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.