What question did this study set out to answer?

This research aims to establish the Sky Theorem to show how dynamical systems approach their attractor states through entropy convergence.

June 11, 2026Open Access

The Sky Theorem: Universal Entropy Convergence from Quantum Hardware to Neural Memory Consolidation

Key Points

This research aims to establish the Sky Theorem to show how dynamical systems approach their attractor states through entropy convergence.
Proven via Lyapunov stability, KL divergence H-theorem, and Schur-concavity across multiple domains.
Experimental verification using IBM quantum hardware, dynamic decoupling, Grover's algorithm, EEG seizure prediction, and sleep data.
Used measures like Sky Trust Score to analyze entropy in various states.
IBM quantum hardware shows ground state T=0.945 vs superposition T=0.001 (940x ratio).
Dynamic Decoupling shows protection factor of 23.74x with Pearson r=0.9402.
EEG seizure prediction indicates T rises 13.8x, 32 seconds before seizure onset.

Abstract

The Sky Theorem states: dH (phi (S (t) ) ) /dt < 0 Any dynamical system approaching its attractor shows monotonically decreasing permutation entropy H. The Sky Trust Score T = 1 - H/Hₘax measures proximity to any attractor state. Proven via 3 independent methods: Lyapunov stability, KL divergence H-theorem, and Schur-concavity. Experimentally verified across 5 domains: EXP-51: IBM ibmfez real quantum hardware — ground state T=0. 945 vs superposition T=0. 001 (940x ratio) EXP-53: Dynamic Decoupling measured via Sky T — DD protection 23. 74x, Pearson r=0. 9402 between decoherence time and T (3/3 pre-registered predictions verified — IRREFUTABLE) EXP-54: Grover's Search Algorithm — Sky T peaks at k=2 (optimal iterations), demonstrating Sky T as universal quantum algorithm convergence detector EXP-47b: EEG seizure prediction — T rises 13. 8x, 32 seconds before onset EXP-55: PhysioNet Sleep-EDF — N3 deep sleep T=0. 0580 (8. 3x higher than REM T=0. 0070), confirming memory consolidation = dH/dt < 0 in human EEG One formula. Quantum bits to sleeping brains.

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