Abstract: Deepfake detection from images and videos has evolved from artifact-specific convolutional baselines toward more generalizable, cross-dataset, and foundation-model-based approaches. The current work focuses on the efficiency and informativeness of frame selection itself, while keeping the downstream detectors fixed. The study compares twelve frame-selection heuristics ranging from simple baselines to landmark-aware strategies. Four pre-trained detectors were included in the present quantitative comparison: Self-Blended Images (SBI), Frequency-Enhanced Self-Lendered Images (FSBI), Generative Convolutional Vision Transformer (GenConViT), and GenD. The results show that GenD achieved the strongest average detector-level performance, with a mean frame-mean AUC of 0.9464. The best single validated configuration is GenD, yielding an AUC value of 0.9607 and a balanced accuracy of 0.9133. FSBI and SBI reached mean AUC values of 0.8953 and 0.8935, respectively, while GenD was the best general candidate. For SBI, the best validation configuration is Landmark cluster with 32 selected frames. GenD achieves the best AUC at the level of selection strategy. The present work demonstrates that inference-time frame selection is an important component of video-only deepfakes under constrained inference budgets.

Abstract: Integration of lead zirconate titanate (PZT) films on metallic substrates is important for flexible piezoelectric devices, but achieving highly textured crystallinity without detrimental interfacial diffusion or oxidation remains challenging. In this work, PZT thick films (~1.3 μm) were deposited on titanium substrates using radio-frequency magnetron sputtering at 400 °C followed by rapid thermal processing at 640 °C for 2.5 min. A conductive LaNiO₃ buffer layer was introduced to promote nucleation of the perovskite phase and suppress interfacial degradation. The resulting PZT films on LNO/Pt/Ti substrates exhibit a strong (001) preferred orientation and dense micro-structure. The films show a large remnant polarization Pr of ~61 μC cm^-2 and a low coercive field E_c of ~56 kV cm⁻¹ at 60 V, together with dielectric constants ε_r of ~1350–1612 and dielectric loss tanδ ≤ 0.06 in the frequency range of 1 kHz–1 MHz. Patterned Pt/PZT/LNO/Pt/Ti cantilevers yield a transverse piezoelectric coefficient e_31,f of ~ –6.7 C m^-2, significantly outperforming reported piezoelectric films deposited on Ti. These results demonstrate that controlled nucleation and rapid thermal crystallization enable highly textured PZT films on reactive metallic substrates, providing a viable route for flexible piezoelectric MEMS devices.

Abstract: Purpose: To validate a deep learning algorithm for automated segmentation and quantitative assessment of the ellipsoid zone (EZ) and RPE–Bruch’s membrane (BM) complex in healthy and geographic atrophy (GA) eyes. Methods: In this retrospective study, SD-OCT volume scans from 30 healthy and 30 eyes with GA were analysed. NMI-Outer Retina Analyzer was used to segment the inner EZ, inner RPE, and outer BM. Average thicknesses of EZ-RPE, EZ-BM, and RPE-BM were calculated from volumes and across nine ETDRS sectors. Manual segmentations were corrected by two masked expert graders and were compared using ICC. Dice coefficients (DC), Pearson correlation, and absolute thickness differences were used to assess agreement between automated and manual segmentation. Heat maps were generated to visualize thicknesses. Results: Thirty healthy eyes and thirty GA eyes were included in the analysis. Mean EZ–RPE, EZ–BM, and RPE–BM thicknesses were 47.55 ± 6.75 µm, 69.49 ± 6.92 µm, and 21.94 ± 3.46 µm, in the healthy eyes and 15.65 ± 11.09 µm, 39.18 ± 23.28 µm, and 23.52 ± 16.21 µm in GA eyes respectively. The model demonstrated high segmentation accuracy, with mean DC of 0.998 in healthy eyes and 0.995–0.998 in GA eyes. In healthy eyes, differences between automated and manual measurements were minimal (1.42 ± 3.39 μm (2.98%) for EZ–RPE, 1.31 ± 3.18 μm (1.88%) for EZ–BM, and 0.67 ± 1.71 μm (3.05%) for RPE–BM) which is within 1.88-3.05% from the gold standard (manual corrections), whereas GA eyes showed greater variability (mean differences of 3.61 ± 8.62 μm (23.06%) for EZ–RPE, 4.28 ± 11.34 μm (10.92%) for EZ–BM, and 4.4 ± 10.45 μm (18.71%) for RPE–BM). Heat maps revealed increased variability at the junctional zone surrounding atrophy. Automated and manual measurements showed strong correlations across all sectors in GA eyes (r = 0.97 for EZ–BM, 0.96 for EZ–RPE, and 0.89 for RPE–BM). Conclusions: The NMI-ORA enables accurate, automated segmentation and quantification of outer retinal layers, with performance comparable to expert graders.

Abstract: Background:Cancer remains a major global health challenge, with treatment efficacy li-mited by drug resistance and adverse effects. Drug repurposing offers opportunities for novel anticancer strategies. This study evaluated the cytotoxic, antiproliferative, and pro-apoptotic effects of metformin and caffeine, alone and in combination, in human cancer cell lines, and their potentialinteraction mechanisms. Methods:Human cervical carcinoma (HeLa), lung adenocarcinoma (A549), and colorectal carcinoma (HT29) cell lines were treated with metformin (0.05–50 mM) and caffeine (0.5–5 mM), alone or combined, for 24 and 48 h. Cell viability and proliferation were assessed using Trypan Blue and sulforhodamine B (SRB) assays. Apoptosis was analyzed by Annexin V/propidium iodide flow cytometry, and p53 expression in HeLa cells was determined by ELISA. Statistical analysis was performed using one-way ANOVA with Tukey’s post hoc test. Results:Metformin induced dose- and time-dependent cytotoxicity in all tested cell lines, with the lowest IC₅₀ values observed in HeLa and A549 cells after 48 h (2.28 and 3.30 mM, respectively; p < 0.05). Caffeine showed moderate antiproliferative activity, with the strongest effects at 2.03 mM in HeLa and 2.01 mM in HT29 cells (p < 0.05). The combined treatment produced effects that varied depending on both the cell line and exposure time. At earlier time points, transient synergistic effects were observed in certain cell lines, particularly HeLa; however, these effects were not sustained over time. With prolonged exposure, the interaction shifted toward predominantly antagonistic effects, indicating a reduced overall efficacy of the combination compared to expected additive outcomes.Increased apoptosis and elevated p53 expression further support the activation of tumor-suppressive pathways. Conclusions:Metformin exhibits significant anticancer activity in vitro, supporting met-formin repurposing in oncology. However,the addition of caffeine does not uniformly enhance its efficacy and appears to exert context-dependent effects.Further in vivo studies are required to confirm its clinical relevance. Keywords:AMPK;Antitumor activity; Apoptosis; Caffeine; Cancer cell lines;Chou–Talalay method; Drug repurposing;Docking;Metfomin;Molecular docking; p53;

Abstract: The radio-wave method for monitoring bronchopulmonary function is attractive due to its simplicity of implementation and safety for patients. The achieved results in imaging the lung air-filling process were encouraging; however, they also revealed several limitations that hinder the development of the method as a diagnostic tool. This paper describes an improved setup for radio-wave monitoring of the breathing process, enabling the measurement of not only amplitude but also phase pulmonograms. The setup is based on the USRP device PlutoSDR and the GNU Radio framework. Using the Helmholtz equations, it was possible to separate the contributions to amplitude and phase variations in the pulmonograms into those associated with changes in lung size during breathing and those related to changes in relative permittivity due to lung aeration. The values of relative permittivity at selected measurement points may serve as a basis for developing diagnostic indicators of various bronchopulmonary diseases. The problem of selecting these measurement points is discussed, drawing an analogy with auscultation points, but focusing on locations that provide information about the lung air filling process. The estimated measurement accuracy indicates that a single breathing cycle is sufficient to determine the relative permittivity at each measurement point.

Abstract: With growing global REE demand, the investigation of cryptic clay-hosted rare earth element (REE) enrichment provides a better understanding of potential new prospects. This study is focused on novel REE enrichment (up to 1.38 wt.% TREO) identified in the regolith overlying the Doradilla Sn skarn prospect, northern New South Wales, Australia. The REE mode of occurrence was investigated through petrographic, field emission scanning electron microscopy (FE-SEM), micro-X-ray fluorescence (µ-XRF), and Laser Raman analyses. Secondary REE-bearing phosphate minerals are the dominant host of the REE in the regolith at Doradilla. The presence of water identified through Laser Raman confirms these minerals as rhabdophane-(La) (La(LREE,Ca)(PO₄)·_nH₂O), hosting most LREE, and churchite-(Y) (Y(HREE,Ca)(PO₄)·2H₂O), hosting most HREE. Through confirming the majority of REE being hosted in hydrated, and therefore, secondary minerals, this cryptic REE-enrichment is confirmed to be the result of secondary mineralization driven entirely by regolith-derived processes. This study highlights the importance of detailed mineral characterization in confirming the deportment of REEs in clay-hosted settings, and suggests that new protoliths (in this case a Sn skarn) have the potential to form significant, secondary REE enrichment in the overlying clay-hosted, regolith environment.

Abstract: Large language models (LLMs) are increasingly used to support writing, translation, reasoning, and consequential decision-making under the assumption that they improve judgment by expanding access to information and reducing human error. This article argues that such optimism overlooks a central psychological problem: LLMs do not engage neutral users, but motivated reasoners. In common patterns of use, people approach these systems with prior beliefs, directional goals, and a desire to reduce cognitive effort. They ask leading questions, search in preferred directions, and often stop once a fluent and coherent answer appears. Under these conditions, LLMs may function less as external correctives than as smart mirrors that reflect users’ assumptions back to them with the authority of machine objectivity. Drawing on research in judgment and decision-making, motivated reasoning, automation bias, processing fluency, and human–AI interaction, the article develops the concept of artificial confidence: an inflated sense of certainty sustained by the structure of the interaction rather than by the quality of the evidence. The paper concludes by outlining a research agenda for identifying when human–AI interaction improves judgment and when it amplifies bias and overreliance, erodes epistemic responsibility, and creates challenges for governance, oversight, and decision-making protocols in AI-augmented systems.

Abstract: The control of highly nonlinear, open-loop unstable dynamics is a prevalent engineering challenge, often benchmarked through Magnetic Levitation (Maglev) systems. While continuous-time adaptive neural networks are commonly used to reject disturbances, their direct digital implementation often induces closed-loop instability due to unaccounted sampling effects. To address this, this paper proposes a Discrete-Time Fourier Series Neural Network (FSNN) control architecture for nonlinear single-input single-output (SISO) systems that can be transformed into the Brunovsky canonical form. The parameter adaptation laws are synthesized strictly in the discrete-time domain using Lyapunov stability theory. This approach yields an explicit upper bound for the digital sampling period, ensuring a proper implementation. Furthermore, it guarantees the Uniform Ultimate Boundedness (UUB) of the tracking error in the presence of bounded unmodeled dynamics and periodic disturbances. Numerical simulations of Maglev dynamics validate the theoretical bounds, demonstrating that the FSNN controller achieves rapid learning and generates a smooth control effort, offering a robust and practical framework for digital control.

Abstract: Background: The integration of Artificial Intelligence (AI) into the management of pediatric metabolic diseases offers unprecedented opportunities for precision medicine. However, the explosive growth of research literature production has led to a fragmented research landscape, often skewed by the indexing biases of major academic databases. Objective: This study aims to conduct a comparative thematic analysis of the Web of Science and Scopus databases to uncover the distinct research paradigms governing AI in pediatric metabolic diseases. Methods: We employed the Synthetic Knowledge Synthesis methodology, integrating automated bibliometric mapping (co-word analysis via VOSviewer) with qualitative content analysis. Metadata was extracted from both databases and author keywords were clustered to evaluate underlying thematic structures. Results: The comparative analysis revealed a significant thematic divergence. Literature indexed in WoS predominantly emphasizes algorithmic novelty and methodological advancement, highlighting the use of Deep Learning, Large Language Models (LLMs), and complex metabolomic integrations. Conversely, Scopus encapsulates a distinctly clinical and translational paradigm, prioritizing Explainable AI (XAI), the integration of Natural Language Processing (NLP) with Electronic Health Records (EHR), and the application of clinical decision support systems like Continuous Glucose Monitoring (CGM). Conclusion: Relying on a singular bibliographic database provides an incomplete view of the field, creating a disconnect between algorithmic development and clinical implementation. To successfully bridge the "algorithm-to-clinic" gap in pediatric endocrinology, researchers must adopt a holistic approach that synthesizes the predictive power emphasized in WoS with the clinical transparency and applicability highlighted in Scopus.

Abstract: The rapidly evolving Android malware that employs obfuscation and adversarial techniques has become a challenge for cybersecurity malware detection systems. This study proposes an explainable adversarial defense framework, namely RFS-MD (Rule-based Feature Scoring for Malware Detection), that integrates feature importance scores derived from classification association rules, along with the rules themselves, into malware detection models to enhance detection performance, robustness, and explainability. Several experiments were performed on a balanced static feature dataset across several machine learning (ML) and deep learning (DL) classifiers to demonstrate that scored features consistently improved. accuracy and recall, compared to non-scored features under both default and tuned parameters across all classifiers. Furthermore, RFS-MD enhanced the model’s robustness against adversarial attacks, reducing attack success rates (ASR) and maintaining a positive recalgain compared to baseline models. In addition, a rule-based explanability approach (RXAI) is introduced to generate transparent and human-readable explanations of the model decisions, where the fidelity analysis confirms that RXAI captures interacting malicious feature patterns that align with classifier results. Overall, the results indicate that the rule-based feature scoring technique, along with rules, presents an effective approach towards android malware detection systems that simultaneously improve accuracy, robustness, and explainability, contributing to trustworthy AI-driven cybersecurity solutions.

Abstract: Each year, poor diets contribute to more deaths in the United States than any other risk factor. Image classification has emerged as a promising opportunity to enhance food analysis capabilities for diet assessment and health monitoring. However, existing models are often limited to single-label classification due to a lack of ingredient-level data, hindering their applicability to food analysis tasks. In this work, we present a novel multi-label classification model powered by a ResNet-50 backbone. We trained a custom head on our self-curated dataset comprising 183 ingredient classes, using focal loss and threshold optimization to enhance classification performance. The model achieved 99.14% validation accuracy and reached a macro F1 score of 63.82% at an optimal threshold of 0.70. Our dataset and model provide a benchmark for further research in automated visual assessments of food items. This work can legitimize a new paradigm for AI-driven ingredient recognition as a foundation for data-driven dietary assessment.

Abstract: This paper starts with surveying the evolution of quantum-like models of cognition and decision making, transitioning from static kinematic representations to a robust dynamical framework based on open quantum systems. We provide a comprehensive analysis of the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation's application in cognitive psychology and decision making, illustrating how it models mental state evolution as a dissipative process influenced by an informational environment. We categorize dynamical regimes into Passive and Active Hamiltonians, demonstrating how non-commutation with projections on decision basis serves as a mathematical signature of cognitive agency and Quantum Escape from classical equilibria. The utility of this framework is further explored through its ability to stabilize non-Nash outcomes in strategic games, such as the Prisoner's Dilemma. Building upon this dynamical foundation, we identify ``cognitive beats'' as a signature of the internal struggle between competing ``flows of mind'' deliberated at approximately equal frequencies. Distinct from the damped oscillations of simple interference, these beats emerge from a structural tension between Liouvillian channels that generates a secondary, slow-scale modulation of conviction. This beat envelope dictates the timing of peak readiness and hesitation, providing a mathematical map of the transition between conflicting cognitive states. By resolving these nested time scales, we provide a new spectral diagnostic for the depth of cognitive agency and the complexity of the underlying deliberation process. This paper develops a theoretical framework linking GKSL dynamics with quantum-like cognition and decision-making (QCDM), highlighting how dissipative quantum models can capture features of human thought and decision processes.

Abstract: Environmental planning is essential for climate action, as cities face air pollution, flooding, drought, and other environmental stresses. Yet research on these challenges remains limited in the state of Amazonas, Brazil. Building on a prior participatory study of 1,242 residents, this article advances a long-term research agenda focused on urban water management. The study pursues three goals: update, identify, and classify Benchmark Smart Sustainable Cities (BSSCs), with priority given to the Gold tier (GBSSCs); map ECO AI and Non-AI initiatives, AI techniques, and digital enablers used by GBSSCs to address urban water challenges (Manaus main concern); propose and disseminate Gate4EcoAI, an interactive platform with GBSSCs' urban water initiatives. This applied research triangulated ten international city rankings using a mixed-methods approach (systematic literature review, bibliometric and documentary analyses, statistical methods, open-science practices, and AI-assisted tools) to collect, clean, analyze, and visualize data. Of 265 cities assessed, 99 were classified as BSSCs (20 as Gold). GBSSCs applied 76 regulatory instruments and adopted at least 243 distinct initiatives to address water challenges. Gate4EcoAI is a multidimensional, queryable evidence-to-policy bridge, with valuable initiatives to support the development of roadmaps for urban water challenges. By linking proven initiative types (e.g., Network Process Control, Quality Monitoring), dominant AI techniques (ML-Anomaly Detection, Supervised ML), and enablers (IoT, Cloud) to real-world statuses, it empowers AI developers, policymakers, utilities, and researchers with evidence-based benchmarking to adapt the best practices locally. For Manaus and analog cities, this structured knowledge base bridges science-to-policy gaps, accelerating resilient water governance amid Amazonian vulnerabilities.

Abstract: As the population ages, the incidence and prevalence of musculoskeletal degeneration, such as osteoarthritis increases. While the currently accepted treatment options provide symptomatic and functional improvement, they do not halt the progression of osteoarthritis. This results in eventual need for surgery for many patients with advanced osteoarthritis. Due to seemingly inevitable progression of OA, many clinicians and researchers have shifted their focus to regenerative therapies. Orthobiologics, a specific type of regenerative therapy designed to treat orthopedic conditions, have been gaining traction in recent years due to utilization of autologous biological substances and synthetic peptides in healing in musculoskeletal injuries and degenerative conditions. Orthobiologics can be distinguished into one of four classes: cell-based, biologic fluids-based, matrix-based and molecular-based, and based on its composition. In this review, key examples of each class, mechanism of action, and current clinical data for each agent are examined. Limitations of current orthobiologics involve lack of standardization in preparation and administration each agent as well as uniformity in assessment end points across different clinical studies. Lastly, we will discuss future directions of orthobiologics as a therapy for treatment in osteoarthritis.

Abstract: A distinct typing interface using surface electromyography (sEMG) can facilitate silent, hands-free typing by interpreting muscle activity in relation to specific keystrokes. Character-level recognition poses challenges compared to the recognition of unseemly gestures, due to insensitivity to slight temporal variations and the fusion of muscle dynamics. Temporal Feature is vital, since when typing, there may be irrelevant dissimilarities in how people press keys, and even in body movements that coincide. This paper proposes TransTCNet, a two-stage deep neural network design with a causal convolutional layer to learn local features and a transformer-based component to learn long-range temporal interactions. We evaluated our network on a publicly available 26-class typing sEMG dataset acquired from 19 individuals. The model achieved a validation accuracy of 96.53%, exceeding the baseline models. Our study revealed generalization among participants, and the AUC values were also high (>0.994) across all classes. The model was significantly reliable and displayed high prediction confidence (>0.9), enabling us to obtain a high training accuracy rate (97.86%) for real-time filtering decisions. TransTCNet could be suitable for wearable and edge devices due to its efficient architecture and low inference cost. The model's ability to consistently decode fine-grained neu-romuscular signals across users makes it a suitable choice for real-time applications such as adaptive user interfaces, virtual and augmented reality, prosthetic control, and communication systems.

Abstract: In the context of the rapid popularization of intelligent monitoring and edge perception, automatic identification of abnormal behaviors in complex scenarios has become a key issue in video understanding. This paper proposes an unsupervised behavior anomaly detection model based on contrastive learning. Through hierarchical organization of normal samples, joint spatio-temporal encoding, time attention aggregation, and "instance contrast - prototype traction - time smoothing" joint optimization, stable behavior embedding representations are learned. In the detection stage, a comprehensive anomaly score is constructed by integrating the recent prototype deviation, second-order temporal residual, and local neighborhood support information, and an adaptive threshold based on the median and absolute median difference is adopted for judgment. Experimental results show that the model achieves an AUC of 97.4% on UCSD Ped2, 91.8% on CUHK Avenue, and 83.7% on ShanghaiTech. The average AUC and average F1 are 91.0% and 88.1% respectively. The study demonstrates that this method can enhance the stability and generalization ability of anomaly detection in complex video scenarios, providing a reference technical path for video intelligent early warning in the absence of labels.

Abstract: Background: Motor precision is a highly innate trait, while ambidexterity in high-precision tasks remains rare and biologically regulated. Few sports necessitate bilateral precision; however, the indigenous sport of picigin uniquely requires symmetrical palm-striking proficiency. Methods: This study investigated bilateral precision and ball velocity in 22 experienced players, divided into competitive (n=11) and recreational (n=11) groups. A specialized bilateral palm-precision test was developed to measure performance across both dominant and non-dominant hands. Key metrics included the asymmetry index for speed and accuracy, and the speed-accuracy trade-off (SAT). Results: Results indicate that competitors significantly outperform recreational players in both precision and velocity. Notably, the SAT analysis suggests that the dominant hand of recreational players performs at a level comparable to the non-dominant hand of competitors. While recreational players exhibited slightly lower asymmetry indices, the inter-manual gap remained stable despite years of experience. Conclusions: Findings suggest that bilateral training induces linear improvements on both sides, maintaining a constant asymmetry ratio rather than diminishing it through long-term practice.

Abstract: The performance of grain storage silos is strongly influenced by discharge flow patterns, hopper geometry, and material properties such as moisture content and impurity levels. However, the combined effects of these factors on flow behavior, discharge rate, and segregation are not yet fully understood. This study experimentally investigated the integrated effects of moisture content, prismatic hopper geometry (hopper angle β), and impurity addition on flow behavior, segregation, and mass flow rate in reduced-scale silos. Experiments were conducted using three prismatic silos with hopper angles of β = 15°, 33°, and 45°, filled with maize at moisture contents of 13.6%, 20.2%, and 26.0% (wet basis), under both clean conditions and with the addition of 10% impurities (fraction passing through a 5 mm sieve). The discharge rate was determined by direct mass–time measurements, flow patterns were inferred from video analysis, and segregation was quantified based on the mass fraction of impurities in samples collected during discharge. The results indicate that moisture content was the most influential factor, reducing the discharge rate by up to 22.8% when increasing from 20.2% to 26.0% w.b. (p < 0.05). Hopper geometry also had a significant effect, with performance differences among configurations becoming more pronounced under high-moisture conditions. The addition of 10% impurities increased the discharge rate under all tested conditions, with gains of up to 29.0% at 26.0% w.b. and β = 15°. Segregation intensified with increasing moisture content, leading to a progressive accumulation of impurities toward the end of discharge. The stick‑slip phenomenon was observed under a critical condition (26.0% w.b., β = 15°, with impurities), resulting in a 23.0% reduction in average discharge rate compared to the equivalent stable condition. These findings demonstrate that granular flow behavior in silos is governed by the interaction between moisture, hopper geometry, and material composition. The results also suggest that operational strategies such as pre-cleaning should be evaluated in conjunction with expected moisture conditions, as pre‑cleaning may adversely affect flow performance under high‑moisture scenarios.

Abstract: This paper consolidates, corrects, and extends a research programme on the shifted-prime problem $p = q + r - 1$ with $p, q, r$ prime and its connections to the binary Goldbach conjecture and the non-trivial zeros of the Riemann zeta function $\zeta(s)$. New material over Version 6. The principal addition is a rigorous three-level treatment of the restricted Goldbach sum \[ P_{R_{3,4}}(N) = \sum_{\substack{p+q=N,\\ p\equiv 3\ (\mathrm{mod}\,4)}} (\log p)(\log q). \] At Level 1 [PROVED] (unconditional), the ``almost-all'' theorem of Montgomery--Vaughan type shows that the exceptional set of even integers $N\leq X$ for which $|R_{3,4}(N) - \tfrac{1}{2}C_2 S(N)N|$ exceeds $CN/(\log N)^3$ has measure $O_A\bigl(X/(\log X)^A\bigr)$ for every $A>0$. At Level 2 [PROVED] (unconditional), a transfer inequality bounds $|R_{a,q}(N)-\phi(q)^{-1}R(N)|$ in terms of twisted sums $S_\chi(N)$ with mean-square control. At Level 3 [COND. PROVED, GRH], for all sufficiently large even $N$ one has $R_{3,4}(N)=\tfrac{1}{2}C_2 S(N)N + O(N^{1/2+eps})$. Anderson's original claim of an explicit unconditional constant $K\leq 28.65$ for all $N$ is identified as relying on the Hardy--Littlewood binary asymptotic for each individual $N$, which is itself a conjecture; the claim is accordingly downgraded and the gap stated precisely. Retained from Version 6. Five analytical gaps (A--E) in the Goldbach--Riemann bridge for $\Psi^*(x)$ are fully closed unconditionally (Gaps D1, D2, D3, E) or under GRH (Gap C). The corrected spectral-detection results stand: $\lambda_1/\lambda_2 = 182.63$ ($n=892\,206$); 129/200 Riemann zeros detected at $p<0.01$ ($n=1\,310\,763$); Mellin--Lomb--Scargle concordance 29/30 versus 0/30; 9/10 direct Pearson correlations significant; heteroscedasticity of $eps(p)$ formally confirmed ($p=4.7\times 10^{-14}$). Principal corrections retained from Version 6. The $k=3$ existence problem is equivalent to binary Goldbach (open). The permutation-test bug in scripts~6.py--8.py is corrected ($199/200\to 129/200$). The formula for $S_\infty^{(k)}$ is corrected for $k\geq 3$. None of these results constitutes a proof of the Riemann Hypothesis. All claims carry explicit epistemic labels.

Abstract: The Pólya-Ostrowski group of a Galois number field K, is the subgroup Po(K) of the ideal class group Cl(K) of K generated by the classes of all the strongly ambiguous ideals of K. The number field K is called a Pólya field, whenever Po(K) is trivial. In this paper, using some results of Bennett Setzer [9] and Zantema [10], we give an explicit relation between the order of Pólya groups and the Hasse unit indices in real biquadratic fields. As an application, we refine Zantema’s upper bound on the number of ramified primes in Pólya real biquadratic fields.