Search Results (1,601)

Obesity is characterized by low-grade systemic inflammation and alterations in gut-related immune pathways that may contribute to metabolic dysfunction. Composite biomarker indices may better capture these complex processes than individual markers, although their performance may differ across biological domains. In this cross-sectional study, 88 adults without diabetes or infection were categorized as BMI < 25 kg/m² (n = 20), BMI 25–29.9 kg/m² (n = 34), or BMI ≥ 30 kg/m² (n = 34). Circulating biomarkers reflecting systemic inflammation (high-sensitivity C-reactive protein, ferritin, interleukin-6, presepsin) and intestinal barrier-related activity (β-defensin-2, regenerating islet-derived protein 3 alpha) were measured and subsequently combined into two composite indices: the Inflammatory Load Index, derived from inflammatory markers, and the Barrier Activation Index, derived from barrier-related markers. Group differences were assessed using analysis of variance with post hoc testing. Additional analyses included effect size estimation, receiver operating characteristic (ROC) analysis, and logistic regression. Individual biomarkers showed limited differences across BMI categories. The Inflammatory Load Index differed significantly across BMI categories (p = 0.040), with higher values observed in individuals with BMI ≥ 30 kg/m² compared with those with BMI 25–29.9 kg/m² (p = 0.032; Cohen’s d = 0.80), while the Barrier Activation Index did not differ (p = 0.257). In ROC analysis, the Inflammatory Load Index discriminated BMI ≥ 30 kg/m² with an area under the curve of 0.720 (95% confidence interval 0.576–0.851), yielding 77.8% sensitivity and 67.7% specificity. Each one standard deviation increase in the index was associated with higher odds of obesity (odds ratio 2.34, 95% confidence interval 1.22–4.49; p = 0.011). In conclusion, a composite inflammatory biomarker index, but not a barrier-related index, differentiates degrees of BMI in individuals without diabetes. These findings support integrated biomarker approaches for reflecting obesity-related biological burden beyond single markers. However, these observations are based on cross-sectional data and do not imply causality. Full article

Background/Objectives: To develop and assess the feasibility of a natural language processing (NLP) framework for automated assessment of radiology–pathology concordance in breast biopsy using machine learning-based analysis of unstructured reports. Methods: This retrospective study included 766 paired radiology and pathology reports from ultrasound- or mammography-guided breast biopsies (August 2020–May 2024). Reports underwent translation, normalization, tokenization, lemmatization, and synonym expansion, followed by structured encoding of BI-RADS and pathology categories. Three models were trained: a Decision Tree, a LightGBM classifier, and a fine-tuned BioBERT model. Concordance labels were defined by multidisciplinary consensus. Performance metrics included accuracy, sensitivity, specificity, F1-score, area under the curve (AUC), and Cohen’s kappa. SHapley Additive exPlanations (SHAP) analysis was used to identify influential features. Results: Among 766 cases, 707 (92.3%) were concordant and 59 (7.7%) were initially discordant. After excluding B3 lesions (n = 46), 13 true discordant cases remained (1.7%). Including B3 lesions increased clinically non-concordant or indeterminate cases from 1.7% to 7.7%, indicating that the apparent performance of the models is likely sensitive to case definition and dataset composition. BI-RADS 4a was the most common category (31.3%), and benign pathology (B2) accounted for 64.4% of biopsies. Within this dataset, LightGBM yielded the highest apparent AUC (0.999) (however, given the extremely small number of true discordant cases, this estimate is likely unstable and should be interpreted with caution), while BioBERT showed the strongest agreement with expert consensus (κ = 0.89). SHAP analysis identified clinically meaningful terms such as calcification, hypoechoic, ductal, and carcinoma as key contributors to model predictions. Given the very limited number of true discordant cases, these performance estimates are likely unstable and should be regarded as preliminary, requiring validation in larger, multi-center cohorts. Conclusions: This study presents a proof-of-concept NLP-based framework for radiology–pathology concordance assessment. The models showed promising performance in identifying potentially discordant cases; however, given the limited number of true discordant samples, these findings should be considered preliminary and require further validation in larger, multi-center datasets before clinical implementation. Full article

Non-muscle-invasive bladder cancer (NMIBC) is characterized by high recurrence rates and necessitates lifelong cystoscopic surveillance, underscoring the need for minimally invasive biomarkers to improve early detection and risk stratification. Therefore, this study aimed to investigate the role of trimethylamine-N-oxide (TMAO) and its precursors as diagnostic biomarkers for NMIBC. A total of 50 male patients with NMIBC (25 pTa and 25 pT1) were included in this study. Additionally, 52 age-matched healthy individuals were included as controls. Serum TMAO and its dietary precursors were quantified using liquid chromatography–tandem mass spectrometry. Group differences were analyzed using nonparametric tests, associations were assessed using Spearman’s correlation, and diagnostic performance was evaluated using receiver operating characteristic (ROC) analysis. Multivariate logistic regression was performed to identify independent predictors, and a composite risk score was generated. Serum TMAO, carnitine, and choline levels were significantly higher in patients with NMIBC than in controls (p ≤ 0.0001), whereas betaine showed a nonsignificant trend toward higher levels (p ≥ 0.05). The pathological stage (pTa vs. pT1) showed the strongest correlation with TMAO levels. The ROC analysis revealed that TMAO had the highest individual diagnostic accuracy (area under the curve [AUC] = 0.875, 95% confidence interval [CI] 0.812–0.939), whereas carnitine and choline provided complementary diagnostic performance. In multivariate models, TMAO, carnitine, and choline remained independent predictors of NMIBC (p ≤ 0.0001). A composite risk score integrating all four metabolites demonstrated excellent discriminatory capacity (AUC = 0.958, 95% CI 0.926–0.991). The TMAO metabolic axis can be used as a minimally invasive biomarker panel for NMIBC. Further large, prospective, multicenter studies integrating metabolomic and microbiome profiling are needed to validate the findings. Full article

Background/Objectives: Percutaneous coronary intervention (PCI) effectively restores coronary flow in acute myocardial infarction (AMI), but myocardial ischemia–reperfusion injury (MIRI) remains a major prognostic determinant. Mitochondrial open reading frame of the 12S rRNA-c (MOTS-c) has shown cardiovascular protective effects, yet its association with MIRI is unclear. This study aimed to investigate the relationship between serum MOTS-c levels and MIRI in AMI patients. Methods: Seventy-two AMI patients undergoing PCI were enrolled and divided into MIRI (n = 34) and non-MIRI (n = 38) groups. Clinical data and MOTS-c levels in peripheral serum and intracoronary blood were compared. Multivariate logistic regression and receiver operating characteristic (ROC) analysis were performed to identify MIRI predictors. Results: The MIRI group exhibited lower systolic blood pressure, preoperative thrombolysis in myocardial infarction (TIMI) grade, and HDL-C, but higher total ischemic time, door-to-balloon time, culprit vessel stenosis severity, Killip grade and adverse event incidence (all p < 0.05). Postoperative peripheral serum MOTS-c levels were significantly lower in the MIRI group than in the non-MIRI group (p < 0.05), while preoperative peripheral and intracoronary MOTS-c levels showed no significant differences between groups. Multivariate logistic regression identified postoperative peripheral MOTS-c levels (OR = 0.986, 95%CI: 0.976–0.996) and preoperative TIMI grade ≥ 1 (OR = 0.036, 95%CI: 0.004–0.309) as independent protective factors for MIRI, whereas serum creatinine was identified as an independent risk factor. ROC analysis demonstrated that postoperative peripheral MOTS-c levels predicted MIRI with an area under the curve of 0.648. Conclusions: Postoperative peripheral serum MOTS-c levels represent an independent protective factor against MIRI in patients with acute myocardial infarction and suggest a potential predictive value for MIRI, although its clinical utility as a standalone predictor requires further validation through dynamic monitoring and larger-scale studies. This finding may offer a potential novel biomarker and therapeutic direction for MIRI. Full article

In response to the pressing need for miniaturized MEMS microphones in wearable technology and mobile devices, and to surmount the technical limitations inherent in conventional piezoelectric microphones, which typically depend on enlarging chip dimensions or decreasing stiffness to attain low resonance frequencies, this study introduces a novel piezoelectric MEMS microphone (PMM) design predicated on a flexibility-enhanced rotating structure. The proposed design utilizes an aluminum scandium nitride (Al_0.8Sc_0.2N) piezoelectric thin film with 20% scandium doping and incorporates four equivalent sensing units formed by four curved cutting lines centrally located on the chip. This configuration employs a nested arrangement of four cantilever beams to substantially increase vibration compliance, thereby effectively lowering the natural frequency without altering the chip’s external size. Three-dimensional finite element simulations reveal that, relative to traditional triangular cantilever beam architectures, the flexibility-enhanced rotating structure reduces the natural frequency from 15.6 kHz to 13.49 kHz while enhancing sensitivity from −44.6 dB to −40 dB. The device was fabricated via a comprehensive microfabrication process and subsequently characterized within a standardized acoustic testing environment. Experimental results indicate that the microphone attains a sensitivity of −43.84 dB at 1 kHz and exhibits a first resonance frequency of 13.5 kHz, closely aligning with simulation predictions. Furthermore, the signal-to-noise ratio (SNR) reaches 58.3 dB across the full range of human-audible frequencies. By leveraging the flexibility-enhanced rotating structure, this work achieves an optimal compromise between elevated sensitivity and reduced resonance frequency within a compact form factor, thereby offering a viable technical solution for the advancement of high-performance miniature acoustic sensors. Full article

Background: Treatment adherence and outcomes for drug-resistant tuberculosis (DR-TB) continue to be subpar in rural South Africa, where structural health system limitations, comorbid conditions, and diverse resistance patterns make clinical management more challenging. This study aimed to assess how demographic, clinical, and programmatic factors, including a Community Engagement–Clinical Governance (CE–CG) implementation period, affect DR-TB treatment outcomes using explanatory predictive modeling. Methods: A retrospective cohort study was conducted using routine program data from 694 DR-TB patients. A complete-case analysis was performed for multivariable modeling (n = 282). Logistic regression and decision tree models were used to examine the relationships between treatment success and selected predictors, including age, sex, treatment regimen, resistance phenotype, comorbidities, and the CE–CG implementation period. Model discrimination and performance were evaluated using receiver operating characteristic (ROC) curves, pseudo-R² statistics, likelihood ratio tests, and multicollinearity diagnostics. Results: The cohort had a mean age of 40.7 years, and 58.8% of patients were male. Overall treatment success was 59.9%. Severe resistance phenotypes were rare (1.7%) but clinically significant. Comparative analysis showed no notable demographic or outcome differences between included and excluded patients, indicating minimal selection bias. In adjusted models, treatment initiation during the CE–CG implementation period was significantly linked to lower odds of treatment success (adjusted odds ratio [aOR] = 0.443; 95% CI: 0.240–0.818; p = 0.009). Severe resistance phenotypes were strongly negatively associated with treatment success (aOR = 0.303; p = 0.056). Logistic regression models had limited discriminatory ability (AUC: 0.523–0.548), while the decision tree model showed modest improvement (AUC: 0.626). Overall, the model’s explanatory power was limited (pseudo-R² = 0.029), although no evidence of multicollinearity was found. Conclusions: Programmatic implementation periods and resistance severity were important factors associated with treatment outcomes in this rural DR-TB cohort. Although model discrimination was modest and explanatory power was limited, the findings provide useful insights into structural and programmatic vulnerabilities that affect treatment success in real-world settings. Strengthening clinical governance, improving routine program documentation, and incorporating more granular adherence, social, and governance indicators into routine data systems may improve both program evaluation and future predictive modeling. Full article

DBSCAN is widely used to identify structured regions in unlabeled data, but its performance depends critically on the selection of the neighborhood parameter $\epsilon$. Traditional heuristics for estimating $\epsilon$ often become unreliable in high-dimensional or varying-density settings because they rely heavily on local geometric criteria and may fail under smooth transitions or topological ambiguity. This work presents a three-level perspective on DBSCAN hyperparameter selection. At the algorithmic level, $\epsilon$ controls neighborhood connectivity and structural transitions in clustering. At the modeling level, the ordered k-distance signal is approximated through a surrogate dynamical estimation framework inspired by a mass–spring–damper system. At the causal level, the resulting estimator is interpreted through interventions on its internal threshold-selection mechanism. The proposed method models the variation of $\epsilon$ using ordinary differential equations defined on the ordered k-distance signal, enabling analysis of structural transitions in density organization via a surrogate dynamical representation. System identification is performed using L-BFGS-B optimization on the smoothed k-distance curve, while the system dynamics are solved with the fourth-order Runge–Kutta method. The resulting estimator identifies transition regions that are structurally informative for $\epsilon$ selection in DBSCAN. To analyze the estimator at the intervention level, Pearl’s do-calculus is used to compute the Average Causal Effect (ACE). The method was evaluated on synthetic benchmarks and on the Covtype dataset, including scenarios with multi-density overlap and dimensionality up to ${\mathbb{R}}^{10}$. The resulting ACE values, $+0.9352$, $+0.5148$, and $+0.9246$, indicate that the proposed estimator improves intervention-based $\epsilon$ selection relative to the geometric baseline across the evaluated datasets. Its practical computational cost is dominated by nearest-neighbor search, behaving approximately as $O(NlogN)$ under favorable indexing conditions and degrading toward $O\left(N^2\right)$ in high-dimensional or weak-pruning regimes. Full article

This study addresses the limited availability of unified experimental datasets comparing ribbed steel and smooth FRP bars embedded in the same hybrid-fiber high-performance concrete (HPC) matrix under identical conditions. It investigates the mechanical and bond behavior of a triple-fiber HPC combining hooked-end steel (ST), basalt (BA), and polypropylene (PP) fibers and reinforced with steel, GFRP, and CFRP bars of identical diameter and embedment. Under a uniform curing regime, the HFRC reached a compressive strength of approximately 82 MPa and exhibited a high fracture energy G_f approximately 3.7 kJ/m² with a stable post-peak response in a notched-beam test, demonstrating effective multi-scale crack bridging within a dense hybrid fiber network. Pull-out tests on 200 mm embedment revealed distinct interfacial mechanisms: ribbed steel developed a pronounced peak bond stress (τ_max = 13.05 MPa) and the largest bond energy (G_b = 146 N/mm) due to mechanical interlock, whereas smooth GFRP and CFRP showed low τ_max (=1.46 and 0.78 MPa) and smoothly decaying τ–s governed by adhesion–friction with G_b = 3–4 N/mm. A consistent experimental framework enabled direct mechanistic comparison of bond–slip behavior across reinforcement types without confounding matrix or curing variables. Simple constitutive laws calibrated to the experimental τ–s curves (ramp–softening for steel and ramp–plateau or exponential for FRP) captured the stiffness, strength, and energy hierarchy with low error. The main contribution of this study lies in providing a configuration-consistent reference dataset and calibrated bond–slip descriptions for hybrid-fiber HPC members reinforced with both steel and FRP bars. The results highlight the role of the hybrid fiber network in improving crack stability and provide design-oriented parameters for anchorage assessment and nonlinear bond–slip modeling. Although the results are based on a limited experimental program, they establish a mechanistically coherent basis for further optimization of hybrid HPC matrices and development of performance-based anchorage formulations in high-performance structural applications. Full article

Five groups of recycled aggregate concrete (RAC) mixtures with mass replacement ratios of emery (0, 5%, 10%, 15%, 20%) were prepared. The cubic compressive strength, splitting tensile strength, flexural strength, and flexural fatigue properties under stress levels of 0.6, 0.7, and 0.9 were tested. The fatigue reliability of RAC was analyzed based on the Miner model. Test results indicate that emery incorporation significantly improves the mechanical properties, flexural fatigue properties, and fatigue reliability of RAC. Compared with the reference group (0% emery), the 28-day cubic compressive strength, splitting tensile strength, and flexural strength of RAC with 20% emery increase by 18.62%, 27.35%, and 20.28%, respectively. The flexural fatigue life increases by up to 135.8% under high stress level (0.9). Flexural fatigue performance and fatigue reliability decrease with increasing stress level. The S-N curve was obtained based on the Wöhler mathematical model with high fitting reliability (R² > 0.95). Full article

To investigate the fatigue performance of a novel green low-carbon steel–AAUHPC (Alkali Activated Ultra-high Performance Concrete, AAUHPC) composite bridge deck and achieve its structural optimization, this paper proposes a steel–AAUHPC composite bridge deck structure featuring double-sided welding of U-shaped ribs. Firstly, the numerical model of a symmetrical composite bridge deck is established by ABAQUS finite element software. The stress response of key fatigue structural details is analyzed, and the fatigue life is evaluated based on the S-N curve method. At the same time, the calculation results are compared with the orthotropic steel bridge deck and the steel–UHPC composite bridge deck. Secondly, the CCD method and RSM method are used to construct a mathematical regression model with the structural weight W per unit area and the fatigue stress amplitude of key details as the target. Finally, NSGA-III is used to optimize structural parameters such as AAUHPC thickness, top plate thickness, diaphragm thickness and spacing to obtain the Pareto-optimal solution set. The results show that the AAUHPC material has both environmental protection and excellent mechanical properties, and its compressive and splitting tensile strength is significantly higher than that of ordinary concrete, which is close to the UHPC level. The steel–AAUHPC composite bridge deck can significantly improve the fatigue performance of the orthotropic steel bridge deck. After laying the AAUHPC layer, the stress amplitude of each fatigue detail decreases, and the C1 detail decreases by up to 69.4%. Except for the C6 detail, the rest of the structural details meet the infinite-life design criteria, and the overall improvement effect is comparable to that of the steel–UHPC composite bridge deck. The constructed response surface model has good prediction accuracy. The optimization results show that the fatigue stress amplitude and the structural weight W are mutually restricted. Among the 15 sets of Pareto-optimal solutions obtained, solution U8 achieves weight minimization under the premise of satisfying the infinite-fatigue-life criterion. The optimal parameter combination is: AAUHPC thickness of 40 mm, top plate thickness of 10 mm, diaphragm thickness of 16 mm, and diaphragm spacing of 2400 mm. The research results can provide a theoretical basis for the fatigue design and engineering application of a new green steel–AAUHPC composite bridge deck. Full article

Compliant mechanisms have contributed to many advances in soft robotics, and there is strong motivation to translate these ideas to assistive devices where adaptive motion at the human interface is required. This work presents novel reconfigurable compliant joints (RCJs) as a parameterized joint element for functional biomimicry in lower-extremity joints for prosthetic knees and ankle–foot orthoses, with concepts that extend to other limb joints. The RCJ uses a rigid hub and outer ring joined by an array of flexible links with centerlines defined by cubic Bézier curves. Link shapes are organized into four Bézier classes (A–D), with base types using 10, 12, or 14 uniformly distributed link slots and variants generated by modifying active-link count and distribution, forming a structured morphology space of 12 configurations for machine design. Dual-extrusion 3D-printed prototypes are characterized by a custom testing apparatus using a 2.2 kN load cell at 25 mm/s over a 0–90° rotation range across six recorded load cycles to measure torque–angle curves and stiffness under large deformations. Angle-dependent stiffness is evaluated over three fixed intervals (0–30°, 30–60°, and 60–90°) to quantify multi-stage behavior. A 2-dimensional corotational frame model and a Simscape Multibody model, including a rolling-contact knee configuration, use the same parameterization to relate geometry, nonlinear mechanics, and system-level motion. Experiments and simulations show multi-stage torque–angle profiles and predictable stiffness modulation across all configurations, with both magnitude and transition angle tunable through Bézier class and active-link distribution, positioning the RCJ as a CAD/CAE-compatible joint architecture for assistive devices or wearable robotic systems and a basis for advancing functional biomimicry in compliant mechanism design. Full article

The tribocorrosion behavior of AZ31 and WE43 was investigated during sliding wear tests in Hank’s balanced salt solution (HBSS) and pure water. While wear volume increased monotonically with load in air and water, HBSS exhibited a distinct non-monotonic trend; the maximum material loss occurred at the minimum load (0.98 N) and decreased at 2.94 N before rising again. This indicates that at low loads, degradation is primarily driven by accelerated chemical dissolution (tribocorrosion) rather than by purely mechanical abrasion. The magnitude of wear followed the order [HBSS] > [air] > [water] in the low-load range (0.98–1.96 N), whereas it shifted to [air] > [HBSS] > [water] in the high-load range (2.94–5.88 N). A comparison of the wear rate of the alloys shows that the wear rate in HBSS differs from that in water, depending on the hardness of the substrate, similar to conditions in air. Notably, the specific wear rate decreased as test duration increased under low loads, further suggesting that corrosion-induced volume loss significantly outweighs mechanical wear in this regime. The static corrosion test revealed that volume loss during tribocorrosion was higher than that under static corrosion conditions. While the deposition of corrosion products affected net volume loss, chemical dissolution remained the primary driver of the observed wear trends at low loads. Electrochemical data from anodic polarization curves confirmed that the specimen tested under a 0.98 N load exhibited lower corrosion resistance. Mechanistically, it was suggested that Cl⁻ ions contributed to the overall increase in wear, while NaHCO₃ specifically contributed to the increase in wear in the low-load range. Full article

Background: The endothelial activation and stress index (EASIX), derived from the serum lactate dehydrogenase, creatinine, and platelet counts, is a composite biomarker for endothelial dysfunction and systemic stress. It has been developed to predict clinical outcomes in hematologic malignancies. This study aimed to investigate the EASIX’s predictive role in contrast-induced nephropathy (CIN) and in-hospital mortality in patients with ST-segment elevation myocardial infarction (STEMI) undergoing primary percutaneous coronary intervention (PCI). Methods: A total of 1552 patients with STEMI who underwent primary PCI were retrospectively included. The patients were divided into two groups: CIN (+) and CIN (−). Baseline demographic, laboratory, clinic, and procedural variables were compared between the two groups. Logistic regression analysis was performed to identify independent predictors of CIN and in-hospital mortality, while receiver operating characteristic (ROC) curves were used to determine the optimal EASIX cut-off values. Results: CIN developed in 7.6% (n = 118) of the study population, and these patients had significantly increased EASIX scores. Those with CIN were older and exhibited higher rates of diabetes mellitus, chronic kidney disease (CKD), and decreased left ventricular ejection fraction (LVEF) (all p < 0.001). In multivariable analysis, age (OR 1.053), CKD (OR 1.338), reduced LVEF (OR 0.965), and EASIX (OR 2.467) independently predicted CIN. EASIX > 0.93 demonstrated strong discriminatory ability (AUC 0.785; sensitivity 72% and specificity 72%). EASIX also independently predicted in-hospital mortality (OR 3.592), with an optimal cut-off > 0.88 (AUC 0.774). Conclusions: By integrating markers of renal function, endothelial activation, and systemic stress, EASIX may serve as a useful and reliable indicator for predicting CIN development and in-hospital mortality in STEMI patients undergoing primary PCI. Full article

Pacific white shrimp (Litopenaeus vannamei) is a major aquaculture product worldwide. For consumers, discriminating domestic from imported sources of shrimp meat, and individual domestic sources, can be highly desirable because of the different meat quality and environmental contamination from geographically different origins of shrimp. This study evaluated the potential of stable isotope analysis (δ¹³C, δ¹⁵N, δ²H, δ¹⁸O) with chemometric models to authenticate the origins of Pacific white shrimp sold in China. Shrimp samples from domestic (Guangxi, Fujian, Shandong, Inner Mongolia) and foreign (Ecuador) sources were analyzed, using statistical analyses. The four-isotope model achieved 89.3% cross-validation accuracy in distinguishing domestic and foreign shrimp, with an overall prediction Area Under the Curve (AUC) of 0.901 (95% CI: 0.819–0.983)—significantly outperforming single-isotope models. Differences in δ¹³C and δ¹⁵N reflected feed source variations, while δ²H and δ¹⁸O (Variable Importance in the Projection (VIP) > 1, key discriminatory indicators) mirrored geographic environmental difference. Although δ¹⁵N did not differ significantly among groups, the combination of all four isotopes reduced limitations of individual δ²H/δ¹⁸O use. This approach enhanced the precision, reliability, and applicability of stable isotope analysis for origin authentication by leveraging complementary isotopic data and robust statistical frameworks. These findings demonstrate the proposed model’s potential as a cost-effective, copyright-compliant framework for shrimp origin authentication, with implications for isotopic traceability across food science fields. Full article

The Zeta-Minimizer Theorem establishes that the Riemann zeta function $\zeta \left(s\right)$ and the primes arise variationally as unique minimizers of a phase functional defined on a symmetric measure space $\left(X,\mu ,G\right)$ equipped with helical operators. Three fundamental axioms—strict concave entropy maximization (Axiom 1), spectral Gibbs minima with non-vanishing ground states (Axiom 2), and irreducible bounded oscillations with flux conservation (Axiom 3)—allow for the selection of the non-proper Archimedean conical helix as the sole topology satisfying all constraints. Primes emerge as indivisible minimal cycles in the associated representation graph $\Gamma$ (via Hilbert irreducibility and Maschke’s theorem), while the Euler product is recovered through the spectral Dirichlet mapping of the helical eigenvalues. The partial zeta product, $Z\left(s\right)=\prod _j{\displaystyle \frac{1}{1-p_j^{-s}}},s\in \mathbb{R}\left\{0\right\},$ constitutes the exact grand partition function of any finite subsystem. Numerical inversion of this product directly recovers the mixture frequency $s$ from any experimental compressibility factor $Z_{\mathrm{m}\mathrm{i}\mathrm{x}}$. Mole fractions $x_i\left(s\right)$, interaction parameters $\Delta \left(x_i\right)$, and the Lyapunov spectrum $\lambda \left(x_i\right)$ then follow deductively via the helical transfer matrix and the closed-form linear ODE for $\Delta$. Occupation numbers $N\left(x_i\right)$ attain sharp maxima precisely at Fibonacci ratios $F_r/F_{r+1}$, leading to the molecular prime-ID rule. For twelve representative purely binary (irreducible) systems spanning atomic noble gases, simple diatomics, polar molecules, and an aromatic ring, the residuals satisfy $|Z\left(s\right)-Z_{\mathrm{m}\mathrm{i}\mathrm{x}}|<1.5\times {10}^{-8}$. The resulting $\lambda \left(x_i\right)$ curves accurately reproduce critical points, liquid ranges, and thermodynamic anomalies with zero adjustable parameters. The Riemann Hypothesis follows rigorously as a theorem: the unique fixed point of the duality functor $s\mapsto 1-s$ that preserves the orthogonality condition $\sum {\mathrm{c}\mathrm{o}\mathrm{s}}^2{\theta }^k=1$ is $\mathrm{R}\mathrm{e}\left(s\right)=1/2$, enforced by Axiom 1 concavity and Axiom 3 irreducibility. The framework is fully deductive and parameter-free and extends naturally to arbitrary mixtures and multiplicities through the helical representation graph. It provides a variational unification of analytic number theory, spectral geometry, thermodynamic phase behavior, and the Riemann Hypothesis from first principles. Full article