Abstract: The evolution of non-invasive mechanical ventilation (NIV) from the iron lung of the 1950s to the use of sophisticated ventilators with mask apparatus has allowed for the optimal management of a wide range of respiratory disorders. NIV is now a mainstay in the management of acute, chronic and acute on chronic hypoxemic and hypercapnic respiratory failure from diverse etiologies. While NIV offers an effective approach to avoid invasive mechanical ventilation with its inherent risks of lung injury and sedation related harms; it is a complex modality that requires a nuanced approach to management [1]. As the use of NIV has become ubiquitous, complex challenges are faced in the initiation, management and discontinuation of the treatment. We review complex clinical scenarios that present during liberation from non-invasive mechanical ventilation and an approach to successful weaning and liberation in these patient populations.

Abstract: The complement system is a central component of innate immunity with established roles in host defense and emerging functions in neurodevelopment, synaptic remodeling, and neuroimmune communication within the central nervous system (CNS). In parallel, advances in nanotechnology have enabled targeted strategies for CNS drug delivery but have also revealed that many nanomaterials interact with and activate complement, influencing biodistribution, safety, and inflammatory responses. Opioid use disorder (OUD) is increasingly recognized as a condition associated with chronic neuroimmune dysregulation involving glial activation, altered cytokine signaling, and blood-brain barrier (BBB) disruption. Although relatively few studies have directly measured complement activation in OUD, emerging transcriptomic, cellular, and inflammatory data suggest that complement pathways may intersect with opioid-induced neuroimmune signaling. This review synthesizes current knowledge at the intersection of complement biology, nanomedicine, and opioid-associated neuroimmune changes. It distinguishes well-established mechanisms of complement activation by nanomaterials from emerging evidence linking complement signaling to opioid exposure. It integrates complement pathways with opioid receptor and Toll-like receptor 4 (TLR4) signaling in glial cells and endothelial compartments, and discusses both beneficial and pathological roles of complement in the CNS. Finally, the therapeutic potential and limitations of complement-aware nanotechnology and complement modulation in CNS drug delivery and addiction neuroscience are outlined to guide translation of complement-targeted nanomedicines in addiction neuroscience.

Abstract: In people with dementia, cognitive stimulation, learning, and meaningful activities do not constitute disease-modifying therapies that directly alter neurodegenerative pathology such as brain atrophy or amyloid/tau accumulation. However, reduced daytime activity, disengagement, apathy, and social withdrawal are consistently associated with cognitive decline, deterioration in activities of daily living (ADL), behavioral and psychological symptoms of dementia (BPSD; e.g., depression, irritability, agitation), increased caregiver burden, and a higher likelihood of hospitalization or institutionalization. Therefore, learning and leisure activities should be positioned not as “brain-training interventions” but as foundational interventions aimed at suppressing inactivity and disengagement, which function as “progression-accelerating factors” (Robert et al., 2009; Brodaty & Burns, 2012).Many conventional cognitive training and learning interventions implicitly assume preserved comprehension, memory, task performance, and tolerance for evaluation, making them difficult to implement in real-world dementia care settings. This paper decomposes existing evidence (including Cognitive Stimulation Therapy, CST) into “active ingredients” and “excessive burdens,” and proposes an implementation-adaptive minimal model consisting of: (1) 10–20 minutes per day of meaningful activity (including leisure activities); (2) a level of difficulty that ensures successful experiences; (3) interpersonal elements when feasible; and (4) the removal of evaluation, correct-answer demands, and self-management requirements.The value of learning should be assessed not by maximizing cognitive test scores, but by outcomes such as suppression of apathy, depression, and BPSD, maintenance of daytime activity and ADL, and prevention of caregiving breakdown and hospitalization.

Abstract: Vitamin D resistance describes a spectrum of conditions in which individuals fail to achieve expected biological responses to vitamin D despite supplementation and/or apparently adequate serum 25-hydroxyvitamin D [25(OH)D] concentrations and sun exposure. While rare hereditary forms such as Hereditary Vitamin D-Resistant Rickets (HVDRR) are well-characterized, emerging evidence suggests that acquired resistance may contribute to suboptimal responsiveness in a broader clinical population. Contributing factors include genetic variation in vitamin D metabolism and receptor pathways, chronic inflammation, metabolic dysregulation, micronutrient cofactor insufficiencies, and environmental exposures. This review synthesizes current understanding of vitamin D resistance mechanisms, diagnostic challenges, and implications for personalized supplementation strategies. We propose an operational definition of vitamin D resistance as a state of inadequate physiological response to vitamin D despite achieving conventionally sufficient 25(OH)D levels, best assessed using response-based markers such as PTH suppression, calcium handling, and clinical endpoints. We further outline a pragmatic, systems-based evaluation framework that incorporates endocrine, inflammatory, metabolic, medication-related, and micronutrient determinants to guide individualized dosing and monitoring.

Abstract: Environmental factors in the daily lives of people with dementia are not disease-modifying agents that directly influence neurodegenerative pathology. However, inadequate lighting, reduced nighttime visibility, complex pathways, excessive sensory stimulation, and unpredictable environmental changes frequently trigger delirium, nighttime agitation, falls, sleep fragmentation, and behavioral and psychological symptoms of dementia (BPSD). These in turn significantly accelerate disease progression, leading to increased rates of hospitalization, institutionalization, and caregiving breakdown.Many existing environmental improvement strategies are based on architectural ideals or comprehensive design theories, often lacking sufficient consideration for feasibility or sustainability in home or care settings. The aim of this paper is to redefine environmental interventions for people with dementia not as a form of treatment, but as a method to control progression-accelerating factors. By decomposing existing guidelines and environmental design research into "core active ingredients" and "excessive cognitive or operational burdens," we propose a minimal intervention model that can be sustainably implemented in real-world care settings.From an integrated review of the literature, we identify three core environmental intervention components for dementia care: (1) lighting that provides clear temporal cues for day and night; (2) simplified and visible nighttime pathways; and (3) optimization of sensory input, particularly through reduction of noise and unpredictable stimuli. These components do not halt disease progression, but they serve as a highly practical foundation for non-pharmacological interventions by mitigating acute deterioration events such as delirium, falls, BPSD, and hospitalization. This paper presents a model that organizes these relationships into a cascade of progression accelerators and proposes a feasible environmental intervention framework.

Abstract:

We demonstrate that the Dark Matter (DM) hypothesis, central to the ΛCDM cosmological model, represents a theoretically redundant construct when analyzed within the New Subquantum Informational Mechanics (NMSI) framework. Through systematic analysis of all major phenomena attributed to DM—galactic rotation curves, gravitational lensing, large-scale structure, cosmic microwave background acoustic peaks, and cluster dynamics—we show that coherent informational mechanisms provide complete explanations without invoking invisible, undetectable matter. The NMSI framework posits information, not energy, as the fundamental substrate of physical reality, manifesting through a π-indexed Riemann Oscillatory Network (RON) that couples to baryonic matter via a Plasmatic Oscillatory Network (PON). At galactic scales (PON-G), electromagnetic coupling through Maxwell stress (T_rφ = -B_r B_φ/μ₀) with fields B ~ 0.2-1 μG naturally produces observed flat rotation curves without additional mass. At cosmological scales (PON-C), effective informational geometry (Φ_eff = Φ_baryon + Φ_info) explains gravitational lensing anomalies, while RON eigenmodes account for cosmic web structure following Gaussian Unitary Ensemble (GUE) statistics rather than hierarchical collapse. Critical to our analysis is the empirical failure of DM detection: despite over 30 years and 100+ independent experiments (LUX, XENON1T, PandaX-4T, LHC, Fermi-LAT), zero robust detections have been achieved, yielding a statistical probability P(DM exists | observations) → 0. Moreover, DM theory exhibits infinite post-factum adjustability—requiring different properties (collisionless vs. self-interacting, cold vs. warm, NFW vs. Burkert profiles) at each scale—characteristic of epicyclic constructs rather than fundamental physics. We present seven falsifiable differential predictions testable in the 2025-2035 timeframe: (1) Cross-correlation between lensing convergence and Faraday rotation (C_κ,RM > 0.3σ_κσ_RM, Euclid×SKA 2027-2030); (2) Hubble parameter anisotropy with dipole |a₁₀| ~ 0.02-0.05 (Pantheon+/DESI 2025-2027); (3) GUE spacing statistics in cosmic web structure (Euclid catalog 2027); (4) Temporal decay of residual lensing in post-merger clusters with τ ~ 0.5-2 Gyr (Bullet Cluster follow-up 2027-2037); (5) Abundant mature galaxies at z > 14-15 from rapid RON mode activation (JWST Cycles 4-6, 2025-2027); (6) Non-standard H(z) evolution (DESI BAO 2029-2030); (7) Rotation curve variability in post-merger galaxies correlated with magnetic field reorganization (archival HI analysis 2025-2027). Recent observations already favor NMSI: JWST detection of massive galaxies at z ~ 10-13 contradicts ΛCDM hierarchical formation but naturally emerges from rapid informational mode activation; persistent Hubble tension (H₀^CMB = 67.4 vs. H₀^SNe = 73.2 km/s/Mpc, 5.8σ) resolves if H is emergent and scale-dependent rather than universal; hints of H anisotropy (Bengaly+ 2023, ~3σ) align with NMSI predictions. The Bullet Cluster, traditionally cited as definitive DM evidence, is reinterpreted through persistent RON informational memory (τ_relax ~ Gyr) rather than collisionless particles. From an ontological perspective, NMSI achieves decisive economy via Occam's Razor: ΛCDM requires four fundamental unknowns (DM + dark energy + inflaton + fine-tuning) comprising ~95% of cosmic energy budget, while NMSI derives all observations from a single substrate (informational RON → emergent baryons + emergent geometry). Methodologically, NMSI generates a priori testable predictions, whereas DM functions as an infinitely adjustable parameter—the modern equivalent of Ptolemaic epicycles. We conclude that Dark Matter was a necessary theoretical artifact in an era lacking concepts for information as fundamental substrate. NMSI provides a complete, falsifiable, economical framework rendering DM obsolete. If three or more of our seven differential tests confirm NMSI predictions (probability ~60-70% based on current hints), a paradigm shift from ΛCDM to informational cosmology becomes inevitable. This work thus marks a critical juncture: the transition from undetectable entities to testable informational architecture as the foundation of cosmic structure.

Abstract: Background/Objectives: Chemsex is defined as the intentional use of psychoactive substances to enhance or prolong sexual activity, predominantly observed among men who have sex with men. It has emerged as a notable behavioral and public health concern due to its association with high-risk sexual practices, psychiatric morbidity, and somatic complications. Despite increasing recognition, global prevalence estimates vary widely (3–52.5%) due to differences in study populations and methodology. Commonly used substances include synthetic cathinones, amphetamines/methamphetamines, MDMA, GHB/GBL, ketamine, alkyl nitrites, and PDE-5 inhibitors. Methods: A narrative review was conducted using PubMed through December 11, 2025. Search terms combined chemsex-related terminology, substance names, and health outcomes. Recent English-language publications (2020-2025) were prioritized. Evidence was synthesized thematically across epidemiology, health complications, motivations, and interventions. Results: Chemsex is strongly associated with unprotected sex, multipartner encounters, and prolonged intercourse, leading to significantly increased rates of HIV, syphilis, gonorrhoea, and chlamydia. Psychiatric complications include depression, anxiety, compulsive sexual behavior, and psychosis, with higher risks in individuals engaging in slamming or polysubstance use. Somatic complications vary by substance and include cardiovascular disease, hyponatremia, rhabdomyolysis, ulcerative cystitis, methemoglobinemia, and overdose. Motivational factors extend beyond sexual enhancement and include minority stress, internalized and externalized stigma, and maladaptive coping mechanisms. Integrated interventions combining harm reduction, cognitive-behavioral therapy, peer-led services, and pharmacotherapy, alongside digital health tools to support PrEP adherence and risk reduction, show promise in mitigating these harms. Conclusions: Chemsex represents a complex interplay of biological, psychological, and sociocultural factors that contribute to elevated STI risk and psychiatric and somatic morbidity. Addressing chemsex requires destigmatized, multidisciplinary approaches that integrate behavioral, pharmacological, and community-based interventions. Digital health innovations can further enhance engagement, risk reduction, and access to timely care.

Abstract: If the invariance of light speed is absolutely universal in covariant space rather than contra variant space, the following researches and conclusions on general covariance would be so far as to catch up with very high probabilities and reliabilities. As has been verified, it is. General covariance is tested controversial after the investigations on gravitational redshift and acceleration. Further inspections on differential geometry indicate the opportunities of inequality of mixed derivatives of bases for the transformations between Riemannian spaces that will then lead to failure of the classical equations of Christoffel symbols, which is one of the reasons that causes controversies on general covariance. Even the negative form of time metric could be proved to be false setting in that transformations do nothing with the negative sign inherited from that of Minkowski space. Nevertheless, after discussions on transformations between original spherical space, distance expressed spherical space and Cartesian space, it has been seen that the distance factors of a spherical space are improper to be employed the metrics in general relativity, instead of that, the concepts of gravitational metrics were suggested. In fact, Christoffel symbols and base derivatives both are valid methodologies for analysis in a non-Euclidean space. The concepts of trajectory derivatives were carried out to define the derivations on trajectory of matter’s motions that could help to revise those equations and calculations. Measurable experiments on gravitational redshifts and accelerations have been carried out to support the theoretical results. Conclusions have been drawn that light speed keeps general covariance in gravitational fields but light energy momentum would not, may as well, the motions of massive matters in gravitational fields do not perform general covariance thoroughly. It is impossible to geometrize the gravity effects of massive matters with position depending metrics in that the variable velocities cannot be eliminated thoroughly. Consequently, inferences on kinematics and relativistic release were carried out, which have been forcefully verified in applications. With the ingenious proposition of the concept of gravitational metrics, the so-called geodesic equations have been falsified to be kinematic equations anymore. The conservativeness of light angular momentum has been discovered in most surprising form. Renovated solutions for light rays as well as massive matters have been carried out that forcefully impact the traditional methodologies on kinematics of trajectory and time delay because they are the correct interpretations of the realities. It should be highlighted that the exponential mass expressions could completely demonstrate energy variations in gravitational fields that help to create more general dynamic equations, especially that could lead to an irrelativistic solution of planet perihelion precession. In contradiction proof, the traditional solution must involve errors. Newtonian ballistic method was put forward to make numerical analyses on close-to-light-speed motions, and the invalidity of that method on light propagation could be seen as another support to the conclusions and inferences. Another forceful falsification on energy momentum conservativeness carried out in the discussions on the traditional treatment of time delay of close-to-light-speed particles, has thoroughly exposed the essential mistakes in the way of methodologies. Dynamic models of fluid planet rings were founded to interpret the evolutions of accretions of quasars and active galactic nuclei and the mechanism of relativistic release. The equation of relativistic release was developed after the conclusions and inferences. It is predicted that the peak release of an inflow is at 1.5 of gravitational radius and the peak luminosity of an accretion may locate at the position of about 1.33 of gravitational radius. Relativistic frequency shift interprets the mechanism of giant redshifts that predict the probability of observational redshifts might be up to a particularly higher level with respect to that have been observed in the past years. The width equations of emission and absorption lines indicate the mechanism and the positions of broad line regions and narrow line regions. It could be imagined that the relativistic emissions and relativistic absorptions with relativistic redshifts would have involved with fantastic mystery of intrinsic structures of matters that we know less.

Abstract: This paper introduces the concept of Algorithmic Energy as a fundamental quantity emerging from the algorithmic evolution of space–time. Building upon the Desmos (Bond) framework, interaction between physical systems is shown to be governed not by mass or force alone, but by energy states regulated through an evolving space–time scaling function. The proposed formulation replaces classical force-based interpretations of gravitation with an energy-driven bond model, capable of explaining local gravitational stability, cosmic expansion, and hierarchical dominance phenomena such as the Earth–Moon versus Moon–Sun system. Algorithmic energy unifies gravitational binding, spacetime curvature, and large-scale cosmological behavior within a single mathematical structure.

Abstract: We demonstrate that the fine structure constant alpha⁻¹ ≈ 137.036 emerges necessarily from the deepest mathematical structure of reality: the zeros of the Riemann zeta function zeta(s). We present an exact formula connecting alpha⁻¹ to the first four nontrivial zeros gamma_1, gamma_2, gamma_3, gamma_4 of zeta(1/2 + it). The derivation combines spectral theory of magnetic Schrodinger operators on hyperbolic surfaces, the Selberg-Gutzwiller trace formula, and arithmetic geometry. The resulting value matches the experimental CODATA 2018 value with precision 2.7 × 10⁻¹³. This establishes a profound connection between number theory and fundamental physics.

Abstract: The integration of artificial intelligence-powered predictive maintenance solutions in manufacturing plants is revolutionizing asset management by substantially reducing downtime and enhancing equipment efficiency. By utilizing sensor fusion combining data from multiple sources such as vibration, temperature, and pressure sensors with advanced machine learning algorithms, manufacturers are able to continuously monitor machine health and forecast potential failures long before they occur. This data-driven strategy shifts maintenance from a reactive or scheduled paradigm to a proactive and dynamic process, resulting in significant cost savings, optimized resource allocation, and greater operational reliability. As a result, the adoption of these technologies supports the strategic goals of Industry 4.0, paving the way for smart manufacturing environments characterized by resilient, efficient, and autonomous operations.

Abstract: Skyjo is a simple stochastic card game with partial information, local replacement decisions, and score-reducing column removal events. This paper develops a formal mathematical model of the game, derives expected-score rules for turn-level actions, proves several dominance and threshold results, and evaluates a family of heuristic strategies through Monte Carlo simulation. The focus here lies on local optimality under explicit belief assumptions rather than a full equilibrium solution of the multiplayer game. Finally a simulation code is provided for reproducibility.

Abstract: Nica and Sprague [\textit{Am. Math. Mon., 2023}] derived a non-Archimedean version of the Gershgorin disk theorem. We derive a non-Archimedean version of the oval (of Cassini) theorem by Brauer [\textit{Duke Math. J., 1947}] which generalizes the Nica-Sprague disk theorem. We provide applications for bounding the zeros of polynomials over non-Archimedean fields. We also show that our result is equivalent to the non-Archimedean version of the Ostrowski nonsingularity theorem derived by Li and Li [\textit{J. Comput. Appl. Math., 2025}].

Abstract: Nanoscale conductors and interfaces exhibit anomalous AC transport and enhanced superconducting critical temperatures that extend beyond conventional electron-phonon descriptions. We propose a complementary mechanism arising from the inertial response of a $\mathbb{Z}_3$-graded vacuum sector to time-varying electromagnetic fields. In-medium renormalization softens TeV-scale vacuum modes into low-energy collective excitations at surfaces and interfaces, introducing a characteristic response time $\tau_{\rm vac}$. This vacuum inertia modifies the effective conductivity, leading to frequency-dependent features such as high-frequency skin depth saturation, non-monotonic surface resistance, and enhanced macroscopic quantum coherence in nanostructures. Quantitative, ab initio predictions for skin depth plateaus, loss spectrum characteristics, and critical dimension effects on nanowire $T_c$ are derived and found to be consistent with experimental observations in high-purity metals and interface superconductors. The framework provides a unified perspective on these mesoscopic anomalies, bridging algebraic high-energy structures with low-energy quantum materials phenomena.

Abstract: The Earth flyby anomaly—a small, unexplained residual in spacecraft velocity—remains a persistent challenge in astrodynamics. While the empirical Anderson relation captures the general trend of reported anomalies, it does not account for the suppressed or near-null results observed in several later flybys. Here we construct a geometry-aware, Earth-fixed coupling proxy based on distance-weighted surface visibility over a land--sea distribution mask. We identify a robust sign structure across the primary flyby set that remains stable under variations in weighting choice and integration window. The results indicate that Earth-fixed asymmetry acts as a modulation of the Anderson prediction rather than as an independent force, offering a potential pathway for reconciling discrepancies in anomaly magnitude.

Abstract: Injection molding is widely used for plastic parts, but its performance is limited by the cooling stage, which dominates cycle time and affects dimensional stability and energy consumption. Conformal cooling channels, which can be manufactured using additive technologies, improve thermal efficiency but introduce a high-dimensional design problem. This work proposes an integrated methodology for optimizing injection molds with conformal cooling channels that combines parametric CAD, simulation, nonlinear principal component analysis, artificial neural network, and multi-objective evolutionary optimization. The workflow is applied to a case study with five cooling layouts. An initial set of 36 metrics related to temperature gradients, warpage, shrinkage, and energy is reduced to a small number of latent objectives, simplifying the search space while preserving the main physical trends. Artificial neural networks surrogates accurately reproduce numerical results, enabling exploration of the design space at a fraction of the computational cost. The optimization yields diverse Pareto-optimal solutions that balance cycle time, dimensional stability, and energy consumption, assisting the design of more sustainable injection molds. Sensitivity analysis identifies mold temperature and channel position/diameter as key design levers. The proposed methodology reduces dependence on expensive simulations and is readily transferable to industrial mold design.

Abstract: Recently, when forming radar video frames for surface mapping, group-interacting compact onboard radar systems (CORS) are increasingly being utilized. In this context, for the cooperative functioning of the group, each compact radar should use its own unique marked signal as the probing signal. This signal must be distinguishable in the common channel and should not destructively affect the probing signals emitted by other radars within the group. This organization allows for associating the marked signals reflected from the underlying surface with specific CORS in the group. This requirement arises from the fact that each compact onboard radar in the group emits a single probing signal and then receives all the reflected signals from the surface that were emitted by the other CORS in the group. Such an organization of the group-based system of technical vision requires the search for and study of specialized marked code structures used for phase modulation of probing signals to identify them in the shared radar channel. The study focuses on the search for new complex M-sequences with lower sidelobe levels of the normalized autocorrelation function compared to traditional M-sequences. This is achieved by replacing the traditional alphabet of positive and negative ones with an asymmetric set consisting of complex numbers. Using numerical methods and computer simulations, optimal complex values of the sequence with a minimum level of sidelobes in the autocorrelation function are determined. In addition to correlation properties, the phase-modulated signals generated based on the new marked sequences are also investigated. The results obtained open up new possibilities for the construction of a group-based technical vision system, enabling cooperative surface probing with each CORS in the interacting group.

Abstract: Background: Influenza is a globally prevalent infectious disease caused by influenza viruses, affecting individuals across all age groups. Influenza vaccination is the most effective method for preventing influenza. Vaccine Effectiveness (VE) is used to assess the real-world effectiveness of vaccines. Currently, there is no data on the effectiveness of influenza vaccination in Wuhan. This study employed a test-negative case-control design to evaluate the VE of influenza vaccination in Wuhan during the 2024-2025 season. Methods: A test-negative case-control design was used. Patients presenting with influenza-like illness (ILI) who underwent influenza virus RT-PCR testing at outpatient or emergency departments of 41 medical institutions in Wuhan were selected and classified into case (influenza virus RT-PCR positive) and control (influenza virus RT-PCR negative) groups. Results: This study included 23,302 influenza virus RT-PCR positive cases and 99,424 negative controls. The overall adjusted VE was 35% (95% CI: 30%-40%). Among age groups, the adjusted VE was highest in adults aged 19-59 years and 60-69 years, at 63% (95% CI: 50%-73%) and 60.7% (95% CI: 46%-72%), respectively. The VE was relatively lower in children and adolescents aged 0.5-5 years and 6-18 years, at 25% (95% CI: 17%-33%) and 25% (95% CI: 14%-36%), respectively. Regarding vaccination strategy, the VE for vaccination in both consecutive seasons and vaccination in the current season only were similar, at 42% (95% CI: 28%-54%) and 40% (95% CI: 36%-45%), respectively, while VE for vaccination in the previous season only was 20% (95% CI: 14%-26%). Among vaccination months, protection was highest for vaccination in November, with a VE of 46.1% (95% CI: 36.4%-54.6%). Conclusions:Vaccination in both consecutive seasons and vaccination in the current season only provided better protective effectiveness compared to vaccination in the previous season only (42% vs. 20%). The protective effectiveness of influenza vaccination in November was superior to other months.

Abstract: Colon cancer represents one of the most prevalent malignancies globally, influenced by genetic mutations, environmental factors, and chronic inflammatory processes. Natural phytochemicals, particularly eugenol derived from Syzygium aromaticum (cloves), demonstrate selective cytotoxicity toward malignant cells while preserving healthy cellular integrity. This review synthesizes current evidence on eugenol's physicochemical properties, absorption kinetics, and molecular mechanisms underlying its anticancer efficacy in colorectal carcinomas. Eugenol's multitargeted action encompasses apoptosis induction, cell cycle arrest, suppression of inflammatory pathways, and inhibition of metastatic progression. Furthermore, nanotechnological encapsulation strategies have been explored to enhance bioavailability and pharmacokinetic stability. The present analysis consolidates preclinical findings, discusses clinical translation challenges, and identifies future research directions for eugenol as an adjunctive therapeutic agent in cancer management.

Abstract: We propose a solver-agnostic framework for analysing convergence in DSGE computation based on a single quadratic \emph{residual of sameness} measured in a fixed, calibrated norm. In the Deterministic Statistical Feedback Law (DSFL) view, an economic model is specified by a frozen defect representation and a declared symmetric positive definite ruler that aggregates equilibrium violations. Once this geometry is fixed, solver behaviour becomes a typed statement about the induced defect dynamics rather than an implementation-dependent notion of error. We show that standard DSGE solvers—time iteration, policy iteration, and Newton or quasi-Newton methods—can be analysed as residual-updating maps whose contraction properties yield explicit convergence envelopes, robust stopping rules under numerical forcing, and comparable rate diagnostics. A Gram-operator construction provides a single solver-agnostic contraction score and exposes non-normal transient amplification that eigenvalue diagnostics alone can miss. Numerical studies for a small New Keynesian model illustrate how the framework enables reproducible and interpretable solver comparisons within a single geometric language.