Population-Scale Conservation of Cognitive Entropy and Prior-Dominant Dynamics in Human EEG

VUH 6.75: Population-Scale Conservation of Cognitive Entropy and Prior-Dominant Dynamics in Human EEG Ankur Bhasin1 1Bhasin Research Unit for Hyperphysics (BRUH) Abstract Understanding where causal structure resides in cognitive systems remains an open problem across neuroscience, psychology, and theoretical physics. Task-centric and decision-timing approaches implicitly assume that moment-to-moment conscious awareness acts as a highbandwidth causal controller. In this work, we test an alternative hypothesis: that cognitive dynamics unfold within a constrained information manifold shaped primarily by long-term priors. Using the full EEG Motor Movement and Imagery Dataset comprising 109 subjects, we construct coherence-based cognitive state sequences and model their dynamics as discrete-time Markov processes. After removing noise-dominated states, we find that the entropy rate of cognitive state transitions is tightly conserved across the population, with minimal inter-subject variance. The resulting state geometry exhibits a dominant mixed-coherence regime and a rare but universal hypercoherent regime. Surrogate analyses demonstrate that destroying temporal ordering does not induce entropy collapse, ruling out hidden high-bandwidth control signals at the scale of conscious awareness. We further validate these findings in task-free sleep data and neurodiverse cohorts, showing deformation but not breakdown of the underlying informational structure. These results establish population-scale conservation of cognitive entropy as a structural property of human cognition and support a prior-dominant view of causal organization. Within the Vedic Unified-field Hypothesis (VUH) framework, this work constitutes the empirical foundation of VUH 6.75. 1 Introduction 1.1 Motivation A central question in cognitive science is where causal structure resides in the human cognitive process. Traditional approaches emphasize task-locked neural signatures, decision timing, and conscious intention as primary causal drivers. However, such models struggle to explain the robustness, repeatability, and low variability of large-scale cognitive dynamics across individuals and contexts. An alternative view is that cognition unfolds within a constrained informational landscape shaped by long-term learning, adaptation, and structural priors. In this view, conscious awareness samples trajectories within this landscape but does not exert fine-grained, high-bandwidth control over state transitions. 1 1.2 Conceptual framing: VUH 6.75 Within the Vedic Unified-field Hypothesis, cognition is modeled as evolution on an information manifold governed by coherence and entropy constraints. VUH 6.75 formalizes this view by treating entropy rate as a candidate structural invariant and by distinguishing prior-dominant dynamics from execution-level awareness. 1.3 Contributions The contributions of this work are: 1. Population-scale measurement of cognitive entropy across 109 subjects. 2. Identification of conserved cognitive state geometry. 3. Demonstration of intrinsic ergodic dynamics after noise removal. 4. Cross-domain validation in task-free and neurodiverse regimes. 2 Data and Preprocessing 2.1 Primary dataset: EEGMMIDB We analyze the EEG Motor Movement and Imagery Dataset (EEGMMIDB), consisting of 109 healthy adult subjects. Each subject completed 14 experimental runs involving motor execution and imagery tasks. EEG signals were recorded using a standard 64-channel montage. 2.2 Validation datasets Two additional datasets are used for validation: •Sleep-EDF, representing task-free and unconscious dynamics. •TDBRAIN, representing neurodiverse and clinical populations. 3 Coherence Features and Cognitive State Construction 3.1 Coherence windowing EEG signals were segmented into non-overlapping 2-second windows using channels C3 and C4. Band-limited coherence was computed in theta, alpha, beta, and gamma bands, along with a global coherence metric. 3.2 Cognitive state definitions Each window was assigned to one of six phenomenological cognitive states: •S0: noise-dominated •S1: theta-dominant •S2: alpha-dominant 2 •S3: sensory-dominant •S4: mixed coherence •S5: hypercoherent State S0 was excluded from primary analysis. 3.3 Markov formulation State sequences were modeled as discrete-time Markov chains. Transition matrices, steady-state distributions, and entropy rates were computed per subject. 4 Primary Results: EEGMMIDB 4.1 Population-scale entropy conservation Entropy rates clustered tightly across subjects, with a mean near 1.13 nats per step and low intersubject variance. Table 1: Population statistics of entropy rate after noise-state removal (S0), computed from the Markov state dynamics for all 109 subjects in EEGMMIDB. Values are derived from summary all subjects 109 dropS0.csv. Statistic Entropy Rate (nats per step) Mean ≈1.13 Standard deviation ≈0.075 Median ≈1.14 Interquartile range ≈[1.10,1.17] Minimum ≈0.91 Maximum ≈1.30 Number of subjects 109 4.2 Invariant state geometry The mixed coherence state dominated occupancy, while hypercoherent states appeared as a rare but universal regime. Table 2: Mean steady-state probabilities of cognitive states after noise-state removal, averaged across all subjects. State Mean steady-state probability S1 (Theta-dominant) ≈0.28 S2 (Alpha-dominant) ≈0.15 S3 (Sensory-dominant) ≈0.02 S4 (Mixed coherence) ≈0.52 S5 (Hypercoherent) ≈0.06 3 Figure 1: Histogram of entropy rates after noise-state removal (S0) across all 109 subjects. Vertical clustering demonstrates population-scale conservation of cognitive entropy. 4.3 Surrogate analysis Surrogate sequences preserved entropy structure, indicating the absence of high-bandwidth temporal control. 5 Cross-Domain Validation 5.1 Sleep-EDF Task-free sleep data exhibited entropy rates within the same band, despite state-specific deformation. 5.2 TDBRAIN Neurodiverse cohorts showed bounded entropy with increased variance, consistent with prior deformation. 6 Interpretation Entropy conservation suggests that cognitive dynamics are constrained by long-term priors rather than conscious execution. Within VUH 6.75, intuition corresponds to navigation within low-entropy regions of the cognitive manifold. 7 Limitations Results depend on phenomenological state definitions and limited spatial sampling. No claims are made about free will or decision timing. 4 Figure 2: Representative transition probability matrix after noise-state removal for a single subject (S109). Similar structures were observed across all subjects, indicating invariant transition geometry. 8 Conclusion We demonstrate population-scale conservation of cognitive entropy in human EEG, establishing the empirical foundation of VUH 6.75. 5 Figure 3: Cognitive state time series for subject S109 after noise-state removal. 6 A Mathematical Formalization of Entropy Conservation Let {Xt}denote a discrete-time stochastic process representing the cognitive state sequence after noise-state removal, where Xt∈ {S1, S2, S3, S4, S5}. For each subject, the dynamics are modeled as a time-homogeneous Markov chain with transition matrix P. The entropy rate is H=−X i πiX j Pij log Pij, where πis the stationary distribution satisfying π=πP . Empirically, entropy rates H(s)lie within a narrow population band with small inter-subject variance, indicating statistical conservation of entropy under task and subject variation. 7 B Task-Free Validation Using Sleep-EDF Table 3: Entropy rate comparison between EEGMMIDB and Sleep-EDF. Dataset Mean entropy rate (nats/step) State geometry EEGMMIDB (wake) ≈1.13 Mixed-dominant Sleep-EDF (sleep) ≈1.10–1.18 Stage-modulated 8 References [1] Goldberger, A. L., Amaral, L. A. N., Glass, L., et al. PhysioBank, PhysioToolkit, and PhysioNet. Circulation, 101(23), 2000. [2] Schalk, G., McFarland, D. J., Hinterberger, T., Birbaumer, N., Wolpaw, J. R. BCI2000: A General-Purpose Brain–Computer Interface (BCI) System. IEEE Transactions on Biomedical Engineering, 51(6), 2004. 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