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Previous months:
2025 - 2507(1) - 2508(1)
2026 - 2608(1) - 2609(1) - 2610(1)
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[5] ai.viXra.org:2610.0025 [pdf] submitted on 2026-10-09 14:55:38
Authors: Prakash Vaithyanathan
Comments: 3 Pages.
The battery management system of an electric vehicle records cell voltage, current and temperature many times a second. Every current method that uses these signals to detect degradation is either reactive, acting after a fault code is raised or a capacity threshold is crossed, or trained, requiring labelled examples of degradation events to build a model. This note proposes a proactive layer that needs neither. It watches how quickly the small, cycle-level voltage fluctuations return to their normal level after each disturbance. In a healthy cell this return is fast. As the cell approaches a tipping point, the return slows, and this slowing can be seen in the signal before any threshold is crossed. The slowing is measured by the lag-1 autocorrelation of the voltage residual within a rolling window. When this statistic rises persistently towards 1, a graded shunt acts on the entities of the BMS domain, adjusting the charge rate, flagging the cell, or pausing the charge, before the cell crosses a danger line. The shunt is the core of the invention. The lag-1 autocorrelation as an early warning signal rests on well-established physics. The application of a graded shunt to the BMS domain, triggered by the statistic rising persistently towards 1, is what this note proposes. It is a concept note. No battery data have been analysed.
Category: Statistics
[4] ai.viXra.org:2609.0078 [pdf] submitted on 2026-09-29 20:46:04
Authors: Lukas Saul
Comments: 13 Pages.
We develop an exact, closed-form statistical mechanics of the equipment-enhancement system of the idle RPG Milky Way Idle. An enhancement attempt advances an item by one level with probability p and, on failure, either resets it to level 0 (protection off) or decrements it by one level at the cost of a consumable protection item (protection on, from a chosen level R upward). We compute the expected total cost E[C] = T·E[τ] + L·E[M], where T is the per-attempt time cost, L the per-protection-item cost, τ the hitting time of a target level N, and M the number of protected failures incurred. The central object is the expected visit-count vector v_k, which we identify as the discrete Green's function of a piecewise birth-death operator and solve in closed form in terms of p, N, and R alone. We recover the unprotected limit C_n = (p^(−n) − 1)/(1 − p) as a special case, matching the result of Chae and Lee. We then present the full path-integral representation of the process as a sum over random-walk histories weighted by exp(−βC), give the transfer-operator resolvent G(x,y) = [(I − W(x,y))^(−1)]_{0,N}, and analyse the continuum limit: the WKB/instanton action S_inst = N·ln(1/σ) reproduces the exact exponent σ^(−N), while Gaussian fluctuations around the instanton yield an erfc-form budget tail P(C ≤ B) ≈ (1/2)·erfc((E[C] − B)/sqrt(2·Var[C])). All exact formulae are rational in p and are tabulated for the base success rates of the game.
Category: Statistics
[3] ai.viXra.org:2608.0078 [pdf] submitted on 2026-08-23 08:46:12
Authors: Po Hu
Comments: 9 Pages.
Consider a gambler with integer capital who gains two units after a win, loses one unitafter a loss, and is removed at the first visit to zero. The first observation is elementarybut striking: with positive drift, the probability of reaching an arbitrarily high finite targetdoes not tend to zero. It tends to the probability of never being ruined. For independenttrials with win probability p, we record the exact ruin law, identify the phase transitionat p = 1/3, and give a closed formula at criticality whose fixed-capital asymptotic is x/m.We then keep the one-step win probability equal to 1/2 and the mean payoff equalto 1/2, but let successive outcomes form a symmetric two-state Markov chain with persistence parameter θ. An explicit bounded harmonic function gives the ultimate survivalprobability1 −1 + r + r22(1 + r)rx−1, r =√(1 − θ)2 + 4θ2 − (1 − θ)2θ.This probability decreases strictly with persistence, although every model in the familyhas the same stationary win rate and the same mean increment. At θ = 1 the survivalprobability is discontinuous: its left limit is 1/4, while its endpoint value is 1/2. Consequently, the high-target limit and the high-persistence limit do not commute. Finally, if(1 − θ)x → λ, the exact transition profile is 1 − (3/4)e−λ/2. These formulas isolate howearly absorption and temporal clustering, rather than the height of a finite target alone,govern extreme-target success.
Category: Statistics
[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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