Abstract: Background/Objectives: Two sociodemographic characteristics of the nursing workforce — formal level of education and length of professional experience — are widely assumed to shape both how often nurses report adverse events and how safe they perceive their workplace to be for patients. Empirical evidence on these associations remains uneven, however, and large multicentre data from Central and Eastern European secondary-care systems are scarce. The present study examined whether educational level and length of work experience are independently related to (a) the self-reported frequency of adverse-event reporting and (b) the perceived level of patient safety, in a national sample of nurses working in Croatian general and county hospitals. Methods: We conducted a cross-sectional, multicentre survey in 2023 covering all 22 general and county hospitals in the Republic of Croatia. A 99-item paper questionnaire — including 81 items distributed across six previously validated scales (Cronbach’s α 0.730–0.951) — was distributed proportionally to the eligible nursing workforce (N = 6,661). Of the 1,657 questionnaires distributed, 1,518 were returned fully completed (response rate 91.6%). Two outcomes were examined in parallel: self-reported frequency of adverse-event reporting in the past 12 months, and global perceived level of patient safety on the respondent’s ward. Group differences were tested with Pearson’s chi-square and Kruskal–Wallis H tests; effect sizes were assessed using the φ coefficient and Cramér’s V. The study followed the STROBE reporting guideline. Results: Educational level was associated with the frequency of adverse-event reporting (χ² = 29.873, df = 8, p < 0.001; φ = 0.14) and with safety perception (χ² = 16.084, df = 8, p = 0.041; φ = 0.10). The same monotonic gradient was confirmed by Kruskal–Wallis tests, with mean ranks rising from secondary (SSS) through bachelor (VŠS) to master’s or doctoral (VSS+DR) levels for both reporting (719.40; 772.93; 836.56; H = 15.901, p < 0.001) and safety perception (735.29; 775.89; 844.86; H = 10.539, p = 0.005). Length of total work experience was associated with reporting (χ² = 22.708, df = 12, p = 0.030; φ = 0.12; H = 9.249, p = 0.026): mean ranks were lowest for nurses with ≤ 10 years and ≥ 31 years, and highest for mid-career nurses (11–20 and 21–30 years). For safety perception, the experience gradient ran in the opposite direction — highest in nurses with ≤ 10 years (mean rank 795.08) and lowest in those with ≥ 31 years (718.17; χ² = 35.036, df = 12, p < 0.001; φ = 0.15; H = 8.517, p = 0.036). Conclusions: Educational level and length of work experience are independently related to both the reporting of adverse events and the perception of patient safety among Croatian hospital nurses, but the two characteristics operate in different ways. Higher education is associated with more reporting and more favorable safety perception, whereas longer experience is associated with more reporting at mid-career but with a less favorable view of workplace safety in late-career nurses. Investing in continuing nursing education and in mid-career retention, while remaining attentive to the deteriorating safety perception of the most experienced staff, may be more effective than redesigning reporting forms alone. The findings inform nursing leadership, continuing-education planning, and national patient-safety policy in Central and Eastern European secondary-care systems.

Abstract: Institutional shuttle fleets with fixed routes and predictable terminal parking are well suited to dedicated photovoltaic–battery (PV–BESS) charging infrastructure, yet siting and sizing are usually solved numerically without clear interpretation of the governing constraints. This study develops a closed-form active-constraint sizing rule, derived via Karush–Kuhn–Tucker (KKT) analysis under verified monotonicity of the net-present-value (NPV) objective over the feasible design region, for a 10-van electric academic shuttle fleet operating between the Huay Kaew and Doi Saket campuses of Rajamangala University of Technology Lanna, Chiang Mai, Thailand. One centralized station is compared with two distributed stations under reliability, cost, solar-fraction, autonomy, charger, budget, and rooftop-area constraints. The two-station configuration eliminates 47,600 km/year of dead-run travel and increases system NPV from USD 36,980 to USD 86,293 after the year-10 BESS replacement cost. The KKT analysis identifies two binding constraints—BESS one-day autonomy and PV rooftop area—giving 30 kWp PV and 94.85 kWh BESS per station, rounded to 100 kWh. The full transition achieves IRR = 12.9%, simple payback = 6.1 years, and 95.9% annual CO₂ reduction. Monte Carlo simulation with 5,000 scenarios yields P(NPV > 0) = 100% within the simulated scenario set, VaR_5% = USD 28,959, and CVaR_5% = USD 21,248, confirming financial robustness under the adopted uncertainty ranges.

Abstract: Large language models (LLMs) embedded in medical Patient Digital Twins (PDTs) exhibit a systemic vulnerability: they can generate fluent, narratively persuasive, yet abductively unsound clinical explanations. In this context, abductive soundness means that an explanation preserves mechanistic plausibility, temporal coherence, explicit handling of missing premises, and sensitivity to counter-evidence. This article reframes the problem as architectural rather than as a mere deficit in training data. We identify three recurrent modes of abductive failure — missing-premise neglect, weak-mechanism support, and counter-evidence discounting. They arise when local semantics, formal world ontology, and the role-specific clinical semiosphere are collapsed into a single surface flow of generation. We propose a governed abductive architecture organised around seven runtime contours and operationalise it in the MS-AGIP platform for multiple sclerosis care. The architecture separates three subsystems: an ontology-guided Research Framework, a clinician-facing Neurologist Digital Twin, and a patient-controlled Patient Digital Twin. We show how disease-specific causal templates, evidence-tiered biomarker reasoning, provenance labels, temporal-coherence checks, molecular-clinical discordance detection, and governed patient-feedback updates jointly transform plausible narrative into sound abduction. The article presents an architectural blueprint and validation protocol aligned with TRIPOD+AI and DECIDE-AI. The architectural-versus-scale distinction has direct implications for safe medical AI: the difference between a fluent and a sound clinical system lies more in architecture and governance than in model size. None of the subsystems has yet been clinically deployed.

Abstract: This research explores the aromatase-inhibitory and estrogen-agonistic/antagonistic properties of two natural naphthoquinones, α- and β-lapachone, which are known for their anticancer effects. Initial tests showed that both lapachones inhibit aromatase in the sub-micromolar range, with IC₅₀(β) = 0.78 ± 0.06 μM and IC₅₀(α) = 10.6 ± 2.4μM, similar to the steroidal aromatase inhibitor Exemestane (IC₅₀: 0.02-0.2 μM). A molecular docking study comparing these compounds with androstenedione, one of the native aromatase substrates, identified their binding sites and specific interactions with the enzyme. The Yeast Estrogen Screening assay indicated that both compounds lacked hERα-agonistic activity but exhibited antagonistic effects, similar to 4-Hydroxytamoxifen (Afimoxifene; IC₅₀ = 0.81 ± 0.65 μM). The IC₅₀ values were 0.33 ± 0.24 μM for β-lapachone and 48.3 ± 18.9 μM for α-lapachone. Overall, the study propose unexplored mechanism of action and highlights the dual role of α- and β-lapachones: inhibiting estrogen synthesis and serving as potent, selective estrogen receptor modulators, emphasizing their potential in cancer treatment, especially for hormone-dependent cancers.

Abstract: Symptomatic dermographism (SD) is the most common form of chronic inducible urticaria, typically presenting with pruritic, linear wheals that appear within minutes after stroking the skin and resolve within 30 minutes. However, not every linear urticarial eruption following friction or scratching is true SD. We present three clinical cases initially misdiagnosed or suspected as classic SD, but which after detailed evaluation proved to be different entities. The first case was an atypical follicular subtype of SD itself, with a false-negative initial FricTest. The second case was cholinergic dermographism — a rare variant of cholinergic urticaria requiring two concurrent triggers (sweating and stroking) — in a patient with hyperhidrosis. The third case was flagellate dermatitis caused by consumption of inadequately cooked Shiitake mushrooms, with lesions persisting for days and no response to antihistamines. These cases highlight that even a characteristic linear wheal pattern is not pathognomonic for SD. A thorough history, recognition of atypical morphologies, and appropriate provocation testing (including combined triggers when needed) are essential to avoid diagnostic pitfalls and initiate effective therapy.

Abstract: Large language models (LLMs) are advancing intelligent writing systems from local text continuation and language polishing toward long-form structured text generation. However, directly generating full-length academic paper drafts remains challenging due to unclear research objectives, unstable discourse structures, insufficient long-text coherence, and the lack of explicit quality control mechanisms. To address this long-form structured generation task, we propose MetricDraft, a metric-driven framework for academic paper draft generation. The framework organizes the drafting process as a closed-loop pipeline comprising research ideation clarification, structural anchoring, section-by-section generation, quality assessment, and feedback-driven revision. Its key components include adversarial research ideation clarification, staged structural anchoring, the PRISM structured metric system, progressive context injection with section-type-aware guided generation (PCI+STAGG), and a metric-feedback-driven generation–evaluation co-optimization mechanism. Experimental results demonstrate that MetricDraft achieves significantly higher composite quality scores compared to one-shot generation, summary-based context passing, and context-accumulation-only baselines, with differences reaching statistical significance. Furthermore, PRISM exhibits moderate-to-high positive correlations with expert ratings, providing preliminary evidence that it can serve as an auxiliary evaluation reference for draft quality diagnosis and iterative revision. This work reformulates academic writing as an adjustable, assessable, and iteratively optimizable long-form structured text generation problem, offering methodological insights for human–AI collaborative writing and intelligent text generation system design.

Abstract: Coastal zones are facing rising exposure to climate-related hazards alongside intensifying human pressures, which highlights the need for robust tools to assess vulnerability. This study uses a GIS-based Coastal Vulnerability Index (CVI) to quantify and map relative vulnerability along ~13 km of shoreline in Al Hoceima Bay (northern Morocco). The proposed CVI integrates eight geological and physical indicators, including geomorphology, shoreline erosion and accretion rates, coastal slope, elevation, natural habitats, relative sea-level rise, significant wave height, and tidal range. Spatial analyses were performed using remote sensing data, historical records, field measurements, and Geographic Information Systems (GIS). The analysis reveals that 37% of the shoreline is categorized as high vulnerability, 44% is moderate, and 19% is low. Highly vulnerable sectors are primarily associated with low elevations, gentle coastal slopes, sandy beach systems, limited natural habitat protection, and proximity to river mouths. These findings demonstrate that the applied CVI provides a rapid and cost-effective framework for identifying priority areas for coastal management and climate adaptation. The proposed approach offers valuable decision-support insights for sustainable coastal planning in Al Hoceima Bay and other Mediterranean coastal environments characterized by limited data availability.

Abstract: The role of human leukocyte antigen F (HLA-F) at the maternal-fetal interface (MFI) during viral infection and its regulation by interferon signaling remains poorly understood. Here, we investigated HLA-F expression and regulation in first-trimester trophoblast cells following activation of the type I interferon pathway and viral infection. We demonstrate that HLA-F is significantly upregulated at both mRNA and protein levels in response to Poly(I:C) and IFN-β in a dose- and time-dependent manner, suggesting its regulation as an interferon-stimulated gene (ISG). Zika virus (ZIKV) infection similarly induced HLA-F upregulation over time. In contrast, HSV-2 infection downregulated HLA-F mRNA while maintaining steady protein levels, indicative of virus-specific regulatory mechanisms. Moreover, we identified a soluble HLA-F secreted following Poly(I:C) stimulation. These findings reveal that HLA-F is dynamically regulated in trophoblasts during viral challenge and type I IFN signaling activation, supporting its broader immunomodulatory role in antiviral defense and immune tolerance at the MFI.

Abstract: Cape Coast is a prominent tourism destination in Ghana, distinguished by its historical landmarks, coastal ecosystems, and cultural heritage. Yet the city faces mounting threats from environmental hazards such as coastal erosion, flooding, extreme heat, and lagoon degradation, which directly compromise the sustainability of its tourism sector. Guided by the Sustainable Tourism Development Theory (STDT) and the Tourism Resilience and Adaptation Theory (TRAT), this study investigates the impacts of these hazards on tourism development, the effectiveness of current disaster risk reduction (DRR) strategies, and the roles of key stakeholders in building sectoral resilience. Using a qualitative research design, data were collected through in-depth interviews with eighteen stakeholders comprising four policymakers, six community leaders, five tourism business operators, and three representatives from non-governmental organisations, alongside documentary analysis of four institutional reports. The study contributes to the literature by demonstrating that fragmented, reactive DRR strategies and weak stakeholder coordination undermine Cape Coast’s tourism resilience, and by showing how urban natural assets, a dimension largely neglected in existing tourism-DRR scholarship, are central to both hazard exposure and adaptive capacity. The findings call for integrated, ecosystem-based DRR frameworks that align governance mechanisms with sustainable tourism imperatives.

Abstract: This study examines how digital income diversification, measured by the non-interest income ratio (NII), affects bank performance and risk in emerging Asian markets. Drawing on panel data from 44 banks across China (36) and Thailand (8) over 2022-2025, the analysis employs fixed-effects regressions, mediation analysis, and subsample testing to unpack the performance implications of digital transformation. Results indicate that NII exerts a statistically significant positive effect on bank profitability (ROA and ROE), with no corresponding increase in risk exposure as measured by Z-score. The relationship is markedly stronger among large banks, consistent with scale advantages in technology infrastructure, network effects, and regulatory compliance cost amortization. Cost efficiency does not mediate the NII-performance nexus, suggesting that revenue-side mechanisms dominate in this context. Cross-country comparisons reveal stable but modest effects in China's mature digital ecosystem against larger but less precise coefficients in Thailand's early-stage transition. These findings challenge the Western-centric complexity-risk narrative and highlight institutional boundary conditions governing digital banking outcomes in emerging markets.

Abstract: This study examines how ESG performance, innovation performance, and policy support relate to organizational resilience in China’s real estate industry. Drawing on the Resource-Based View, Institutional Theory, and Configurational Theory, the study conceptualizes organizational resilience through recovery and resistance capacities. Using panel data from 80 Chinese A-share listed real estate firms during 2015–2024 (800 firm-year observations), the study applies fixed-effects regression, robustness tests, and heterogeneity analyses. The findings show that ESG performance positively influences accounting-based recovery, particularly return on equity, but negatively affects market-based recovery, reflected in Tobin’s Q in the baseline models. Additional analysis reveals a U-shaped relationship between ESG performance and Tobin’s Q, suggesting that initial market valuation penalties may decline as ESG engagement deepens. Innovation performance shows limited baseline effects but becomes more relevant in alternative specifications related to recovery and leverage. Policy support demonstrates limited direct effects, indicating a more conditional role. Overall, organizational resilience is shaped by heterogeneous interactions among ESG, innovation, and policy-related factors.

Abstract: Accurate prediction of significant wave height (SWH) is essential for fisheries management, coastal socio-economic activities, and marine ecological conservation. In recent years, deep learning-based bias correction has shown considerable potential for improving numerical wave forecasts. However, many existing approaches are still constrained by limited receptive fields and often struggle to capture long-range spatiotemporal dependencies in wave forecast errors. To deal with this issue, we adapt and improve a video prediction framework, namely the Vision Mamba Recurrent Neural Network (VMRNN), to model and correct the spatiotemporal patterns of SWH prediction biases. Comprehensive evaluations show that the multi-channel VMRNN achieves consistently high predictive accuracy across different forecast lead times and sea-state conditions. When validated against reanalysis data, the proposed model reduces the root mean square error (RMSE) of WAVEWATCH III forecasts by 28.2%, 26.1%, and 24.7% at lead times of 24, 48, and 72 hours, respectively. It also preserves the spatial structure of SWH fields quite well, with the spatial structural similarity index remaining as high as 0.945 even at the 72-hour lead time. Regional assessments over high-wave areas further indicate that VMRNN can effectively reduce both the mean error and the systematic overestimation commonly found in numerical wave models. Additional validation using in-situ buoy observations confirms that the model has a robust ability to correct systematic positive biases, especially for wave heights ranging from 0.5 m to 2 m. Taken together, these results suggest that VMRNN has strong spatiotemporal modeling capability and can serve as a promising post-processing framework for improving operational physics-based wave forecasting systems.

Abstract: This paper addresses the robust trajectory tracking problem of an Unmanned Aerial Vehicle (UAV) equipped with a 2-DOF manipulator, designed for fast aerial manipulation of varying payloads. To overcome the high computational cost and adaptability limitations of traditional model-based controllers, this work introduces a novel hybrid gain-scheduling framework that shifts the computational complexity to the pre-flight phase. The approach utilizes an approximate inverse dynamics linearization, based on fixed nominal models, which transforms the complex nonlinear system into a simple linear plant with bounded, structured uncertainties. The entire configuration space, including manipulator states and a range of payload properties, is partitioned into dynamically similar regions using K-Means clustering. For each local region, a dedicated robust PD controller is designed using a multi-objective Genetic Algorithm (GA). This framework also successfully implements a gain interpolation technique to mitigate the potential for abrupt control actions. Simulation results validate the controller’s ability to maintain high-precision tracking during fast maneuvers and payload switching, confirming the robustness and adaptability of the offline-tuned design.

Abstract: This position paper argues that, for long-horizon tasks evaluated across models with comparable frontier capability, the agent execution harness, namely the infrastructure layer that governs context construction, tool interaction, orchestration, and verification around a language model, is often a stronger determinant of agent performance than the model it wraps. We formalize and defend the Binding Constraint Thesis: in this regime, performance variance is governed more by harness configuration than by model choice, and current evaluation protocols therefore systematically misattribute harness-level gains to model improvements. We support this thesis along three lines. First, a control-theoretic formalization treats the harness as the controller of a closed-loop dynamical system and the LLM as the stochastic policy it governs, which explains why small harness changes can produce performance shifts that exceed those obtained by substituting one model for another. Second, published benchmarks, industry deployments, and a controlled variance decomposition show that harness-induced variance can substantially exceed model-induced variance, including cases of model ranking reversal. Third, we propose a harness-aware evaluation framework with a disclosure standard and a variance decomposition protocol. Until harness specifications are disclosed, leaderboard comparisons for long-horizon agents should be treated as incomplete and potentially misleading.

Abstract: Deep learning classifiers deployed in scientific applications often encounter inputs that violate physical laws (e.g., due to sensor failure or corruption). Standard methods cannot detect such violations and may produce confident but wrong predictions. We propose UA-PBR, a framework that combines a physics-informed autoencoder (to detect physics violations) with a Bayesian CNN (to quantify predictive uncertainty). Inputs are rejected if either the PDE residual exceeds a threshold or the predictive entropy is too high. As a proof-of-concept, we evaluate UA-PBR on a synthetic Darcy flow dataset (32×32 grid) under severe computational constraints (Google Colab, 10 seeds). Despite these limitations, UA-PBR reduces classification risk by over 90% on heavily corrupted samples while accepting 89.7% of clean inputs with 99.99% accuracy on accepted samples. Ablation studies confirm that both components contribute synergistically. These preliminary results on a synthetic benchmark illustrate the potential of physics-aware rejection and motivate further investigation with larger-scale experiments. Code is available at: https://github.com/UA-PBR/UA-PBR.

Abstract: Background: Cervical cancer is the fourth most common cancer among women globally, with the highest burden in low- and middle-income countries. Limited access to screening and treatment contributes to high mortality, despite effective screening methods like HPV testing and cervical cytology. Objectives: To establish the degree of correlation between cervical cytology, colposcopy, and histological features among patients with abnormal cytological smears seen at Nelson Mandela Academic Hospital and MthathaRegional Hospital. Methods: This was an analytical cross-sectional study conducted from June 1, 2024, to June 30, 2025. Two hundred twenty-five participants were enrolled through a convenience sampling method. Demographic and clinical data were collected using a structured questionnaire. Categorical data were expressed as frequencies and proportions, and continuous data were summarized into means ± SD or medians (IQR). X² was used to determine the correlation, and a p-value of <0.05 was significant. Results: The mean age was of the participants was 45.5 years, with 72% being HIV positive. Most cytology results showed high-grade squamous intraepithelial lesions (HSIL). Colposcopy classified 77% of participants as CIN II or III. Both cytology and colposcopy correlated positively with histology p< 0.05. Cytology showed 92% sensitivity and 33% specificity for detecting CIN 2+ lesions, while colposcopy had 87.4% sensitivity and 49% specificity. Micro-invasive cervical cancer was prevalent in 4% of the participants and was associated with age ≥ 50 years and treatment delay of > 4months. Conclusion: Both colposcopy and cytology demonstrated good sensitivity but poor specificity for the diagnosis of CIN 2 or higher dysplastic lesions of the cervix. Early colposcopic evaluation and treatment of women with HSIL can help prevent incident cervical cancer.

Abstract: This paper makes a review for the studies of Space Energy Internet. Based on introducing the background of related networks, this paper discusses several key components of the Space Energy Internet (mainly including Space Solar Power Station, Energy Internet, and Artificial Intelligence Data Center), focusing on their corresponding system architectures, main research directions, and related technical challenges. Subsequently, supporting technologies such as discrete signal compression and coding, communication technology, energy transmission, power electronic devices, and artificial intelligence are discussed and analyzed. Furthermore, a highly integrated “data-computing-energy-networks” framework is established based on star computing networks and multi-orbital star link systems, and adopting the technologies like plug-and-play and modular design, which can support many innovative applications further.

Abstract: Decoherence is the primary obstacle to reliable quantum computing, yet real-time, measurement-driven early warning remains unavailable. Standard metrics (fidelity, entanglement entropy) are computed post-hoc or require full state tomography. We propose KA-Quantum, a thermodynamic early warning framework grounded in the Karimov–Alekberli (KA) causal entropy formalism [1], monitoring three quantum channels: C₁ (von Neumann entropy deviation), C₂ (bipartite correlation entropy coupling decay), and C₃ (fidelity residual). Using Qiskit Aer density-matrix simulation [2] of N=5 qubit circuits across three circuit classes (GHZ, random, variational) and three noise models (amplitude damping, phase damping, depolarizing; 30 Monte Carlo runs each, linearly increasing noise ramp), we find: 5 of 9 configurations achieve DR = 100% (30/30); overall DR = 56% (150/270) including physically non-decaying regimes where the specific noise type does not drive fidelity below the 0.9 threshold within the simulation window. FPR = 0.00 in all calibration periods. Median lead times of 1–15 gate cycles (F < 0.9); lead time is invariant to KA threshold θ (2.0/2.5/3.0 tested), confirming empirical threshold invariance [3]. The C₂ entanglement channel provides the earliest indicator, consistent with the structural coupling precursor that distinguishes KA across prior KA classical applications [4].

Abstract: Both Noise Radar (NR) and Quantum Radar (QR), with alleged common features, aim to use the randomness of the transmitted signal to enhance radar covertness and to reduce mutual interference. While NR has been prototypically developed and successfully tested in many environments by different organizations, research and development investments on QR did not bring to practically operating prototypes. Starting from the well-known fact that radar detection depends on the energy transmitted on the target, the detailed evaluations in this work show that the detection performance of all the QR types proposed in the literature are well below the ones of a much simpler and cheaper equivalent “classical” radar set, for example of the NR type. Moreover, the absence of a “Quantum radar cross section” different from the well-known radar cross section is explained. From these facts it results that, in spite of alleged advantages in some literature, Quantum Radar proposals cannot lead to useful results, including, of course, the detection of stealth targets.

Abstract: In this paper, whose main results are conditional on the density hypothesis or the Generalized Riemann Hypothesis, we establish a complete conditional hierarchy for the restricted weighted Goldbach sum $R_{a,q}(N) := \sum_{p_1+p_2=N,; p_1 \equiv a \pmod{q}} (\log p_1)(\log p_2)$, with expected main term $M_{a,q}(N) := C_2 S(N) N/\varphi(q)$, for fixed $q \geq 1$ and $\gcd(a,q)=1$.Under the Density Hypothesis DH($A$) (any $A \geq 2$), the exceptional-set exponent is shown to equal $\theta(A) = 1 - 2/(A+2)$ via a saddle-point argument, correcting prior formulas $\theta = 1 - 1/A$ and $\theta = 1 - 2/A$, which are both wrong. Under the Generalized Riemann Hypothesis (GRH), we prove the pointwise bound $R_{a,q}(N) = M_{a,q}(N) + O_{q,\varepsilon}(N^{1/2+\varepsilon})$ for all even $N \geq N_0(q)$, and derive the explicit threshold $\log N_0(4) = 45.93$ via a fixed-point iteration. We present both normalizations of the effective constant ($C^2_{4,\text{eff}} \approx 529$ and $\approx 2111$) and give a complete account of the discrepancy. A complete constant-chain audit carried out in Section 7 shows all three normalizations (values 529, 2111, and the independently reconstructed 2375) are consistent, and the worst-case certified bound is $\log N_0(4) \leq 46.1$, with no remaining caveat.We further provide:A certified computation showing all 122 primitive real Dirichlet characters of conductor $q \leq 200$ are free of Siegel zeros in the Stechkin critical interval, with global minimum $L_{\text{cert}} = 0.2344$ at $q = 163$. An unconditional restricted Chen-type theorem $N = p + P_2$, $p \equiv a \pmod{q}$, via Bombieri–Vinogradov. A conditional short-interval lower bound under GRH. None of these results proves the binary Goldbach conjecture or GRH. The paper establishes conditional results under explicitly stated hypotheses. This paper is a companion to "An Almost-All Theorem for a Restricted Goldbach Sum over Arithmetic Progressions with Explicit Unconditional Constants", whose results are used here as a black box.