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2025 - 2507(1) - 2508(1)
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[2] ai.viXra.org:2508.0025 [pdf] submitted on 2025-08-12 18:39:03
Authors: Stephen P. Smith
Comments: 14 Pages.
This paper proposes a unified framework that reinterprets probabilistic inference, information theory, and semantic flow through the lens of recursive symmetry and homeostatic balance. Beginning with the foundational structure of Bayes’ theorem and its role in defining semantic boundaries given by Roy Frieden’s extreme physical information, we explore the duality between Fisher information I and the semantic bound J as a dynamic tension that governs coherence. We show that the interaction between I and J is not merely algebraic but semantically directional, invoking a Janus-faced duality reminiscent of Arthur Koestler’s holons that reveal a sematic duality. This duality necessitates a symmetry-preserving operator that we identify with CPT invariance, leading to a recursive sublation mechanism that maintains semantic homeostasis. We formalize these insights into a semantic field theory using a Lagrangian formalism, curvature tensors that adjust flat space, bijection plains in flat space, and a recursive action principle that governs the evolution of mirrored manifolds. The result is a metaphysical geometry of meaning—where probability, inference, and coherence are unified under a recursive, symmetry-informed framework. Moreover, it is argued that symmetry breaking, often seen as irreversible loss, can instead be understood as sublation—a transformation preserving a deeper bilateral symmetry beneath visible asymmetry. Drawing on Hegel’s dialectics, CPT symmetry, and Karl Friston’s free energy principle, it proposes a universal homeostat that balances two mirrored space-time manifolds. This "extrinsic gravitation" maintains ontological symmetry while allowing epistemic differences, making physical laws the product of recursive balancing. Perception mirrors this process, aligning inner and outer realities. Broken symmetries are thus appearances, not destructions, revealing a cosmos where coherence is preserved beyond what is visible, uniting physics, cosmology, and epistemology.
Category: Statistics
[1] ai.viXra.org:2507.0083 [pdf] submitted on 2025-07-15 03:04:16
Authors: Michael Zot
Comments: 4 Pages.
We present a symbolic regression framework for detecting the smallest resolvable step change (∆) in noisy time series, approaching the detection boundary where ∆ ≈ σ (noise standard deviation). Unlike classical methods such as the t-test, this approach uses residual structure analysis and entropy collapse in symbolic space to identify shifts without assumptions of distributional normality or fixed window sizes. The detector is interpretable, model-free, and does not require labels, training, or convolutional priors. It works as a symbolic microscope, surfacing structural inflection points buried under stochastic variance.This tool was constructed from scratch to isolate step changes near the theoretical limit of detectability. It outperforms standard hypothesis tests in edge-case scenarios and reveals hidden transitions in behavioral, financial, biological, and simulated data. The method operates using a single-pass symbolic signature engine, relying solely on residual breakdowns and phase transitions in model fit error.The tool is open-source for academic and personal use under a restricted license: scientific invention or derivative work based on this detection method requires attribution and explicit permission. This constraint ensures credit to foundational symbolic techniques while enabling researchers to explore novel applications and insights using the method.Code repository: url{https://github.com/mikecreation/symbolic-step-detection}
Category: Statistics
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