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GPT-5.4 Pro: counterexample to GCI for non-centered measures

https://sudonull.com/gpt-5-4-pro-counterexample-to-gci-for-non-centered-measures

GPT-5.4 Pro disproved the hypothesis of the Gaussian correlation inequality for shifted Gaussian measures. Counterexample in 2D with strips, generalization to n≥2. Solution details on solveall.org. Study for AI in mathematics.

NEES/NIS Diagnosis of Kalman Filters under Nonlinearity

https://sudonull.com/nees-nis-diagnosis-of-kalman-filters-under-nonlinearity

Comparison of KF, UKF and Particle Filter under Non-Gaussian Noises and Nonlinear Dynamics. NEES and NIS Metrics for Filter Consistency Assessment.

Circulants and DFT: properties and computations

https://sudonull.com/circulants-and-dft-properties-and-computations

Breakdown of circulants, their connection with discrete Fourier transform, FFT and Gaussian sums. Eigenvalues, algebraic structure for developers. Study the theory and algorithms.

Prime Numbers in Black Holes: Primon Gases

https://sudonull.com/prime-numbers-in-black-holes-primon-gases

Learn how prime numbers and the Riemann zeta function describe black hole singularities. Primon gases, conformal symmetry, and Gaussian primes in quantum gravity. For physicists and mathematicians.

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