Physical Sciences

Abstract: This paper studies phase formation, continuous comparison, and cross-state transport when the observation map varies with the state of an observer. Starting from the classical model y = h(x), we prove that a complete representation of a nontrivial family of observation maps requires an independent variable position for the current map. State realization and its canonical quotient then yield an observer O = (S_O, Γ_O) and an observation map F_O : X × S_O → Y , establishing a three-layer paradigm of the physical world, the observer, and the observation world. For a selected scalar coherent complex readout, the observation map induces the response g = r ◦ (F_O|M). On the nonzero domain B = {m : g(m) = 0}, the observed-phase one-form is \( A_g = \operatorname{Im}\left( \frac{\mathrm{d}g}{g} \right). \) Amplitude–phase reduction of the full complex-response bundle produces a principal U(1) phase bundle. Given g and the standard phase normalization, we prove the existence and uniqueness of the compatible connection \( \Omega_g = p r_{\mathrm{U}(1)}^* \omega_{\mathrm{U}(1)} - \pi_{\mathrm{ph}}^* A_g, \) whose horizontal condition reproduces the local phase law. The first-order differential functional equation on lifted path space, \( \widetilde{c}^* \Omega_g = 0 \), is established as the basic phase-transport equation. It is equivalent to the group-valued differential form, the covariant-derivative form, the continuously lifted real-phase form, and the finite path-transport functional. The equation is uniquely induced by the complex response, is equivalent to horizontal lifting under the unique compatible connection, uniquely determines finite transport and path composition for prescribed initial data, is covariant under local phase-gauge transformations, and is invariant under positive amplitude rescaling. Inverse same-source double-state phase transport follows directly on fixed-physical-state slices. Finally, three representation levels are constructed: the full complex-response level G₀, the phase-differential and transport level G₁, and the task-quotient observation level G₂. Their relative completeness is proved for their respective problem classes, providing a unified mathematical structure from variable observation maps, complex responses, and phase connections to phase transport, maximal invariants, and target recoverability.

Abstract: We propose a context-first framework for future AI agents engaged in scientific discovery. Instead of assuming objects, variables, or coordinates, an agent starts from histories of contexts and observations and compares finitely describable predictive programs. The comparison uses one prequential Minimum Description Length (MDL) code: prediction and description costs share a common coding unit, task frequencies are fixed by an external evaluation protocol, inherited paradigms enter through conditional code length, and covariance tests are coded as held-out predictive channels rather than attached with arbitrary penalty coefficients. Predictive quotients, studied objects, attributes, and coarse generative world sketches thereby become model-class choices rather than priors. An open-world context-action dictionary can reuse, compose, split, merge, or introduce primitives under held-out compression. We also formulate local observation generally as a possibly stochastic, noninvertible channel with restricted support; pointwise warps exist only on shared latent support, while the remaining region requires posterior prediction. A finite implementation alternates continuous parameter fitting with discrete structure proposals, evaluates them on ordered held-out blocks, and requests observations that best discriminate the surviving programs. A Solar-System telescope specializes this construction to bounded circular fields, rotation, zoom, parallax, point-spread matching, and active follow-up. The framework is a theoretical and computational blueprint, not an empirical validation, and its selections are conditional on the supplied candidate programs, coding protocol, intervention coverage, and optimization. Overall, this work is intended to serve as a comprehensive operational handbook and practical guide for future autonomous AI agents conducting scientific discovery.

Abstract: Physics is intrinsically a complex subject. We review some of the results coming from researchers in physics education, who identified several common patterns in how pupils learn physics and how they differently apply the relative concepts when solving classroom problems with respect to dealing with everyday situations. As pointed out by some researches, a correct and fruitful approach to teaching physics should be based on a validated cognitive model of a student, which is however not still available. In this paper we propose to consider the origin of “intuitive physics” as due to the cognitive mapping of concept on the physical body (embodiment), which is particularly relevant for the concept of force, and also the role of the “knowledge illusion”, i.e., the undervaluation of the complexity of a concept that is perceived as “well known”. We profited of an existing extensive survey, based on the Force Concept Inventory, on first-year university students in scientific and technological disciplines by which we confirm previous findings and show that the non-Galilean concepts are not organized in a coherent structure. We also develop a conceptual model of cognitive conflicting structures in students, and extract, by stochastic optimization, a Boolean circuit mimicking the expected behavior of a “physics-aware” student.

Abstract: In Nigeria, onchocerciasis (river blindness), which is caused by the filarial worm Onchocerca volvulus and spread by Simulium blackflies, is still a significant public health concern, especially in riverine populations in the northeastern states of Adamawa, Bauchi, Borno, Gombe, Taraba, and Yobe. Due to non-compliance, drug ineligibility, migration of infected individuals and gaps in vector control, transmission continues in a number of endemic foci despite thirty years of mass drug administration (MDA) with ivermectin. In order to overcome major shortcomings of previous deterministic models that assumed homogenous human and vector populations, this study offers a stochastic, individual-based, geographically explicit, and time-dependent mathematical model to represent the heterogeneous transmission dynamics of onchocerciasis. Incorporating temperature and rainfall as climatic drivers of vector breeding and disease transmission, the model divides the human population into compliant and non-compliant susceptible, exposed, infectious, treated, and recovered compartments and the blackfly vector population into larval, susceptible, and infectious stages. Proofs of positivity and boundedness of solutions were used to establish the well-posedness of the model, and a disease-free equilibrium was obtained. R0 = 0.0202 was the result of applying the Next Generation Matrix technique to calculate the fundamental reproduction number (R0) and parameterizing it with values taken from the literature and estimation. The model indicates a long-term decrease in disease incidence and prevalence because this value is much less than unity, which is in accordance with Nigeria's goal of eradicating onchocerciasis by 2030. With an exponential decay pattern shared by all classes, simulations conducted over a five-year projection period (2026–2030) revealed decreasing trends in infected non-compliant, infected compliant, and treated populations along with decreased vector infection rates shown in Figures 1 to 4. Comparative intervention scenarios showed that when ivermectin treatment is combined with public health education, the disease is eliminated more quickly than when either technique is applied independently. The findings underscore that sustained ivermectin distribution, improved compliance through education, and integration of climatic variables into predictive models are critical to achieving elimination targets, while highlighting that any relaxation of intervention efforts could allow disease resurgence.

Abstract: Ring-core optical fibers support guided electromagnetic fields whose energy can be localized in an annular region rather than near the fiber axis. Such structures are important for higher-order vector modes, annular guided fields, and vortex-compatible optical states. This tutorial presents a step-by-step Maxwell-based derivation of vector modes in a three-layer ring-core optical fiber consisting of an inner cladding, an annular core, and an outer cladding. The purpose is pedagogical rather than to introduce a new eigenmode theory. Starting from Maxwell’s equations in a source-free, lossless, nonmagnetic dielectric medium, we introduce time-harmonic fields, the longitudinal propagation factor exp(iβz), and the azimuthal dependence exp(ilφ). The curl equations are then written explicitly in cylindrical coordinates, yielding six coupled first-order equations for the electromagnetic field components. The system is reduced to the two longitudinal components E_z and H_z, which satisfy Bessel-type radial equations in each homogeneous layer. Regularity at the fiber axis, decay at radial infinity, and continuity of the tangential field components at the two interfaces lead to a homogeneous matrix equation M_l(β)x= 0. The characteristic condition det M_l(β)= 0 determines the allowed propagation constants and effective refractive indices of the guided vector modes. The physical meaning of β, n_eff, l, radial localization, and annular power confinement is discussed. Particular attention is given to the distinction between annular intensity and vortex phase: an l = 0 mode may be ring-shaped but is not a vortex mode, whereas l ≠ 0 modes possess azimuthal phase winding and are vortex-compatible. Representative numerical illustrations and supplementary code are provided to connect the analytical derivation with modal profiles, intensity maps, phase maps, and power localization in the annular core.

Abstract: On July 2, 2023, a destructive two-component precipitation event occurred between O’Hare and Midway Airports in Chicago. 9 in (~225 mm) of precipitation fell over a focused region accompanying four observed mesoscale convective systems (MCS) in less than 12 hours. Three systems were quasi-linear convective systems (QLCS) that subsequently built upscale into a fourth system which exhibited many similarities to a mesoscale convective vortex (MCV). The larger scale precursor environment that organized these features included: 1) an upstream deep cold trough, 2) mid-upper tropospheric jet streak, 3) dual coupled mid-upper tropospheric potential vorticity maxima, 4) near surface west to east stationary warm boundary and deformation zone with poleward moisture advection, and 5) west-southwesterly low-level jet equatorward of that stationary boundary. As these meso-α scale systems approached the city they organized the first propagating QLCS#1 from central Illinois during the night prior to the heavy rain event. As that QLCS formed, the upper-level divergence and mid-upper tropospheric height falls migrated from the jet streak right entrance to left exit region strengthening in phase with the developing QLCS#1 thus allowing that QLCS to propagate over the city. The remnant trough accompanying this QLCS#1 subsequently was reorganized and modified by: 1) another QLCS #2 forced by the next morning’s Lake Michigan breeze convergence zone and then 2) an eastward-propagating QLCS# 3 from west-central Illinois closely coupled to the upstream cold trough. The first component of the heavy precipitation resulted from the interaction of these three QLCS followed by that precipitation system’s subsequent upscale growth into an MCS (system 4) with many characteristics consistent with a long-lasting massive MCV that controlled the second heavy precipitation component.

Abstract: Accurate characterization of surface ultraviolet (UV) irradiance is important for public health, environmental monitoring, and atmospheric chemistry. However, this remains challenging in regions of complex terrain where atmospheric and surface heterogeneity introduce significant uncertainty. Radiative transfer (RT) models provide physically rigorous simulations but can be limited by simplified or climatological input parameters, while satellite-derived UV products offer broad spatial coverage but can exhibit some systematic biases in heterogeneous environments. This study develops and validates a multi-sensor satellite-integrated framework that combines MODIS-derived aerosol optical depth with TROPOMI-derived ozone and nitrogen dioxide within the Tropospheric Ultraviolet and Visible (TUV) radiative transfer model. The methodology is applied to three mountainous sites in the southwestern United States and evaluated under clear-sky conditions using high-resolution UV-MFRSR measurements at 332 nm and 368 nm. Results demonstrate strong agreement between modeled and observed irradiance across all sites, with coefficients of determination exceeding 0.97 and normalized RMSE generally below 6%. Model performance was consistently higher at 332 nm, while a small systematic underestimation was observed at 368 nm. The framework improves the representation of atmospheric variability and enhances irradiance prediction accuracy in complex terrain, demonstrating a scalable and accessible approach for data-sparse regions.

Abstract: The use of the non-thermal electromagnetic waves to inactivate viruses has been proposed by a few groups; how microwave irradiation may alter virus infectivity is still object of investigation. In fact, the alleged transformation of a microwave photon into a phonon, in water or in organic media, has never been demonstrated. Microwave energy absorption in these media leads to heating, which generates many thermal phonons across a wide frequency spectrum, not a single coherent phonon at a specific frequency, able to produce an alleged Structure Resonance Energy Transfer (SRET) as strong as to break the capsid of a virion. The effective conversion of a single microwave photon to a single GHz phonon in water and/or organic media has been sometimes supposed but never demonstrated. However, there is still some emphasis on using non-thermal electromagnetic fields to destroy viruses. Hence, this paper poses the question: can human-safe microwave irradiation inactivate respiratory viruses?

Abstract: The transition from paper-based to electronic trade documents (eTDs) represents a critical step in modernising global supply chains; however, the absence of reliable mechanisms to verify the physical movement of goods vis-a-vis the eTD workflow remains a significant challenge. This study proposes the PROGRESS framework, an integrated digital trade architecture that combines AI-driven document verification with real-time physical tracking to ensure end-to-end assurance of consignments. The approach leverages advanced Optical Character Recognition (OCR) techniques, including Transformer-based attention models, Convolutional Recurrent Neural Networks (CRNN) with Connectionist Temporal Classification (CTC), and Vision Transformers (ViT), enhanced through context-aware validation to ensure semantic consistency across key trade documents such as commercial invoices, packing lists, airway bills, and certificates of origin. A simulation involving 5,100 consignments was conducted and benchmarked against real-world operations at Teesside International Airport. Results indicate that the proposed system reduces document processing time from 24–72 hours in traditional paper-based systems to approximately 1–2 minutes, achieving a validation accuracy of 98%. Furthermore, integration with RFID-based tracking, geofencing, and private 5G connectivity enables continuous monitoring of consignments, reducing customs dwell times from 72 to 44 hours and increasing throughput by up to 65%. The findings demonstrate that combining digital documentation with verifiable physical assurance significantly enhances transparency, efficiency, and regulatory compliance. This research contributes to the advancement of digital trade by addressing key limitations in current eTD implementations and supporting the effective adoption of the United Kingdom’s Electronic Trade Document Act.

Abstract: We present a portable, cost-effective, and innovative method for experimentally verifying Ohm’s law in alternating current (AC) resistive circuits using two smartphones: one functions as a signal generator (audio output) and the other as an oscilloscope (microphone input). By connecting identical resistors in series, we systematically increase the total resistance and measure the voltage across a fixed reference resistor. Our results reveal an inverse relationship between the reference voltage and the total resistance, in agreement with Ohm’s law. Fitting the data to a power law yields an exponent of -1.004, which deviates by only 0.4% from the theoretical value of -1. The proportionality constant obtained differs by only 0.7% from the value calculated directly from the measurements. These minimal discrepancies, achieved using non-traditional, uncalibrated equipment and commercial resistors, demonstrate that our methodology is accessible, reproducible, and accurate. This approach validates Ohm’s law with high precision and underscores the potential of mobile devices as reliable experimental tools for physics education, particularly in unconventional or remote laboratory environments.

Abstract: In the present work, the potential applications of Cu thin films and Ag/Cu bilayer thin films obtained by the pulsed laser deposition (PLD) technique are investigated in terms of the physicochemical effects resulting from their interaction with an aqueous solution containing Reactive Blue 21 (RB21) dye and sodium bicarbonate (NaHCO₃). The thin-film deposition process was carried out using a Q-switched Nd:YAG laser system operating at a wavelength of λ = 532 nm, with a pulse duration of τ = 10 ns, a repetition rate of ν = 10 Hz, a pulse energy of E = 180 mJ, a laser spot diameter of d = 336 μm, and an angle of incidence of α = 45°. Two types of thin films were prepared: a Cu thin film and an Ag/Cu bilayer thin film. The thermal effects induced by the interaction of the laser beam with the target materials were investigated by numerical simulations performed in COMSOL, allowing the evaluation of melt-phase formation for each material separately and providing a better understanding of the morphology and topography of the deposited thin films. The simulation results were validated through scanning electron microscopy (SEM) observations and surface roughness analyses. The two thin films were subsequently treated with an aqueous solution containing 10 g/L RB21 dye and 10 g/L NaHCO₃. Physicochemical analyses performed after treatment, including scanning electron microscopy (SEM), optical microscopy (OM), profilometry, Fourier-transform infrared spectroscopy (FTIR), energy-dispersive X-ray spectroscopy (EDS), and UV–Vis spectroscopy, revealed significant degradation of the RB21 dye accompanied by corrosion of the thin films, with the corrosion process being more pronounced in the case of the Cu thin film. The obtained results indicate that the method analyzed in this study may represent an alternative approach for the decomposition of recalcitrant organic dyes using thin Cu films, without relying on conventional photocatalytic processes. Equally important are the potential applications of the RB21/NaHCO₃ solution as an etching and patterning medium for thin Cu layers, while the Ag overlayer may provide a protective effect during such processes. These findings may contribute to the development of novel fabrication techniques for optoelectronic components, including solar cells, photovoltaic windows, and other industrial and laboratory applications.

Abstract: Empirical science does not begin from direct access to dynamical laws, but rather from records, i.e. persistent physical states that function as evidence. It is argued here that such records already define an asymmetric relation between what has become evidentially available and what has not. Time-symmetric laws, when discovered, are therefore reconstructed from within an asymmetric evidential domain, and not the other way around. As opposed to the standard bottom-up view that asks how evidently time-asymmetric Universe can emerge from fundamentally time-symmetric physical laws, empirical science must start from an evidential time-asymetric Universe and leads to the top-down view that the fundamental laws can be equally well symmetric or asymmetric, thereby weakening the Arrow of Time puzzle. This top-down mediation is described as an evidential transfer function; the physical selection, amplification, stabilization, and retention of correlations as records. The proposal explains why empirical access to any law is necessarily record-based and temporally asymmetric, with no recourse to the thermodynamic arrow.

Abstract: The standard historical account traces the second to astronomical timekeeping, sexagesimal subdivision of the day, and later metrological standardization. This story explains the arithmetic ancestry of the unit, but it does not by itself explain why this particular fine subdivision, rather than other arithmetically natural alternatives, became so useful, stable, and persistent. The thesis put forward here is that the second is not merely a sexagesimal convention; it is, more fundamentally, close to a natural planetary-organism time scale. Specifically, for sufficiently large mobile organisms capable of carrying relatively large brains and acting under habitable planetary gravity, free fall, balance, gait, inverted-pendulum instability, and simple pendular motion are all controlled by a time of order \(\sqrt{H/g}\), where H is an organism-scale height and g is the local surface gravity. Since habitable rocky planets and large mobile organisms occupy a restricted macroscopic range, this scale naturally falls near one second. I therefore propose that the historical second was physically selected by its proximity to the planetary-organism time scale. This does not mean that the second was consciously derived from pendulums or biomechanics, nor that the sexagesimal story is wrong. Rather, the sexagesimal story explains how the unit became arithmetically available, while the particular subdivision of an hour into 60 × 60 parts became historically stable because it landed on the organism-gravity time scale. As with the geodetic definition of the meter as one part in 10 million of the distance between the equator and the pole, historical standardization need not explain why the resulting unit lies near a practically natural organism-scale quantity.

Abstract: Diabetes mellitus affects over 500 million people worldwide, yet most machine learning prediction models remain opaque, poorly calibrated, or untested against statistical benchmarks—limiting their clinical utility. This study proposes a comparative explainable machine learning (XML) framework that combines the Marine Predators Algorithm (MPA) for hyperparameter optimization with SHAP-based interpretability to improve both the accuracy and transparency of diabetes risk prediction. Three models—Logistic Regression (LR, baseline), Random Forest (RF), and MPA-optimized XGBoost—were evaluated on a large-scale, class-imbalanced dataset of approximately 100,000 records. A seven-stage preprocessing pipeline incorporating mean imputation, one-hot encoding, Min-Max normalization, and SMOTE class balancing was applied strictly within stratified 10-fold cross-validation folds to prevent data leakage. Model performance was assessed using accuracy, ROC-AUC, F1-score, sensitivity, specificity, precision, and Brier score. Statistical significance was confirmed via Wilcoxon signed-rank tests with Bonferroni correction. MPA-optimized XGBoost achieved 96.72% accuracy, 97.70% precision, 95.70% recall, 96.71% F1-score, and 99.56% ROC-AUC—outperforming both LR and RF across all metrics with statistically significant margins (p < 0.001). Calibration analysis yielded a Brier score of 0.0262. SHAP analysis identified HbA1c level, blood glucose level, and age as the three strongest global predictors, with feature interaction analysis revealing a synergistic effect between HbA1c and blood glucose. While results are specific to the Kaggle-sourced dataset and require external validation before clinical deployment, the framework demonstrates that MPA-driven optimization paired with SHAP explainability can produce models that are both high-performing and clinically interpretable. This work establishes a methodological baseline for transparent, statistically rigorous diabetes prediction systems.

Abstract: In-use heat transfer coefficient (HTC) measurements are useful for retrofit evaluation, heating system sizing, and thermal performance assessment in occupied homes. Quantifying the variance in the in-use HTC when, necessarily, utilising a range of assumptions and simplifications is therefore crucial, and also critical for further method development. Two empirical sensitivity analyses were used to explore how changes in commonly assumed in-use factors affect HTC estimates in occupied homes. The factors investigated were measurement uncertainty, solar gains, metabolic gains, boiler efficiency, water use, party wall heat transfer, and ventilation rate - parameters that are impractical or impossible to routinely measure, and as such default values are generally adopted. The sensitivity analyses used data from seven occupied homes and a single, common, HTC estimation method. Input distributions for each factor were derived from available data and current assumptions. A local sensitivity analysis examined how changes in each input affect the HTC and a global analysis quantified the contribution of the inputs’ variance to the HTC’s variance. Conducting parallel analyses enabled a more complete picture to be obtained, and the alignment of the two approaches provided confidence in their results. The factors with the greatest overall effects on the HTC were ventilation and party wall heat transfer; however, this was not the case for every home. In particular, HTCs from homes with higher occupancy exhibited stronger HTC sensitivity to metabolic gains and water use. The use of real data from occupied homes enables the results to be applicable to typical imperfect datasets. The results will inform future applications of in-use HTC measurements and methods for determining their uncertainty. Further work expanding this analysis to a larger dataset with more building typologies, and gathering data to define the sensitivity analysis more accurately would strengthen these conclusions.

Abstract: Linear Dichroism (LD) optical absorption spectroscopy historically has had substantial but limited application in various domains of science. In particular, full-tensor reconstruction has been tedious and difficult, usually requiring extensive measurements on single crystals at many orientations using a four-circle goniometer. As a consequence it is very seldom done. Here we propose, and test by numerical simulation, a simple, novel method of determining the full dipole optical absorption tensor of homogeneous planar films in real-time as a function of energy (or wavelength), while requiring only minimal additional time and instrumentation. The full-tensor spectrum, after construction from the experimental data, allows one to instantly calculate the absorption for any selected polarization direction, even those that are physically inaccessible to experimental measurement. Although our specific application in this paper is to X-ray Absorption Fine Structure Spectroscopy, the method should be adaptable to UV-Vis, IR, THz, microwave, and other wavelengths. A strength of this measurement modality is that full tensor data can be acquired using essentially the same sort of scanning geometry that is normally used for XAFS, with only a one discrete shift in spin axis orientation between groups of scans. The additional instrumentation needed to determine the five Fourier components of the signal at each energy is minimal; two angles gives up to ten parameters, while six are needed, and the others can be put to good use. Outside of XAFS, FTMAS also should be applicable to diverse scientific and technological areas such as oriented bio-molecular films, semiconductor and materials physics, and process control of thin-film photovoltaics and semiconductors.

Abstract: We elaborate on computational emergence (CE), understood as the emergent acquisition of specific abilities from specific forms of computation, such as artificial neural networks and cascades of rule iterations found in cellular automata. CE leads to the acquisition of properties such as learning abilities, morphological pattern formation, and coherence, and arises from computational mechanisms. We also elaborate on emergent computation (EC), understood as the emergent acquisition of computational abilities by communities of phenomenologically interacting agents, potentially through appropriate interlinkages among them, as in emerging networks. Processes of interaction are understood generically as forms of mutually active interdependence, which can be modeled as self-generated networks. EC arises from phenomenological mechanisms of interaction among agents and leads to the acquisition of properties such as coherent behaviors, resilience, robustness, and collective intelligence. The reason for distinguishing between these two types of emergence is that doing so may open new approaches to modeling collective behavior, especially in artificial ones, such as swarms of unmanned aerial vehicles (UAVs), where introducing parametric and structural changes is more feasible. Combining the two approaches—(a) phenomenological, networked EC arising from populations of interacting (b) in turn computationally emergent agents—allows the consideration of research directions such as identifying relationships between combinations of CE and emergently acquired computational properties within the conceptual frameworks of networked neural networks and intersected neural networks, i.e., networks that share nodes. Such research directions are expected to enable approaches for influencing collective behaviors and complex systems in a non-invasive way, including swarms of UAVs (or drones), autonomous cyborg swarms, and coherent communities of artificial devices equipped with sensors, edge artificial intelligence, and secure communications. We consider the mesoscopic nature of complexity in collective behaviors as a continuous negotiation between these two forms of emergence, with EC playing a macroscopic role and CE a microscopic role. We conclude that this general framework relates to the concept of “The Middle Way” in physics by focusing on what occurs “in between” systems (such as between intersecting neural networks and their dynamic networking) and within transient spaces where non-invasive intervention may be possible and appropriate for guiding, modifying, and inducing changes in complex emergent systems.

Abstract: The traditional paradigm of natural science treats the laws of nature as eternal and immutable. This review examines a powerful alternative tradition that views these laws as historically evolving and constructed entities, tracing this shift from ancient roots to evolutionary epistemology, radical constructivism and physics. We address the resulting methodological crisis—where different branches of science optimize their own laws and isolate from one another—by proposing a strict hierarchical framework. Under this method, invariant basic concepts are strictly separated from flexible models. Crucially, the Entropic Measure of Time (EMT) is presented as the central operational tool. By defining time through entropy production, EMT enables the deductive derivation of physical laws from specific models, restoring a unified, cohesive structure to modern science.

Abstract: We discover a synchronization admissibility boundary defined solely by the states of oscillators. The boundary is independent of structure and determines whether any two oscillators share a cluster in real time, unifying global synchronization, cluster partition, and the real-time onset of synchronization loss. This uniformity has been validated through dozens of adversarial tests. Mathematical proofs show that this boundary is mathematically equivalent to the constraint that the synchronous frequency must be a real number. This constraint is a direct corollary of a cornerstone of physics long taken for granted: all measurable physical quantities are real numbers. This equivalence reveals that the synchronous admissibility boundary (a key function) emerges directly from the principle that is logically prior to any specific structure.

Abstract: The purpose of the present study was to carry out measurements of the activity concentrations of radon (222Rn) and thoron (220Rn) in homes, to calculate the annual effective inhalation dose and the induced risk of lung cancer associated with the exposure to 222Rn and 220Rn, for individuals living in the towns of Moanda and Franceville, in Gabon. One hundred (100) radon-thoron detectors of the brand RADUET were deployed in these localities, 50 per city, i.e., one detector per home. The results of the radon concentrations varied in the range 91-156 Bq m-3 in Moanda, with arithmetic and geometric mean values of 113.2 ± 2.8 Bq m−3 and 111.8 (1.0) Bq m−3, respectively, and in the range 76-139 Bq m-3 in Franceville, with arithmetic and geometric mean values of 105.0 ± 1.9 Bq m−3 and 104.2 (1.0) Bq m−3, respectively. These mean values are above the United Nations Committee on the Effects of Atomic Radiation (UNSCEAR) worldwide average values of 40 Bq m−3 (arithmetic mean) and 45 Bq m−3 (geometric mean). For thoron, the concentrations varied in the range 3-945 Bq m−3, with arithmetic and geometric mean values of 69.5 ± 0.4 Bq m−3 and 24.4 (3.9) Bq m−3 at Moanda, and in the range 4-78 Bq m−3, with arithmetic and geometric mean values of 18.4 ± 0.4 Bq m−3 and 11.6 (0.4) Bq m−3 in Franceville. This shows that the mean concentration values of thoron were significantly higher than the UNSCEAR world average value of 10 Bq m−3. Overall, the highest concentration values were recorded in the town of Moanda and the lowest in the town of Franceville. The dose values estimated in the present study demonstrate that the population in Moanda and in Franceville may be exposed to a relatively significant potential risk of radon-and thoron-induced cancer.