quantum measurement is not adequately described by a simple unidirectional causal chain, but may instead reflect a temporally extended constraint in which past, present, and future states are jointly structured, consistent with a retrocausal loop interpretation. The quantum rotation angle of $72^\circ$ employed in this study is derived from the five-fold symmetry of the Five Energy Star (FES) framework, ensuring that analytical parameters are intrinsically constrained by the underlying theoretical structure. Taken together, these results provide statistical and structural evidence that consciousness is not merely a passive observer of physical reality, but an active constituent that participates in the determination of quantum probability through the alignment of energetic and geometric conditions.