Computer Science and Mathematics

Abstract: The word agent now names systems as different as a tool-using language model and a chemotactic cell, with no shared definition across the fields that use it. We argue that these uses converge on one substrate-independent structure—the algorithmic agent: model-mediated regulation built from an implicit or explicit Modeling Engine, a scalar Objective Function, and a Planning Engine. Its root is algorithmic persistence: a pattern whose compressed identity survives the filter of time. Holding a pattern bounded under perturbation takes a load-bearing regulator somewhere in the pattern–world system—a structure that absorbs, cancels, or exports what interaction would otherwise let accumulate. By the Algorithmic Regulator Theorem, this regulator shares mutual algorithmic information with the world: it carries a model of what it regulates and can be read as-if acting through an objective and a planner. The pattern is an agent only when this regulator is localized within it (self-regulation), and telehomeostatic only when the regulator’s objective is the pattern’s own persistence. Regulation in macroscopic systems acts on coarse-grained, many-to-one variables. It is therefore irreversible and exacts a Landauer cost — a price that scales with the coarse-graining and vanishes for reversible, equilibrium persistence (e.g., an isolated atom). Hence the thesis: a macroscopic agent is a persistent pattern that conserves its own bounded code through a thin, thermodynamically costly boundary, in a world that, when closed and reversible, conserves algorithmic information up to the fixed description of its law and time index. We use it to reframe the free-energy principle, evolution, and alignment: in a collective the parts need not share an objective, so alignment is an objective-distribution problem—the design of local objectives and of the constraints that bound them so that the whole persists, not the search for one correct reward.

Abstract: The Minimum Vertex Cover problem is NP-hard. Its classical polynomial-time approximation ratio is 2, and Khot and Regev showed that, assuming the Unique Games Conjecture (UGC), no polynomial-time algorithm can achieve a factor 2 − ε for any fixed ε > 0. We present FINDVERTEXCOVER, an algorithm that reduces any graph to a linear-size planar forest core via a weighted Minimum Independent Dominating Set (MIDS) gadget and solves that gadget with an accuracy-controlled Baker-style PTAS whose layering width is k = ⌈1/ε⌉; non-core edges are then covered by a greedy repair step and a final redundancy-pruning p ass. For any fixed ε the algorithm runs in near-linear time and always returns a valid vertex cover. We include a reproducible experiment, stored in the car/ folder, that computes exact optima without MILP through a branch-and-bound maximum-independent-set solver, with K˝onig/maximum-matching certificates on bipartite i nstances. Under the default call ε = 0.1, across 1,718 feasible graphs—the graph atlas through seven vertices, random and structured bipartite families, grids, and random general graphs—every returned cover is valid and the maximum ratio is 7/4 = 2 − 1/4, attained by an explicit eleven-vertex bipartite graph; no instance exceeds 7/4. We therefore conjecture a universal 7/4 approximation ratio, a bound that the experiment shows is tight. If this 7/4 bound were proved, then, under the standard assumption P ≠ NP, the Khot–Regev UGC-based hardness theorem for Vertex Cover would force the Unique Games Conjecture to be false. An open-source implementation is released as the Salvador package (v0.0.6).

Abstract: We present Furones, a linear-time candidate-comparison algorithm for the Minimum Dominating Set (MDS) problem on undirected graphs. The algorithm (version v0.3.8) applies a TSCC-style pendant cascade, solves the reduced instance by a Baker-style routine used only as a validated candidate generator, and compares the lifted candidate against several original-graph candidates: closed-degree coverage, witness sweeps, order ownership, seed completion, a Salvador-style auxiliary, a max-cut double-cover auxiliary, and reverse-delete scans. We prove two unconditional guarantees. First, every normal return is a valid dominating set. Second, because the portfolio contains the dynamic greedy maximum-coverage dominator, every returned set D satisfies |D| ≤ H(∆ + 1) γ(G) ≤ (1 + ln(∆ + 1)) γ(G), where ∆ is the maximum degree and H(k) is the k-th harmonic number; this is a constant factor on bounded-degree graphs and sub-logarithmic in n for sub-polynomial degree. We also record the near-threshold ratio hypothesis that Furones meets ratio max{4, ln n} on all graphs; proving it would imply P = NP. The hypothesis is already proved for all graphs with ∆ ≤ √n/e. Exact benchmarks on 11,000 small instances with exhaustive optimum certificates record zero violations of the conjectured bound.

Abstract: In the Kolmogorov Theory (KT) of consciousness, an algorithmic agent is an information-processing system that compresses sensory data into simpler models to plan actions that optimize an objective function, while operating under limited data access, finite computational resources, and the fundamental limits of algorithmic information theory (AIT). We show how these limitations naturally give rise to probability, Bayesian inference, precision, and emergence. Using a toy example of an agent compressing pages fromalarge library, we recover a weighted multi-model strategy in which probabilistic reasoning and Occam’s razor appear as the agent navigates between models. We then introduce precision—the confidence the agent assigns to its model relative to noisy data—as the second-order quantity that arbitrates the trade-off between trusting the prediction and trusting the observation. We formalize precision as inverse-variance weighting of prediction errors at the Comparator and show what it gives the agent: a principled model-updating process carried out by the Updater (a submodule of the Modeling Engine), in which a confidence-dependent gain determines how much each prediction error revises the model — so that reliable, persistent errors reshape the model while structureless errors are retained as residual noise, and structural learning saturates once the compressible regularity has been captured. We then connect the picture to Karl Friston’s Free Energy Principle and Active Inference, which appear as the variational-Bayesian special case of the bounded-agent story, and flag the main differences rather than collapsing the two. Finally, we propose a formal, agent-centric definition of emergence in terms of coarse-graining and Kolmogorov complexity, and connect it to cellular automata, the renormalization group, and partial models. The result is a unified account in which probability, precision, and emergence are all consequences of an agent’s drive to compress and model a noisy world under bounded resources.

Abstract: Schrödinger (What Is Life?, 1944) and Anderson (More Is Different, 1972) argued thathigher levels of organization obey novel laws not straightforwardly derivable from microscopicones. We make this precise in Kolmogorov Theory (KT), where agents model the world bycompressing coarse-grained data. Emergence here is agent-relative: algorithmic emergenceoccurs when an agent empirically finds a concise, predictive macro-model that it could not havealgorithmically derived from the micro-rules alone. The emergent entity is that macro-model.Beyond a trivial resource barrier (o)—simulation is possible but infeasible—three barriersseparate micro-knowledge from macro-models. (i) A weak barrier: for bounded finite-statesystems an agent can simulate step by step but cannot in general shortcut the simulation.(ii) A strong barrier: with unbounded size, coarse-grained questions encode the haltingproblem and become undecidable. (iii) Our main result, the algorithmic barrier, in twoparts: for generic data no concise macro-model exists (most trajectories are Kolmogorov-random), and even when one exists no algorithm can find it (the structure function isuncomputable). Concise macro-laws are guaranteed neither to exist nor, where they exist, tobe derivable—even for bounded systems. Anderson’s “reduction ̸= construction” is thus acorollary of uncomputability: knowing the micro-laws rarely yields the compressed macro-laws.Effectivemacro-modelingstaysempirical. Favorablesymmetries—renormalization-groupflows,hydrodynamics, some elementary cellular automata—sometimes permit concise descriptions,but as exceptions, not algorithmic guarantees.

Abstract: The Minimum Independent Dominating Set problem (MIDS), equivalently the problem of finding a smallest maximal independent set, is strongly inapproximable: unless P = NP, no polynomial-time algorithm approximates it within any fixed constant factor. This rules out a single universal constant, but it does not rule out constant factors that are specific to structured graph classes. This manuscript studies Siriaisa, the unweighted MIDS algorithm distributed as the siriaisa package, and proves such family-restricted guarantees. Siriaisa removes isolated vertices, processes each component independently, solves an LP relaxation whose values serve only as priority scores for a maximal-independent-set sweep; for every component it assembles a deterministic pool of candidates (two lifted degree-four seeds, the direct LP sweep, six fixed orderings, and single- and paired-seed sweeps) and shrinks each feasible candidate by a bounded local-exchange compression built from reverse-delete and one-add/two-add exchanges, returning the smallest verified independent dominating set. We give two unconditional guarantees. First, every returned set is independent and dominating. Second, because every returned component set is a maximal independent set, it is a ∆-approximation of the component optimum; hence Siriaisa is a constant-factor approximation on every bounded-degree family (factor 2 for paths and cycles, 3 for ladders, 4 for grids, r for r-regular graphs), and it returns the exact optimum, ratio 1, on structurally rigid families of unbounded degree: cliques, stars, complete bipartite graphs, and double stars for all parameters, and crown graphs within the seed-pool range. A separate consequence of the compression is that every returned set is reverse-delete minimal and locally optimal under the implemented one-add and two-add exchanges. We make explicit what is not claimed: the LP ordering carries no universal approximation guarantee, and a universal constant factor would contradict Irving’s theorem unless P = NP, so we claim no graph-independent constant. We validate the theory against exact SciPy MILP optima on a small adversarial DIMACS suite and on a large-scale reproducible harness, the car suite, that runs ten thousand instances across the structured families and random graphs: every instance stays within its family constant, 99.85% are solved exactly, and the largest ratio across the whole suite is 1.20.

Abstract: We present Aegypti, a triangle-detection framework for an undirected simple graph \( G=(V,E) \) with \( n=|V| \) vertices and \( m=|E| \) edges, built on the duality between triangles and independent sets: a triangle of \( G \) is exactly a three-vertex independent set of the complement \( \overline{G} \), which is what a small vertex cover of \( \overline{G} \) leaves uncovered. Aegypti dispatches on density at \( \lceil n^{4/3}\rceil \). When \( m \le \lceil n^{4/3}\rceil \) it runs the exact Chiba--Nishizeki routine, whose \( \mathcal{O}(m^{3/2}) \) cost is \( \mathcal{O}(n^{2}) \) on inputs this sparse. When \( m > \lceil n^{4/3}\rceil \) it covers \( \overline{G} \) with the linear-time Hvala algorithm and reads three uncovered vertices, certified as a triangle in \( \mathcal{O}(1) \). We prove unconditional soundness for both variants. The fast variant is a quadratic-time, one-sided certificate procedure: in the dense regime it is complete exactly when the Hvala cover of \( \overline{G} \) leaves at least three vertices uncovered, a condition the factor-\( 2 \) bound guarantees only for graphs with\( \omega(G) \ge \lceil(n+3)/2\rceil \); its failure to return a triangle is not, by itself, evidence of triangle-freeness. The safe variant adds a Chiba--Nishizeki fallback and is therefore unconditionally complete, with worst-case running time \( \mathcal{O}(n + m^{3/2}) \). We make no claim against any fine-grained lower bound. Empirically, across a deterministic benchmark---random and structured families, adversarial dense families with small clique number, and an exhaustive sweep of all graphs on at most seven vertices---all routines agreed with an exact oracle and the fast dense branch recorded no miss. A public reference implementation is provided in the aegypti Python package, which depends on hvala.

Abstract: We study synchronization transitions in financial markets via persistent homology applied to time-varying correlation networks. Vietoris–Rips filtrations on rolling Mantegna distance matrices (49 Fama–French industry portfolios, 1976–2026) capture one-dimensional homological cycles (H₁) that reflect intransitive sectoral triples—configurations where two pairwise correlations are strong but the third is weak. Exact analytical null distributions for the persistence and count of such intransitive precursors in random metric spaces are derived. The data reveal a two-scale topological response: stress amplifies intransitivity among the most strongly correlated industries while dissolving it among weakly and moderately correlated ones. Because static topological summaries are highly collinear with average correlation, we assess the predictive ability of the momentum of topological reorganization for market stress onset. At short horizons (5–20 days) the momentum of average pairwise correlation dominates, but at 80–100 day horizons the standardized rate of change of the persistence-weighted mean cycle birth (dAvgBirth) significantly outperforms both a correlation-only control and the momentum of average correlation itself. Decomposing cycles into sectoral triples maps abstract topology onto interpretable linkages. The findings show that higher-order topological momentum captures a slow, structural component of stress build-up complementary to fast-moving correlation dynamics.

Abstract: Background Hahnemann’s Materia Medica Pura encodes the primary proving evidence for 67 classical remedies in prose structured for clinical reading rather than computational processing. Symptom boundaries, authority attributions, and editorial annotations remain embedded in unstructured text, making reproducible audit at the symptom and provenance level difficult without governed extraction logic. Objective We present a reproducible computational framework for parsing, section-aware similarity modeling, and provenance analysis of the full Materia Medica Pura corpus. Methods The pipeline implements seven analytical stages: corpus parsing with authority-block-constrained symptom extraction; canonicalization audit; section-aware similarity modeling with conservation validation; and authority/provenance graph construction with two-tier edge generation. Downstream stages add temporal onset signal extraction across six time buckets, promotion-gated editorial footnote integration, and potency marker normalization with OCR correction. Results The framework processed all 67 source remedy files, yielding 31,086 canonical symptoms in JSON and Markdown formats with full source-to-output parity and section conservation PASS at zero mismatch. Section-aware similarity across 77 units produced 5,929 matrix cells; the strongest pair was Hyoscyamus Niger::MAIN and Stramonium::MAIN (cosine similarity 0.025856843427458604). The provenance graph comprises 2,732 authority entities and 16,764 remedy-symptom-authority edges, with 115 promotion-gated footnote nodes integrated. Temporal onset extraction yielded 8,607 records; potency-signal classification identified 168 of 169 events (99.41%) as potency-context. Conclusion The framework delivers a verified, reproducible corpus layer for Materia Medica Pura supporting downstream similarity comparison, provenance tracing, and interpretive analysis. This manuscript reports computational methods and text analytics only; no therapeutic claims are made.

Abstract: The multi-dimensional Elo rating system was designed to be a method of extending the more popular Elo system to model a wider variety of phenomena based on pairwise comparisons. This is useful in comparing the behaviours of machine learning models that would otherwise be black boxes. Unfortunately, the mElo rating system as it is currently formulated in the academic literature contains feedback loops that prevent the mElo rating system from correctly inferring an expected pairwise comparison matrix. In this paper, we propose an altered version of the mElo rating system that removes the feedback loops and ensures that a certain level of accuracy can be achieved. Furthermore, we demonstrate how the geometry associated with the model behind the multi-dimensional Elo rating system introduces complexities not present in the Elo rating system. We discuss some of these differences and how they affect the use and interpretation of the mElo rating system. We conclude the paper with a list of recommendations for the practitioner to ensure that the mElo rating system is being used correctly to infer a unique pairwise comparison matrix.

Abstract: The Traveling Salesman Problem (TSP) remains a pivotal NP-hard challenge in combinatorial optimization, with critical applications spanning logistics, manufacturing, and industrial scheduling. While Ant Colony Optimization (ACO) is renowned for its distributed search and positive feedback, conventional variants frequently encounter premature convergence and “combinatorial explosion” in computational costs as problem scales expand. To overcome these bottlenecks, this paper proposes the Globally Adaptive Ant Colony System (GACS), a robust metaheuristic incorporating stagnation recovery and candidate-list pruning. The GACS framework integrates three synergistic strategies: (1) A K-nearest neighbor candidate-list compression that significantly reduces the search tree’s branching factor, maintaining high-quality solutions while ensuring effective linear scalability under fixed parameter configurations; (2) A global-adaptive pheromone weighting scheme that dynamically calibrates reinforcement intensity, facilitating a seamless transition from broad exploration to localized refinement; and (3) A multi-level stagnation recovery mechanism utilizing pheromone smoothing to preserve population diversity and bypass sophisticated local optima. Comprehensive evaluations on synthetic datasets and 33 benchmark instances from TSPLIB demonstrate that GACS consistently outperforms several recently published metaheuristic algorithms (including ABCSS, DSMO, and DWHO). Notably, GACS achieves a 5.5-fold acceleration in computational efficiency over hybrid genetic-ACO models and secures a favorable Average Rank of 1.44 across standard benchmarks. These results confirm that GACS provides a competitive balance between optimization accuracy and computational economy, offering a scalable and resilient paradigm for large-scale combinatorial optimization.

Abstract: The rapid digitalization of energy systems and the increasing integration of distributed energy re-sources, renewable energy technologies, and prosumer-oriented infrastructures have accelerated the development of IoT-enabled Smart Grids as a foundation for intelligent and adaptive energy management. Modern Smart Grids increasingly depend on the coordinated interaction of IoT ar-chitectures, artificial intelligence, distributed analytics, and decentralized control mechanisms to ensure reliability, scalability, and real-time operational flexibility. Despite extensive research activ-ity, existing studies remain predominantly technology-centric, focusing on isolated architectural layers or individual intelligent methods without providing a unified system-level perspective on their coordinated operation and interoperability. This article presents a system-level integrative review and challenge-oriented comparative synthesis of intelligent operational and architectural foundations of IoT-enabled Smart Grids. The study analyzes data-driven, model-driven, knowledge-driven, agent-based, and hybrid-oriented intelligent paradigms within multi-layer IoT energy infrastructures. In addition, the research establishes a cross-layer mapping between Smart Grid operational challenges, enabling technologies, and corresponding analytical approaches while identifying interoperability constraints, scalability limitations, and coordination challenges associ-ated with decentralized energy ecosystems. The conducted synthesis demonstrates that hy-brid-oriented intelligent approaches represent the most promising direction for future Smart Grid evolution due to their ability to integrate AI, ML, digital twins, semantic reasoning, and decen-tralized multi-agent coordination within unified IoT architectures. The presented results provide a conceptual foundation for the prospective development of adaptive, interoperable, scalable, and explainable Smart Grid ecosystems integrating decentralized computing, distributed energy re-source coordination, vehicle-to-grid interaction, and intelligent cyber–physical orchestration.

Abstract: We propose a framework that isolates a precise complexity-theoretic bottleneck between counting complexity and the Birch–Swinnerton-Dyer conjecture (BSD) via Tunnell’s theorem. The framework rests on two number-theoretic conjectures: a Reduction Conjecture asserting the existence of a polynomial-time reduction from any #P-complete problem to the counting of integer representations D_n = #{(x, y, z) : n = 8x² + 2y² + 16z²} (with counts preserved up to a polynomial factor), and a Solution Density Conjecture asserting that the values {D_n : n even square-free congruent} are sufficiently densely distributed (within the Eichler–Deligne ceiling D_n = O(n^1/2+ε)) to support iterated polynomial descent. We do not claim that P = NP implies #P = FP (the natural binary-search route fails because the threshold predicate [#I ≥ k] is PP-complete, not in NP, and PP is not known to collapse under P = NP). Instead, we prove a structural equivalence: under the two conjectures, BSD, and P = NP, #P ⊆ FP if and only if the specific family TunnellCount := {n 7→ D_n} is in FP. The framework thus does not resolve the #P ?= FP question; it converts it into a concrete, falsifiable arithmetic question about the polynomial-time tractability of representation counts on one specific ternary quadratic form. We identify three concrete open problems—parsimony in Matiyasevich representations, the distribution of weight-3/2 Fourier coefficients viaWaldspurger’s formula, and the FP-tractability of D_n itself—whose resolution would substantiate or refute the framework.

Abstract: Despite millennia of successful biological reproduction, the daily execution of child-rearing remains notoriously fraught and highly resistant to optimization. Society frequently attributes parental burnout and daily perceived failures in parenting tasks to psychological shortcomings, a lack of patience, inadequate education or organizational failure. Here, we propose a mathematically rigorous defense of the exhausted human parent by modeling routine domestic tasks as formal computational problems. We demonstrate that the pursuit of “Optimal Parenting” (OP) is (assuming P ≠ NP) fundamentally intractable. By performing polynomial-time reductions from classic NP-complete problems—specifically 0-1 Integer Linear Programming, Maximum Independent Set, and MAX-3-SAT—to simplified models of moral development, contradictory behavioral curricula, and developmental milestones, respectively, we prove that OP is strictly NP-hard. Consequently, we establish that finding an optimal parenting strategy requires exponential resources (energy, time), vastly exceeding the processing capabilities of any parent, biological or otherwise. Indeed our results indicate that optimal parenting is, in at least some instances, not achievable by any means, including with the aid of quantum computers (QC) or artificial intelligence (AI). Our results mathematically absolve both parents and children of domestic guilt and formally validate constraint relaxation (e.g. convincing a child to eat a piece of broccoli by pretending it is actually a very small tree), colloquially known as “doing one’s best”, as a necessary strategy for surviving a computationally hostile environment.

Abstract: The calibrated model reproduced the overall trend of specimen-to-specimen mechanical variation observed experimentally. Predicted stiffness values were in reasonable agreement with measured data. Fracture force predictions showed moderate agreement for dynamically tested specimens (R² = 0.60), which improved to R² = 0.88 after exclusion of one statistically identified outlier. Compared with a purely linear elastic formulation, the proposed viscoelastic model demonstrated modest improvement in stiffness prediction and more substantial improvement in fracture force prediction. These findings indicate that incorporating density-dependent viscoelastic effects improves representation of vertebral mechanical behavior, particularly at higher loading rates. Owing to its simplicity and computational efficiency, the proposed model requires only limited imaging input and may be useful for future biomechanical investigations, rapid screening, and injury risk prediction.

Abstract: Fragmentation of data is common in the U.S. healthcare system, which leads to substandard patient safety, excess administration waste, and impediments to public health monitoring. This paper proposes a relational database design, the Centralized-Decentralized Health Management System (CDHMS) that achieves a balance between conflicting requirements of local autonomy and federated access to data. The system is based on 15 normalized relations that are organized in 6 functional layers: core clinical infrastructure, Master Patient Index, Interoperability Mapping layer, Audit and Break-Glass logging subsystem, Patient consent and access-control framework, and a Role Based plus Attribute Based Access Control (RBAC+ABAC) model with 6 different user roles. The schema is deployed in MySQL Workbench 8.0 CE, with some sample mock data, and tested using 12 test queries. Results show the architecture enables no duplicate patient identities, reconciliation of incompatible coding vocabularies, granular patient consent management, and a tamper evident audit trail of all patient data access, including emergency overrides.

Abstract: To address the problems of strong noise, high asynchrony, pronounced subjectivity in risk labels, and insufficient model stability under extreme market conditions in multi-source risk signals within trading environments, a low-noise investment risk prediction method based on multimodal sensing signals and self-supervised representation learning is proposed. Market quotations, order books, terminal interactions, network transmission, device status, and news sentiment are uniformly modeled as risk perception signals. A temporal masking-based risk structure modeling module, a risk-oriented contrastive learning representation constraint mechanism, and a risk representation and downstream prediction task alignment strategy are designed to learn stable, transferable, and interpretable risk features. Experimental results show that the proposed method achieves the best performance in investment risk prediction, with mean squared error (MSE), mean absolute error (MAE), and root mean square error (RMSE) reaching 0.0164, 0.0851, and 0.1281, respectively, outperforming baseline models including generalized autoregressive conditional heteroskedast (GARCH), multi-layer perceptron (MLP), long short term memory (LSTM), temporal convolutional networks (TCN), and Transformer. The IC, RankIC, and AUC reach 0.496, 0.462, and 0.817, respectively, indicating stronger risk ranking capability and improved discrimination between high-risk and low-risk states. At the classification recognition level, the proposed method also demonstrates superior accuracy, precision, recall, and F1-score, indicating that potential high-risk assets can be identified more accurately. Ablation experiments verify the effectiveness of multimodal fusion, temporal masking, self-supervised contrastive constraints, and task alignment modules. Robustness experiments further show that lower prediction errors and higher AUC can still be maintained in high-volatility and extreme-shock markets, demonstrating strong noise resistance, stability, and practical application potential in complex sensing scenarios.

Abstract: Shannon entropy and Kolmogorov complexity describe complementary facets of information. We revisit Q2 from 27 Open Problems in Kolmogorov Complexity: whether all linear information inequalities including non‑Shannon‑type ones admit $\mathcal{O}(1)$-precision analogues for prefix‑free Kolmogorov complexity. We answer in the affirmative via two independent arguments. First, a contradiction proof leverages the uncomputability of $K$ to show that genuine algorithmic dependencies underlying non‑Shannon‑type constraints cannot incur length‑dependent overheads. Second, a coding‑theoretic construction treats the copy lemma as a bounded‑overhead coding mechanism and couples prefix‑free coding (Kraft's inequality) with typicality (Shannon-McMillan-Breiman) to establish $\mathcal{O}(1)$ precision; we illustrate the method on the Zhang-Yeung (ZY98) inequality and extend to all known non‑Shannon‑type inequalities derived through a finite number of copy operations. These results clarify the structural bridge between Shannon‑type linear inequalities and their Kolmogorov counterparts, and formalize artificial independence as the algorithmic analogue of copying in entropy proofs. Collectively, they indicate that the apparent discrepancy between statistical and algorithmic information manifests only as constant‑order effects under prefix complexity, thereby resolving a fundamental question about the relationship between statistical and algorithmic information structure.

Abstract: We derive a penalty strength criterion for ridge regression using stochastic complexity, which is a refined variant of the minimum description length principle. Since stochastic complexity doesn’t typically account for the effect of regularisation on complexity, despite its ability to simplify models, we are required to make a slight modification to the un- derlying coding scheme. Our scheme makes use of a weighted ensemble of regularised model fits rather than a mixture of maximum likelihood estimates. Under this modification, regularisation is interpreted as reducing model complexity by constraining flexibility. In the case of ridge regression, the complexity penalty term that we derive can be expressed analytically as the log determinant of the residual operator. We demonstrate the effect of this complexity penalty by fitting a linear readout to a reservoir computer.

Abstract: Artificial Intelligence (AI) systems are increasingly embedded in development contexts across the Global South, yet limited evidence explains how individuals within marginalized communities behaviorally adapt to these technologies beyond structural access and governance conditions. Building on prior framework-based analysis, this study examines the micro-level processes through which users internalize and operationalize AI-enabled systems in everyday livelihood and learning activities. A mixed-method sequential explanatory design was employed using the same population across urban, peri-urban, and rural settings, integrating structured surveys with ethnographic observations, digital usage tracing, and behavioral mapping. The findings identify three dominant adaptation pathways: instrumental adoption driven by efficiency gains, socially negotiated use shaped by contextual constraints, and reflexive adaptation linked to learning and trust formation. Quantitative analysis indicates that user agency significantly mediates the relationship between access and effective utilization, while qualitative insights reveal that learning styles and socio-cultural conditions influence the depth and sustainability of engagement. The study concludes that inclusive AI outcomes depend not only on infrastructure and governance but also on dynamic human–technology interactions, where cognitive engagement and iterative feedback mechanisms play a central role. These findings extend existing models by introducing a behavioral adaptation dimension critical for designing context-sensitive and sustainable AI interventions.