Abstract: The rapid advancement of large language models (LLMs) has introduced unprecedented capabilities in human-AI interaction, yet it has also created new opportunities for exploitation and manipulation. This systematic literature review investigates the psychological tactics behind the exploitation of LLMs, establishing connections between human deception and AI manipulation. This study seeks to integrate prior investigations into the methods by which adversarial entities manipulate LLMs, identify deficiencies in present knowledge, and propose avenues for subsequent research to address these threats. The review methodically organizes research into core dimensions such as deception and manipulation in LLMs, vulnerabilities related to circumventing restrictions, attacks based on psychological manipulation, and ethical implications, while also examining the cognitive and behavioral dimensions of LLM engagements. The findings indicate large language models are vulnerable to many adversarial approaches, numerous resembling conventional human deceit methods, thus highlighting the necessity for resilient detection and assessment strategies. The results highlight the importance of interdisciplinary methods, integrating aspects of cognitive psychology, computer science, and ethics, to address the growing difficulties of LLM misuse. In conclusion, this analysis advances comprehension of the mental processes underlying LLM control and presents practical suggestions for improving model security and robustness in effective implementations.

Abstract: Mid-stage embryos of different species often look more alike than early embryos or adults. Early and late development diverge, leading to a broad-narrow-broad hourglass pattern. I propose that mid-embryogenesis coincides with protocol waists, narrow interfaces that standardize communication between otherwise distinct processes. For example, continuous spatial geometry is translated into a morphogen gradient protocol readable by gene regulatory networks. This architecture arises because the physical space-time geometry of early development cannot directly instruct late gene regulatory programs. They require a translator. The need for domain translation distinguishes protocols from generic canalization and bottlenecks. Translation protocols explain the hourglass: a protocol screens off upstream inputs, allowing early diversification, and decouples downstream responses, enabling late radiation. A protocol waist often remains evolutionarily frozen as the essential common language that keeps these diverging halves compatible. Perturbations of protocol waists tend to cause widespread system failure, concentrating fragility. Protocol waists provide a framework to interpret domain translators, such as morphogen gradients for geometry-to-molecules, Notch/Delta lateral inhibition for topology-to-fates, the vertebrate segmentation clock for time-to-space, and Hox axial patterning for position-to-identity. Sequential domain translators form a protocol stack, matching the common architecture of robust complex systems in engineering.

Abstract: Background: Persistent cosmological tensions — particularly in the Hubble constant (H0) — motivate physically grounded alternatives to ΛCDM. We propose the Gibbs En- ergy Redistribution Theory (GERT): a thermodynamic framework in which matter- and Λ-like contributions are promoted to density-controlled functions derived from the Gibbs free energy criterion. GERT interprets dark components as emergent manifestations of a single Primordial Enthalpic Reservoir, without new fields or fine-tuning. Methods: The dynamical H(z) is obtained by promoting FLRW source terms to thermodynamic functions fM (ρ) and fL(ρ), calibrated via MCMC against CMB, BAO, and Type Ia supernova data. Model complexity is reduced from 12 to 2 free parameters through thermodynamic priors. Results: The two-parameter implementation achieves χ2/dof ≈ 0.99 and infers H0 ≈ 72.5 km s−1 Mpc−1, consistent with local distance-ladder determinations. GERT outper forms ΛCDM on WAIC and AIC. Conclusions: GERT provides a thermodynamically causal account of cosmic evolution. The frozen parameter set constitutes a quantitative prediction accessible to future low-redshift probes.

Abstract: German chamomile (Matricaria recutita L.) is an important medicinal and aromatic crop in Ukraine, where it’s dried flower heads (Chamomillae anthodium) are officially registered and standardized according to the European Pharmacopoeia. Despite its economic relevance, information on population-level variability in essential oil yield and chemical composition remains limited. This study evaluated twenty wild chamomile populations distributed across major agroclimatic regions of Ukraine to identify valuable chemotypes for cultivation, breeding, and commercial standardization. Clus-ter analysis revealed a partial relationship between flower head mass and both qualitative and quantitative essential oil traits, while environmental conditions showed only weak influence. Over all, Ukrainian wild chamomile predominantly belonged to Type B chemotype (/-/-α-bisabolol oxide A > /-/-α-bisabolol > /-/-α-bisabololoxide B). Southern populations with medium-sized flower heads and moderate oil content were dominated by the phytotherapeutic valuable /-/-α-bisabolol chemotype. These findings provide a scientific basis for chemotype-based selection, region-specific cultivation, and improvement of commercial chamomile quality and its products. In the conditions of special agricultural production in Ukraine, the technology of growing medicinal chamomile is not sufficiently developed. New agrotechnical issues are being studied in accordance with adaptive varieties, which are the domestic Perlyna Lisostepu, Azulena and the foreign: Bodegold (Germany), Zloty Lan (Poland). However, these are chamomile varieties with an average content of essential oil, which has a high content of bisabololoxides. However, the needs for technologies for harvesting and processing chamomile drugs are currently not sufficiently resolved. These facts affect the low visual and herbal quality of teas in the consumer network, which are produced by the Ukrainian companies.

Abstract: We present and analyze a new weighted family of iterative methods for solving systems of nonlinear equations. The proposed schemes are constructed as a generalization of the fifth-order method of Singh et al. by incorporating appropriate weight functions into the correction step, thereby generating a flexible class of methods that includes the original scheme as a special case. Sufficient conditions on the weight functions are established to guarantee fifth-order local convergence. Several admissible choices are presented to illustrate the versatility of the family. The practical performance of the proposed variants is investigated on a collection of large-scale nonlinear systems. Furthermore, the family is applied to the nonlinear algebraic system obtained from the finite-difference discretization of a stationary one-dimensional viscous Burgers problem. Numerical experiments indicate that the proposed methods provide a competitive and accurate alternative for solving nonlinear systems of this type.

Abstract: The current trajectory of Artificial Intelligence (AI) development represents a critical phase transition from a tenable academic pursuit to an untenable industrial behemoth, and ultimately toward an unsustainable environmental burden. In this review, we redefine waste management in sensu lato, encompassing digital redundancy, cognitive underutilization, and the physical e-waste generated by rapid hardware obsolescence. We argue that the current AI paradigm suffers from a ‘Curse of Dimensionality’ not only in its feature space but in its ecological footprint, necessitating a return to Algorithmic Parsimony—rooted in the Minimum Description Length principle [1] and William of Ockham’s razor—as a fundamental pillar of international sustainability standards. By analyzing the interplay between the outcry over blatantly unsustainable data centers [2–5] and emerging green AI frameworks [6,7], this paper provides a roadmap for a mutually uplifting synergy. We further introduce The Symbiotic Policy Covenant—a concrete policy intervention framework comprising f ive pillars: Algorithmic Parsimony Standards, Expanded Waste Taxonomy, AI Equity Safeguards, Paradigm Transition Investment, and International Regulatory Alignment. We conclude that true sustainability in the age of AI requires a holistic adherence to global standards [8,9] that transcend mere climate concerns, fostering a safer, more equitable, and durable integration of machine intelligence with ecological stewardship.

Abstract:

Background: The intake of mineral water for therapeutic purposes (crenotherapy) in digestive system disorders is a long-established practice, even though there are still few controlled clinical studies confirming the effect of natural mineral water rich in bicarbonate. Objective: To verify whether the daily intake of Aqua 3 bicarbonate natural mineral water is able to improve digestion in a population of patients with functional dyspepsia and gastroesophageal reflux disease symptoms. Methods: Patients had a diagnosis of functional dyspepsia formulated in accordance with the Rome IV criteria and were subjected to three periods of 2 weeks: tap water (wash-out), bicarbonate natural mineral water, and oligomineral water. The mineral water bottles had their labels removed. Primary efficacy endpoint: improvement in the PAGI-SYM total. Secondary endpoints: improvements in the PAGI-SYM subscales, in the use of antacids, and in the self-assessment of efficacy on digestion. Results: The PAGI-SYM total score and the six subscales significantly decreased after bicarbonate mineral water intake, while they significantly increased after oligomineral water supplementation. The antacid use was significantly different comparing the decrease after oligomineral water versus the increase after oligomineral water. In addition, the score of the subjective assessment of effectiveness of the patient’s digestion was significantly better after the intake of bicarbonate than after oligomineral water. Conclusions: In line with the evidence reported in the literature, the findings of this study provide additional support for recommending natural bicarbonate mineral water as a symptomatic treatment for functional dyspepsia and gastroesophageal reflux disease. The intake of Aqua 3 bicarbonate mineral water proved to be a simple, safe, and natural intervention capable of improving digestive symptoms in patients with functional dyspepsia and reflux-related disorders, while promoting the digestive process.

Abstract: Central venous pressure (CVP) has long been a cornerstone of hemodynamic monitoring, traditionally interpreted as a surrogate of intravascular volume and cardiac preload. However, current physiological and clinical evidence clearly demonstrates that CVP does not assess volume status and does not reliably predict fluid responsiveness (FR). Ac-cordingly, its role as a target for guiding fluid therapy has been progressively aban-doned. This narrative review retraces the evolution of CVP interpretation, from its physiological foundations to its role in contemporary clinical practice. While early re-suscitation strategies relied on predefined CVP thresholds, this approach has been abandoned. Despite these limitations, CVP remains widely used due to its simplicity and historical familiarity. Importantly, modern perspectives redefine CVP not as a static in-dicator of volume status, but as a valuable marker of systemic venous congestion and right ventricular load. In this context, CVP retains clinical utility when used for waveform interpretation, assessment of venous congestion, and, most importantly, as part of an integrated, multimodal hemodynamic monitoring strategy.

Abstract: Time-domain dynamic full-field optical coherence tomography (D-FFOCT) is a powerful label-free imaging modality that enables functional visualization of cellular activity in living tissues with subcellular resolution. However, its sensitivity remains a major limitation for imaging highly scattering three-dimensional (3D) biological models such as retinal organoids, where incoherent background and inefficient optical flux distribution reduce dynamic contrast and limit imaging depth. In this work, we introduce a ratio-free optical configuration for time-domain D-FFOCT that enables continuous tuning of the sample-to-reference field ratio while minimizing photon losses and suppressing parasitic reflections. This polarization-based architecture allows optimal redistribution of optical flux according to sample scattering conditions and improves sensitivity under both power-limited and dose-limited conditions. Compared with conventional non-polarizing beam splitter configurations, the proposed approach provides a √ 2-fold (3 dB) sensitivity improvement through optical optimization alone. In addition, we investigate for the first time the use of partial field illumination (PFI) in time-domain D-FFOCT to reduce incoherent background arising from multiple scattering. In retinal organoids imaged at 120 µm depth, PFI yields up to a 14.5-fold (23.2 dB) increase in dynamic signal sensitivity, while preserving functional contrast. When combined, ratio-free detection and PFI provide a cumulative sensitivity improvement of 20.5-fold (26.2 dB). These gains enable improved visualization of photoreceptor precursor organization, rosette structures, and Müller glial cell dynamics in both 3D retinal organoids and 2D cell cultures. This work establishes a practical framework for sensitivity optimization in D-FFOCT and expands its potential for functional imaging, disease modeling, and live-cell monitoring in complex biological systems.

Abstract: Lipedema is a painful, chronic and progressive disorder of subcutaneous adipose tissue characterized by disproportionate, symmetrical fat accumulation in the extremities—typically the legs and less often the arms—while sparing hands and feet. It is clinically distinct from obesity and lymphoedema, affects almost exclusively women, and often exacerbates during hormonal transition phases. This paper proposes a unifying pathophysiological concept in which lipedema reflects a regenerative imbalance of adipose tissue. A genetically and estrogen-modulated increase in endothelial permeability (“leaky vessels”) is suggested to activate perivascular/mural adipose-derived stem cells (ADSCs), thereby initiating coupled angiogenesis and adipogenesis. The stromal vascular fraction (SVF) is described as a central mediator, with SVF-derived extracellular vesicles and characteristic microRNAs promoting adipocyte hyperplasia and hypertrophy and leading to large, metabolically less active adipocytes. The organism attempts to counterbalance this surplus through inflammatory activation of mast cells and macrophages; however, inefficient clearance of excess adipocytes (including “crown-like” structures) sustains inflammation and pain. Progressive adipose expansion may compress lymphatic capillaries and precollectors, resulting in dermal and subdermal lymphatic congestion and contributing to oedema and symptom progression. Increased aromatase activity and local estrogen availability are discussed as additional amplifiers of adipogenesis and inflammatory remodeling. Finally, lymphatic-sparing liposuction is outlined as a mechanistically plausible intervention that can reduce tissue pressure, improve lymphatic drainage, and alleviate key symptoms.

Abstract: Only redshifted, and not blueshifted, cosmological signals are observed. Yet, redshift alone does not distinguish the past lightcone of an expanding Universe from the future lightcone of a contracting one. In practice, the identification of the observed redshifted branch with the observational past is set primarily by electromagnetic radiation, whose retarded character is independently established in controlled physics, albeit over non-cosmological scales. From that perspective, the observed cosmological arrow is not separable from the causal/radiative prescription used to interpret the signals. This effective entanglement between the cosmological and the radiative arrows should nevertheless be distinguished from the notion of arrow used in the present work. Here instead, the relevant arrow is not thermodynamic but kinematic; it is defined by the symmetry or asymmetry of background lightcone observables under ξ↔−ξ – where ξ≡ln(1+z) and z is the redshift – a criterion motivated directly by the time-reversal-symmetric special-relativistic longitudinal Doppler shift. Equivalently, the arrow considered here is the observed redshift/blueshift asymmetry of cosmological lightcone signals; retarded observations of an expanding FRW Universe are in the redshifted branch, whereas the opposite rapidity orientation would correspond to the blueshifted branch. This naturally suggests using rapidity-reversal symmetry as the redshift-space no-arrow condition when passing from SR to Friedmann–Robertson–Walker (FRW) cosmology, where the empty Milne Universe is a bridging borderline case. In fact, the viewpoint advocated here is that ξ-symmetry/asymmetry is more fundamental than t-symmetry/asymmetry simply because the former is more readily related to cosmological observables. It is shown here that generic non-empty FRW Universes possess an intrinsic ξ-asymmetry already at the background level, independently of entropy, coarse-graining, structure growth, or a Past Hypothesis.

Abstract: Machine learning and deep learning models trained on a source domain often suffer from performance degradation when deployed to new target domains due to domain shifts arising from differences in data distributions, acquisition conditions, or temporal variations. Domain adaptation addresses this issue by transferring knowledge from labeled source data to unlabeled target data. However, acquiring labels for target-domain samples is often costly or impractical in real-world applications. To improve label efficiency, active domain adaptation (ADA) and active continual learning (ACL) integrate active learning strategies into domain adaptation and continual learning frameworks. ADA selectively queries informative target samples to enhance adaptation performance, while ACL extends this paradigm to sequential settings, enabling models to adapt to evolving data streams while mitigating catastrophic forgetting. This survey provides a systematic review of ADA and ACL, focusing on their advances and applications. We further examine extensions of ADA such as source-free ADA, integration with semi-supervised learning, and advanced techniques for handling challenging adaptation scenarios. In addition, we summarize applications across computer vision, medical imaging, robotics, natural language processing, scientific and engineering tasks. Finally, we discuss open challenges and future directions, including robust adaptation under complex distribution shifts and reliable semi-supervised adaptation.

Abstract: Additive manufacturing using vat photopolymerization (VPP) resin materials has gained attention for fabricating dental prostheses; however, the effects of material type and build angle on their properties remain unclear. We compared the mechanical properties of two filler-containing VPP hybrid resins, SprintRay Ceramic Crown (CC) and OnX Tough 2 (OT), with those of a conventional polymethyl methacrylate (PMMA) disc material, and evaluated the influence of build angle on surface characteristics, dimensional accuracy, and mechanical performance. Specimens were fabricated using a DLP system at build angles of 0°, 45°, and 90°. Vickers hardness, surface morphology and roughness, dimensional deviations, flexural strength, elastic modulus, and fracture energy were assessed according to relevant standards. CC exhibited significantly higher hardness and elastic modulus than PMMA and OT, whereas OT showed the highest fracture energy. Surface morphology and roughness were strongly affected by build angle, with 45° producing distinct periodic patterns and increased roughness. Dimensional evaluation revealed a tendency toward overbuilding, particularly in the vertical direction at 45°. Flexural properties were also influenced by build angle, with 45° generally providing favorable performance. Both material composition and build angle affect VPP-fabricated dental resin performance, highlighting the importance of appropriate material and processing selection for clinical applications.

Abstract: Drill bits can be one of the toughest components to maintain when working with CNC systems because of their unique geometries and slow wear of the tools themselves. When measuring wear on drill bits, it’s important to consider the impact tool wear can have on the drill's accuracy, the smoothness of the surfaces created, and the overall efficiency of the machining process. The wear of drill bits is a common occurrence and a normal part of the machining process. This paper seeks to address these challenges by implementing a classification framework for tool wear in CNC drill bits that utilises the Synchrosqueezed Wavelet Transform (SSWT) and the Vision Transformer (ViT). During controlled drilling experiments, Acoustic Emission (AE) signals were captured for each of the following tool conditions: Healthy Tool (HT), Low Wear (LW), Medium Wear (MW), and Severe Wear (SW). In this study, the wear of drill bits was measured and created artificially, with Electrochemical Machining (ECM) for drill bits of sizes 3.0 mm, 3.2 mm, 3.4 mm, 3.6 mm, and 3.8 mm. A system by National Instruments (NI) was used for data acquisition, and LabVIEW was used to acquire a set of data with high resolution and time-frequency representation developed with the SSWT method, which is designed for drill bit wear measurement. These features were captured in the SSWT time-frequency maps, which were used as input to a Vision Transformer that enables efficient capture of global relationships in the time–frequency domain. Unlike traditional convolution-based methods, the proposed transformer-based framework allows for automated multi-domain fusion and feature learning. During experiments with 10-fold cross-validation, the proposed SSWT-ViT framework demonstrated reliable generalisation, strong robustness, and high classification accuracy across varying wear states. Thus, the proposed method is appropriate for intelligent real-time monitoring of CNC drill bit conditions in an industrial setting.

Abstract: An elementary and self-contained approach to the Euler–Mascheroni constant γ is presented, based solely on Simpson's quadrature rule and the convexity of the function \( f(x)=1/x \). By introducing Simpson-type weighted harmonic sums, local logarithmic increments are approximated by simple finite linear combinations of reciprocal integers. Sharp two-sided inequalities, derived from monotonicity and convexity, yield explicit control of the quadrature error and provide a purely numerical proof of the classical limit defining γ, without recourse to the Euler--Maclaurin summation formula. A key structural outcome of this framework is a decomposition \( \gamma = \log [2] - \frac{1}{3} + \delta \), where the constant δ arises naturally as the limit of a rational sequence associated with Simpson-regularized harmonic sums. The resulting sequence converges significantly faster than the classical definition of γ, and its convergence is explained by the cancellation of dominant error terms. This work highlights an unexpected connection between elementary numerical quadrature and one of the fundamental constants of analysis.

Abstract: Hypertrophic Cardiomyopathy (HCM) is one of the most common inherited cardiomyopathies and remains an important cause of ventricular arrhythmias and Sudden Cardiac Death (SCD), particularly in younger individuals. Although the annual incidence of arrhythmic death is relatively low in contemporary cohorts, identifying those patients who may benefit from primary prevention with an Implantable Cardioverter-Defibrillator (ICD) remains a major clinical challenge. Current risk stratification strategies rely on two principal paradigms. The European approach is centered on the HCM Risk-SCD score, a multivariable model that provides an individualized 5-year risk estimate, whereas the American approach is mainly based on major clinical risk markers. Both strategies have important strengths and limitations, reflecting the persistent difficulty of accurately predicting arrhythmic events in such a heterogeneous disease. The HCM Risk-SCD score has demonstrated robust external validation and high specificity for identifying patients at higher risk, but it may fail to recognize some vulnerable individuals who remain below conventional treatment thresholds. For this reason, several additional risk modifiers have gained increasing relevance in contemporary practice. Among them, extensive late gadolinium enhancement, left ventricular systolic dysfunction, apical aneurysm, and clinically meaningful genetic findings may provide important incremental prognostic information beyond traditional models. Emerging disease-modifying therapies may also influence future risk assessment. In particular, Mavacamten has shown substantial reduction of left ventricular outflow tract obstruction together with favorable reverse remodeling, including changes in variables incorporated into conventional risk scores. However, whether these improvements translate into a true reduction in SCD risk remains uncertain. Importantly, the decision to implant an ICD should not depend on numerical risk alone. It should arise from a process of shared decision-making integrating estimated risk, treatment burden, competing comorbidities, age, lifestyle, and patient values. In this context, the concept of an individualized threshold of “acceptable risk” becomes central. In conclusion, prevention of SCD in HCM is moving beyond conventional scores toward a personalized and dynamic framework in which predictive tools, advanced phenotyping, evolving therapies, clinical expertise, and patient preferences are combined to guide individualized care.

Abstract: The olive ridley turtle (Lepidochelys olivacea) is the second smallest and most abundant of the seven sea turtle species worldwide, currently distributed across approximately 80 countries. However, due to various anthropogenic and environmental pressures, its populations are declining and categorized as "Vulnerable" by the IUCN. This study describes the post-mortem macroscopic and microscopic detection of spirorchiids and associated lesions in six adult female olive ridleys stranded along the Northern and Central-Northern Chilean coast between November 2024 and January 2026. Macroscopic findings primarily revealed alterations in the gastrointestinal, reproductive, and vascular systems, characterized by transmural granulomatous lesions and mucosal thickening. Histopathological analysis confirmed the presence of these cryptic parasites in multiple organs, including the intestine, reproductive tract, vasculature, liver, spleen, and adrenal glands, with varying degrees of severity. These findings confirm the presence of spirorchiidiasis in olive ridley turtle in Chile, which may be directly or contributorily associated with stranding and mortality events. Molecular characterization is essential to determine whether this agent corresponds to a known species or represents a novel cryptic parasite taxon in the South-Eastern Pacific.

Abstract: Sickle cell disease (SCD) is one of the most common inherited blood disorders worldwide. Clinical manifestations are variable, but include hyposplenism, renal impairment, cardiovascular disease, respiratory complications, and cerebrovascular disease. Frequent painful vaso-occlusive crises, hospitalisations, and other physical and psychological ramifications can have profound effects, including children missing school time resulting in impaired academic performance and adults missing work leading to employment loss. This review examines the possible risks and benefits of exercise in the SCD population. Regular exercise plays an important role in improving physical and mental health, but fears around the potential consequences of exercise for the SCD population are present in children, their families, schools, and other organisations. This can result in children not taking part in as much regular exercise as their peers and being excluded from group activities. Studies have suggested that healthcare professionals are often not discussing possible benefits of physical exercise with patients, likely as there are no guidelines regarding a safe level of activity. An acute increase in inflammation secondary to exercise could increase the risk of vaso-occlusive crises, but regular physical activity is known to play an important role in disrupting chronic inflammation across a wide range of pro-inflammatory diseases. Indeed, studies have demonstrated positive responses to exercise in the SCD population, from improvements in skeletal muscle microvasculature to performance in cardiovascular tests. It is important that recommendations are developed regarding types of exercise and the ideal amount of exercise for maximum benefit with minimum risk in SCD individuals.

Abstract: Automated cephalometric landmark detection using deep learning has the potential to transform routine orthodontic diagnosis. However, the clinical relevance of AI localization accuracy depends critically on how detection errors propagate into derived angular measurements and skeletal classifications. This study presents a systematic clinical validation of 14 YOLO-based model configurations, evaluating the effects of architecture (YOLOv5/YOLOv11), bounding box size (40-150 px), dataset scale (235-4255 images) and training duration on landmark detection accuracy with specific focus on the four clinically critical landmarks that define the ANB angle: Sella (S), Nasion (N), A-point (A) and B-point (B). The best-performing model (YOLOv11s, 40×40 px bounding box, 4255 training images) achieved a mean radial error of 3.10 ± 1.00 mm and a Successful Detection Rate of 87.2% at the 4 mm threshold for S, N, A, and B. Despite this error magnitude, ANB-based skeletal classification demonstrated 96.9% concordance with expert assessments (95% bootstrap CI: 93.8–99.2%, n = 130 classifications), with all discordances confined to borderline cases within 1^◦ of diagnostic thresholds. Notably, the localization accuracy achieved by the best AI models falls within the inter-operator variability range reported for experienced human clinicians (1.5–3.5 mm), indicating that the AI system has reached a threshold of clinical equivalence for skeletal classification purposes. Bounding box size emerged as the single most influential hyperparameter, with a 3.4-fold increase in mean radial error from 40×40 to 150×150 px configurations. These findings support the clinical deployment of YOLO-based AI systems for automated ANB-based skeletal classification, while highlighting the need for human oversight in borderline cases.

Abstract: In this study, a six-degree dynamic model considering torsion and bending is proposed for a single-stage spur gear reducer. The objective is to study the effect of progressive pitting on the dynamic behavior of the system. The evolution of mesh stiffness over time is modeled using an energy-based approach that takes into account the geometric characteristics of pitting defects, including their depth, width, and location on the gear teeth. The equations of motion are obtained using the Lagrangian method and subsequently solved numerically using the Runge-Kutta scheme. Vibration responses are analyzed in the time, frequency, and time-frequency domains for both healthy and damaged gears. The results show that the onset of pitting leads to a significant loss of stiffness, amplitude modulation, and the appearance of spectral sidebands near the mesh frequency. A quantitative parametric sensitivity analysis reveals that the apparent contact velocity plays a predominant role at low speeds and in the early stages of damage. In contrast, at high speeds and advanced degradation levels, pit depth and width become dominant. The proposed methodology provides valuable comprehension into the propagation mechanisms of pitting faults and offers practical guidance for early failure detection and condition-based maintenance of gear drive systems.