The Extended Zeta Function: Analytic Symmetry, De-Randomizing Gaussian Envelopes (DERANGE), Orthogonal System Stabilization, Reverse Time Effects, and Significant Improvement in Prediction Probability

This paper develops an analytic framework for orthogonal drift elimination within the helical representation of the Zeta structure. By coupling Gaussian stationary-phase analysis with an orthogonal Mellin transport, cumulative phase drift is transformed into a single, reversible projection error. The resulting discrete-time dynamics constitute a contraction on the drift subspace, yielding exponential precision growth: the effective RMSE decreases to roughly 30% of the naive baseline and information density increases by an order of magnitude. A quantitative stabilization threshold, e λ(A)τ ρ < 1, separates controllable from entropically unstable regimes and unifies analytic, numerical, and statistical results. The mechanism reproduces, within a deterministic setting, the attenuation pattern of WKB tunneling-an entropic tunneling analogy in which orthogonality replaces dissipation. Numerical simulations confirm exponential drift suppression and phase-symmetry restoration at the stationary-phase anchors of the Riemann-Siegel lattice. This establishes a general analytic mechanism for deterministic stabilization of probabilistic systems, transforming stochastic drift into orthogonal symmetry and achieving exponential precision gain within DTIME = Θ(W (n) log(1/ε)). Supplementary Material File (zeta_orthogonal_prediction1.pdf) - Download - 550.12 KB Information & Authors Information Copyright This work is licensed under a Creative Commons Attribution 4.0 International License

Authors Metrics & Citations Metrics Article Usage 331views 210downloads Citations Download citation Thomas Richter. The Extended Zeta Function: Analytic Symmetry, De-Randomizing Gaussian Envelopes (DERANGE), Orthogonal System Stabilization, Reverse Time Effects, and Significant Improvement in Prediction Probability. Authorea. 04 December 2025. DOI: https://doi.org/10.22541/au.176159485.50333001/v2 DOI: https://doi.org/10.22541/au.176159485.50333001/v2 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu.