Physical Sciences

Abstract: A generalized canonical representation of the Hilbert-Einstein action is obtained within the De Donder-Weyl formalism, preserving the equality of space-time coordinates. Unlike the conventional canonical formalism with a distinguished time parameter, the generalized Hamiltonian function does not reduce to a linear combination of constraints, and the energy of a closed universe is non-zero. Its distribution is a 4D scalar density. The contribution of the Yang-Mills field to the scalar energy density of the universe is found. To quantize the theory in generalized canonical form, a quantum principle of least action is proposed, in which the action integral is an operator on the space of wave functionals depending on the world history of the universe in the region under consideration. The secular equation for the action operator is considered as the fundamental dynamic equation on the space of wave functionals. As a consequence, a local wave equation is obtained that functions as a non-stationary Schr\"{o}dinger equation for the components of the wave functional. The role of the time derivative in this equation is played by the covariant 4D divergence operator, and its source is the non-zero 4D scalar energy density of the universe.

Abstract: Two features of fundamental physics are normally taken as brute postulates: that the spacetime metric is four-dimensional with Lorentzian signature, and that matter obeys the Dirac equation. We obtain both from a single definition, which we introduce: that of an observer-bearing spacetime. A spacetime is observer-bearing if some frame within it admits a positive-definite probability density—read along an observer's direction—together with a conserved vector current; that is, if it can carry a readable, conserved probability at all. The "observer'' here is algebraic, a direction of positive-definite conserved current, not a physical organism. For this criterion to have force, the amplitude must be a multivector in the Clifford algebra of the tangent space, rather than the usual complex amplitude; the two are isomorphic in 3+1 dimensions but diverge in others, and that divergence is the source of the selection. To recover the dynamics, we then ask for the information-preserving transport of the conserved current—the flow that produces no net entropy. The result is the Dirac equation, in which the relativistic mass term emerges automatically as the constraint that makes the flow entropic, the mass appearing as its Lagrange multiplier. We distinguish this from anthropic (Tegmark) and orbital-stability (Ehrenfest–Tangherlini) accounts of dimensionality, and from Fisher-information (Frieden) and quantum-cellular-automaton (D'Ariano–Perinotti) reconstructions of the Dirac equation.

Abstract: InGaN/GaN quantum wells on polar substrates exhibit a pronounced quan-tum-confined Stark effect, which significantly limits their efficiency as light emitters. Surprisingly, this detrimental effect is significantly reduced when wider wells (above 10 nm) are used; their emission kinetics are the central focus of this work. A time range spanning 9 orders of magnitude, from picoseconds to milliseconds, is explored through various experiments. This includes experiments on the optical visualization of slow decays of charge in the ground states (called “dark charge”) in the millisecond range, experiments on radiative recombination of excited states in the nanosecond range and on the relaxation of hot carriers in the picosecond range. All data are explained within the framework of qualitative and semi-quantitative models. The highly diverse kinet-ics of ground and excited states is due to the fact, that the ground states of electrons and holes have negligible overlap and screen the built-in field, are optically inactive, and recombine nonradiatively in milliseconds. Meanwhile, when the field is screened, the excited states recombine radiatively in the picosecond/nanosecond range. The pulses of photo- and electro-luminescence depend strongly on the excitation period. The application of negative-voltage pulses allows to deplete the well from charge and generates short pulses of light.

Abstract:

This paper proposes the Information-Kinetic Theory (IKT) – a background-independent graph-topological paradigm in which metric spacetime, fields, and particles are regarded as infrared interfaces of stochastic complex-phase routing on a dynamic graph. The fundamental microdynamics is formulated in terms of the local quantum-walk operator U_m acting on the oriented edges of the graph. Under prethermal coherent and statistically isotropic vacuum conditions, the effective Floquet dynamics yields the Weyl/wave envelope. The electromagnetic, strong, weak, and gravitational sectors are described as different macroscopic interfaces of a single graph microdynamics: the U(1)-link phase, SU(3)_route color routing, the chiral weak gateway, and phase refraction χ_G. The Topological Transition Calculus (TTC) reformulates continuum UV integrations as finite sums over admissible graph transitions, while running and polarization corrections are treated as graph-computational matching and inference problems. Elementary particles are modeled as stable topological cycles of the graph, and rest mass is represented by the monodromic phase gap or by the integral algorithmic cost of maintaining a closed route. Within this framework, channel-topological anchors are formulated for a number of phenomenological quantities, including α{\rm top}^{-1}=4π³+π²+π, the parameter-rank interpretation of the minimal electronic skeleton ne(0)=10, the reduction of G to the effective configuration volume of the electron route, the leading proton confinement anchor m_p/m_e≃6π⁵, and the logarithmic anchor for the neutron isospin splitting △m≃m_eln(4π). On cosmological scales, IKT formulates the dark-energy component as the two-component interface $\Lambda_{{\rm DE},time}^{\rm IKT} = \Lambda_{{\rm par},time} + \Lambda_{{\rm noise},time}^{\rm valve}$. The dynamic parent-throughput background is proposed to drive the late acceleration, while the finite throughput of the parent valve limits the early insertion noise and leaves a small valve-limited t⁻² tail in the late epoch. This dark-energy component is separated from the total expansion scalar 3H², which also contains matter, radiation, neutrinos, the vortex/dark-matter sector, curvature, and coarse-graining corrections. Dark matter is modeled as a vortex topological sector, testable via CMB/LSS observables, BTFR, lensing, and cluster collisions. The theory also introduces TTC as a discrete calculus of topological transitions and formulates a set of falsifiable tests: DSR corrections to the propagation of high-energy massless packets, including photons; objective macroscopic decoherence; a cosmological birth-imprint scale for neutrino masses; constraints on stable fermion generations; and a statistical upper cutoff in the supermassive-black-hole mass function. IKT thus sets up a unified computational framework for reducing physical structures to the topology, spectrum, and routing of a dynamic graph. The material is organized in a three-level format: the introductory level gives a compact map of IKT and its main predictions; the technical corpus develops the mechanisms and derivations; and the audit and supplementary sections collect parameter classes, status labels, notation, and navigation aids.

Abstract: The reconstruction of galaxy assembly histories from contemporary stellar populations remains a central challenge in astrophysics. Both stellar population synthesis and Galactic Archaeology represent special cases of the same Bayesian inverse problem: inferring evolutionary history from present-day observables. This unification constitutes the central contribution of the present work. We formalise it as Unified Galactic Reconstruction (UGR), in which the full posterior over the evolutionary state is conditioned simultaneously on chemical and dynamical observables, rather than treating them sequentially. The Starlight Synthesis Algorithm operates as the integrated-light limiting case of UGR, while large-scale chemo-kinematic tomography represents the resolved-star limit. We additionally introduce the Galactic Reconstruction Number, R_G = N_chem × N_kin / N_pop, as a dimensionless heuristic index for comparing reconstruction methodologies. UGR naturally subsumes existing approaches as limiting cases and provides a conceptual foundation for next-generation Galactic studies with forthcoming surveys, including 4MOST, WEAVE, and the Roman Space Telescope.

Abstract: Galaxy dynamics and the accelerating expansion are the two standing tensions of large-scale gravitation. We develop both from one finite relational substrate on which gravitation is the synchronisation of elementary clocks. Synchronisation reproduces Newton's law at high acceleration and carries an intrinsic resolution floor, fixed by the expansion rate, at \(a_{0}=cH_{0}/2\pi\) - within ten percent of the observed scale, with no free parameter. Below the floor the field is read in a Fourier-conjugate chart where the registered force is an amplitude rather than a gradient, giving the geometric-mean law \(g_{\mathrm{eff}}=\sqrt{g_{\mathrm{bar}}a_{0}}\), hence flat rotation curves and the baryonic Tully-Fisher relation \(v^{4}=GMa_{0}\). The crossover is fixed by a finite first-passage registration and reproduces the empirical radial acceleration relation \(g_{\mathrm{obs}}=g_{\mathrm{bar}}/(1-\exp(-\sqrt{g_{\mathrm{bar}}/a_{0}}))\) with no fitted function; the intrinsic scatter follows as the disk's dynamical temperature and the external-field effect as the total-field dependence of the registration. In merging clusters the coherence-weighted enhancement follows the collisionless galaxies, predicting the lensing offset, and the cluster-core excess is predicted to be the coherent amplitude addition of the core's synchronised components. The cosmological constant is the curvature of the finite chart, \(\Lambda\sim1/\Omega\). The single quantity left to the totality is the \(\Omega\)-hard running of \(a_{0}\) across cosmic scale. Every exact claim is \href{https://github.com/gamayos/frc-numerics/tree/main/32-dark}{verified in finite-field or cyclotomic arithmetic}, the continuum entering only as a labelled degenerate idealisation.

Abstract: A physical claim rests on three separable supports: internal formal control, operational experimental contact, and reproducible computation. At laboratory scales these three move together. At extreme scales (Planck-regime gravity, cosmic horizons, high-dimensional simulations) they decouple. nWe develop the Clampdown Effect as a precise mathematical theory of that decoupling. A validation score $V_Q\in[0,1]$, formal pressure $W_Q$, operational pressure $S_Q$, and a six-channel error budget $E_Q$ are defined. A Pareto obstruction theorem is proved: under generic inter-channel coupling no admissible theory-instrument-computation triple simultaneously minimises all six error channels. The empirical equivalence classes of $T_Q$ under a fixed corridor threshold carry a natural metric $d_\theta$, and $S_Q$ descends to a Lipschitz-$1$ function on the quotient. Seven foundational axioms are shown to be mutually independent by explicit countermodels. The dynamic corridor criterion, the controlled avoidance theorem, the channel separation bound, and the stochastic Chebyshev corridor complete the calculus.

Abstract: Standard pushers for the relativistic equations of motion of a charged particle in an electromagnetic field—Boris, Vay, Higuera–Cary—do not, in general, preserve the full symplectic structure of the underlying Hamiltonian system, while high-order non-symplectic schemes such as Runge–Kutta accumulate secular error over long times. We propose a symmetry-preserving physics-informed neural network framework (SP-PINN) for the 3+1-dimensional relativistic dynamics of a charged particle in a prescribed field, including a focused Gaussian laser pulse. The method is two-stage: an unsupervised physics-informed neural network learns a surrogate relativistic Hamiltonian from the covariant equations of motion using a Lorentz-invariant loss that enforces the mass-shell constraint H=mc²γ; the surrogate is then advanced with an explicit symplectic map built on Tao’s extended phase space, valid for the non-separable relativistic Hamiltonian. We benchmark against the Boris pusher and Runge–Kutta on three test problems. The magnetic-field test illustrates the contrast between bounded and secular error growth: Runge–Kutta drifts secularly, the Boris pusher conserves the invariants to machine precision as a volume-preserving gyro-integrator, and the symplectic map keeps the error bounded for all time; on a non-integrable magnetic trap, where no exact volume-preserving rotation exists, the symplectic map alone keeps the energy error bounded. The learned surrogate is the current accuracy bottleneck; for the demanding laser case a vector-potential light-cone reformulation reduces its error to (3.0±0.1)×10⁻⁴ (three seeds) and yields learned trajectories that remain phase-coherent over essentially the whole interaction. The framework targets laser–plasma acceleration, synchrotron-radiation modeling, and particle tracking.

Abstract: Quantum computing is a potential solution to the limitations of current computing devices, but the need for superconductivity has led to prohibitively high operational costs and energy consumption. A major bottleneck is the low critical temperature needed to achieve superconductivity. Here, a quantum diode system is proposed that utilizes a circuit approach to achieve superconductivity at room temperature. Two opposed p–n diodes are connected to another junction in one of two configurations (A and B systems) that cancels the electric field in the depletion layer of each diode, which causes electrons and holes to reappear and prevents their recombination. Thus, the combination energy of a Cooper pair (i.e., exciton) is very strong, and Bose–Einstein condensation is maintained even at room temperature. When a bias voltage is applied between the A and B systems, Lorentz conservation imparts momentum (i.e., wavenumber) to the carriers in the absence of any internal voltage, so a superconducting bias current density appears without any need for cooling. Numerical calculations including many-body interactions revealed that constant phases for the macroscopic wavefunctions of p- and n-type semiconductors converged, which confirmed that Bose–Einstein condensation and the Meissner effect occurred. Moreover, the quantum diode system exhibited rectification characteristics and a switching speed on the order of 10⁻¹⁴ s. These switching properties and large superconducting bias current were used to develop NOT and NAND gates with direct quantum correlations that are unaffected by random and thermal noise.

Abstract: Dynamic stall and its control using synthetic jets are investigated for a sinusoidally pitching NACA 0018 airfoil at a chord-based Reynolds number of 40000, a reduced pitch frequency of 0.112, and two pitching amplitudes. An array of ten circular-orifice actuators is installed near the leading edge to examine the effects of low- and high-frequency burst-modulated forcing. Particle image velocimetry (PIV) is employed to measure phase-locked velocity fields along the airfoil centerline, while hot-wire anemometry is used to characterize wake frequency spectra. The baseline pitching cases exhibit complex vortex dynamics, with a wide range of coherent structures and vortex formation processes occurring over the entire airfoil surface. The formation and detachment of a leading-edge vortex (LEV) are identified as the primary features of dynamic stall across all cases. Both low- and high-frequency forcing are found to delay the onset of static and dynamic stall, although their influence on the boundary layer transition differs. The actuator placement near the leading edge is shown to be a critical parameter governing control effectiveness. Furthermore, the disparity between the forcing and pitching frequencies introduces additional unsteady vortex interactions associated with rapid variations in the adverse pressure gradient, which are unique to the dynamically stalling flow.

Abstract: Star formation in Galactic dense clumps is commonly interpreted using nearly uniform protostellar evolutionary timescales, yet the extent to which such assumptions obscure variations in star formation efficiency remains uncertain. Using 60 ATLASGAL dense clumps associated with MIPSGAL Class I protostars and \( \mathrm{NH_3} \) velocity information, we show that compactness and dense-gas evolutionary state provide a stronger explanation of instantaneous and cumulative star formation behavior than adopting a universal Class I lifetime. By combining cumulative efficiencies with a dense-gas star formation calibration, we find that star formation proceeds with systematically mass- and density-dependent timescales, implying that a single evolutionary clock can significantly bias inferred efficiencies across the clump population. The lower-limit cumulative star formation efficiency was observed to increase with decreasing clump radius following \( R_{\mathrm{cl}}^{-1.30 \pm 0.09} \), while no significant correlation is found with Galactocentric radius. Upper- and lower-limit cumulative efficiencies exhibit a sublinear relation with slope \( 0.66 \pm 0.08 \), suggesting possible stellar initial mass function incompleteness. The dense-gas star formation timescale follows \( \tau_{\mathrm{SF,dense}} \propto M_{\mathrm{cl}}^{-0.77 \pm 0.04} \), with a median value of \( 0.54\,\mathrm{Myr} \). Assuming a relatively uniform timescale of \( 0.50\,\mathrm{Myr} \) could overestimate and underestimate star formation rates in low-mass and massive clumps by factors of \( \sim 32 \) and \( \sim 25 \), respectively.

Abstract: In 2000, Carver Mead introduced a time-symmetrical theory of energy exchange between two atoms, building on the Transactional Interpretation of Quantum Mechanics by John Cramer in 1986. In 2020, Cramer and Mead developed the theory further, proposing a conceptual path integral formulation by which energy could be completely transferred over long distances, and showing that this theory can explain the Einstein-Podolsky-Rosen paradox, the Hanbury–Brown–Twiss effect, and the Freedman-Clauser entanglement experiment. In this paper, we develop the theory further, proposing a specific formulation of the interaction between Emitter and Absorber atoms, in which the energy density is proportional to the root-mean-square of the product of retarded and advanced four-vector potential waves, and show how this interaction efficiently and completely transfers energy from the Emitter atom to the Absorber atom over arbitrary distances. We use Mach’s Principle and conservation of energy to find the proportionality constant by matching the mean transition time constant for all possible absorbers in the universe to the mean transition lifetime computed from Fermi’s Golden Rule, leading to a complete solution with no adjustable parameters. The solution represents the exchange of energy between two atoms, valid over 26 orders of magnitude in Emitter-Absorber distance, from about 0.52 m to the radius of the Hubble Sphere 1.27×10²⁶m. We define this Wave-Particle Model as the product of a retarded emitter vector potential wave and an advanced absorber vector potential wave, which exhibits the particle-like properties of losslessly carrying energy at the speed of light in a straight line from emitter atom to absorber atom in a vacuum in the absence of gravity.

Abstract: Quantum mechanics is characterized by several distinctive features: (1) wave–particle duality, (2) the uncertainty principle, (3) superposition of states, (4) wave function collapse, (5) the tunneling effect, (6) quantum entanglement, and (7) the dominance of probability. Proposed interpretations include the Copenhagen interpretation, the de Broglie–Bohm pilot-wave theory, and the many-worlds interpretation. Despite sustained debate, no unified consensus has emerged. A central obstacle may lie in the unresolved ambiguity over whether a quantum entity is fundamentally a wave or a particle. Although photons and electrons exhibit wave-like and particle-like properties, the concepts of “wave” and “particle” are inherently mutually exclusive. This paper proposes that the true nature of a quantum is a quantized wave interacting at a single spatial point. Based on this premise, the study investigates the vacuum structure and interactions, together with the relationship between wave function collapse and the conservation of physical quantities. The mechanisms underlying the photoelectric effect and quantum tunneling are reexamined, along with the double-slit and delayed-choice quantum eraser experiments. By treating photons and electrons as quantized waves confined to point interactions, this work demonstrates that puzzling quantum behaviors, long considered obstacles to a coherent understanding of quantum mechanics, admit straightforward explanations.

Abstract: We review arguments showing that Big Bang, subsequent cosmic inflation, present accelerating expansion of the universe (dark energy) and lightness of elementary particles have the same physical origin. Namely, these phenomena are manifestations of the negative value of the gravitational field energy in the vector theory of gravity, which causes these effects and yields value of the cosmological constant and masses of elementary particles in excellent agreement with experiment without free parameters. We also explain how arrow of time emerges in vector gravity. According to the latter, universe is a region of 4-dimensional space with geometry of Minkowski signature, embedded in a fixed Euclidean background. The theory predicts that cosmic inflation exponentially expands the spatial size of the universe and exponentially contracts its temporal size. As a result, size of the universe along the temporal dimension is close to zero, and universe as a whole is moving through the Euclidean background along the time direction, which yields a unidirectional flow of time.

Abstract: We believe that the origin of the universal dark energy may crucially depend on the behavior of the gravitational constant G. If G is constant throughout the universe, then the dark energy density u₀ is supported by the vacuum via its constant and evolving properties. On the other hand, in varying-G gravity (whose low-acceleration limit is MOND), u₀ is a manifestation of radial G-gradients in the source of gravity. We estimate the present-day dark energy density of the universe in these two independent cases without using conventional Planck-2018 modeling. The constant-G derivation uses dimensional analysis, vacuum constants, and a newly discovered evolving bridge between vacuum mechanical and electromagnetic quantities. The varying-G derivation relies on the MOND critical acceleration a₀, the source of gravity that falls off as ∼1/r² at large distances r, and the assumption that the Planck-2018 value reflects a volume average over the history of the post-Stoneyan universe, which is nevertheless heavily weighted toward the very recent (observed) past. The agreement between these two determinations and the Planck-2018 results from ΛCDM modeling is outstanding, so much so that the results cannot distinguish clearly between constant-G or varying-G gravity. The analysis further indicates that the Newtonian constant G₀, the MOND constant a₀, and the Planck units of force, power, voltage, and current are vacuum invariants of the same stature as the well-known resistive properties of the vacuum; whereas charge, capacitance, inductance, and various fields are scale-dependent properties evolving in the expanding universe since the Stoney era. Ultimately, the vacuum behaves as a remarkably stiff elastic medium under stress, irrespective of the presence or absence of matter. This property has long been encoded, albeit inconspicuously, in the much discussed Tully-Fisher and Faber-Jackson relations, as well as in the Casimir effect and the field equations of General Relativity.

Abstract: A current-residual reconstruction problem for a four-dimensional Lorentzian branch is analyzed. An Alena-Codazzi collar gives a local current-Codazzi closure on the punctured collar, and a penalty-dominant thin-core limit gives an integral-current core whose primitive regular component is read as a worldline defect with controlled boundary charge. Resolving the core gives a projective link $\mathbb{CP}^1$, while the primitive transverse class gives the line $\mathcal O(1)$. The positive Borel-Weil tower and the $\mathbb{CP}^1$ Toeplitz cutoff then turn a filtered transverse source into a finite internal support. After the scalar trace is separated, a transverse two-jet has only two non-scalar principal channels, the phase-current $V_1$ channel and the trace-free Codazzi-gap $V_2$ channel. In the Alena-Codazzi realization these channels are principal Codazzi-Gauss link charges, and their boundary superselection supplies the central separation. Toeplitz visibility then selects the rank-five carrier $E_3\oplus E_2$, with the degree-one class as the unique positive degree giving separated first thresholds. The split top-form condition and the local determinant-obstruction count have the same kernel, giving the compact carrier group $S(U(3)\times U(2))$. The determinant-compatible even exterior package gives the local one-generation Standard-Model module, while the determinant global form gives a $\mathbb Z_3$ family-response torsor. Exact family multiplicity, masses, mixing, CP, Majorana, and contact-class coefficients are treated as finite Schur-Kuranishi diagnostics of the completed Dirac-Callias/Riesz/Schur-Berry branch.

Abstract: The Haber-Bosch process dominates industrial ammonia synthesis but incurs massive energy consumption and carbon emissions. Here, we demonstrate a catalyst-free approach for direct ammonia synthesis from atmospheric nitrogen and water under ambient temperature and pressure, leveraging ultra-fast laser-induced plasma at the gas-liquid interface. By optimizing irradiation parameters (irradiation time, pulse energy, number of beams) and implementing a concentric laser scanning strategy, we achieved a maximum ammonia concentration of 0.624 μmol/20mL. This method bypasses the need for high temperature/pressure or catalysts, offering a sustainable path for distributed ammonia production. Our work underscores the potential of strong optical fields in activating inert molecules like N₂ and H₂O, with implications for decarbonizing chemical synthesis.

Abstract: Traumatic brain injury (TBI) triggers complex molecular responses that remain incompletely understood at the structural level, where it's highly connected to neurodegeneration and synaptic dysfunction. Growing evidence implicates intrinsically disordered proteins (IDPs), and proteins with intrinsically disordered regions (IDRs), as key regulators of stress-responsive signaling. In this study, we represent an in silico study of the 24 TBI-relevant proteins, such as MAPT, SERF2, SERBP1, BEX3, TDP43, NFL, C9orf16, C9orf58, APP, NRN1, NEFM, SYNGAP1, SNAP25, DLG4, APOC2, HCLS1, HMGB1, FUS, EPHA4, SEMA4D, S100B, PLEK, CAMK2A, and SNCA, integrating analysis of the predisposition for intrinsic disorder and liquid–liquid phase separation (LLPS) through RIDAO, FuzDrop, and AlphaFold platforms. We demonstrate that more than 90% of residues in SERF2, BEX3, MAPT, SERBP1, HMGB1, SNCA, and FUS are predicted as disordered. The amino acid sequences of NEFM, HCLS1, C9orf16, NEFL, C9orf58, SNAP25, SYNGAP1, S100B, and TDP43 contain between 50% and 90% of disordered residues, and the disorder contents of APP, APOC2, and DLG4 are 47.53%, 45.54% and 33.29%. Only five proteins (SEMA4D, PLEK, CAMK2A, EPHA4, and NRN1) have less than 30% disordered residues. The high prevalence of disorder in TBI-associated proteins correlates with their strong propensity for spontaneous liquid-liquid phase separation (LLPS). In fact, 15 proteins (FUS, SYNGAP1, MAPT, NEFM, SERBP1, HCLS1, SERF2, BEX3, C9orf16, TDP43, HMGB1, APP, NEF, DLG4, and SNCA) are expected to act as droplet drivers, and five more proteins (SEMA4D, C9orf58, SNAP25, CAMK2A, and EPHA4) can serve as droplet clients. The gene ontology analysis emphasized that the 24 TBI-related proteins (TBIome) are functionally associated with synaptic regulation, RNA metabolism, cytoskeletal dynamics, and mitochondrial stress response. We also show that human proteins interacting the members of TBIome are on average a bit more disordered than the human brain proteins in general. This extended TBI interactome is functionally connected to cytoplasmic translation, translation, synaptic vesicle cycle, modulation of chemical synaptic transmission, regulation of neurotransmitter levels, regulation of synaptic plasticity, neurotransmitter secretion, synaptic vesicle exocytosis, protein localization to synapse, and trans-synaptic signaling. Many of these proteins have strong LLPS potential as well. Therefore, high intrinsic disorder propensity and strong LLPS potential represent shared structural and functional features of proteins linked to the TBI-related pathophysiology. Collectively, these findings support a model in which disorder-based mechanisms contribute to post-traumatic molecular reprogramming, which underlie the pathological roles of TBI-related proteins.

Abstract: Pure Topology Results We establish the unique topological setting of any unified gauge theory with quantized charge, and derive its physical consequences. We prove that given charge quantization and the existence of a unified field theory (a single indecomposable gauge field accounting for all configurations), the theory must be formulated, up to homotopy equivalence of the base and isomorphism of bundles, on the universal complex Hopf fibration $S^1 \longrightarrow S^\infty \longrightarrow \mathbb{CP}^\infty$ and its finite approximations $S^1 \longrightarrow S^{2n+1} \longrightarrow \mathbb{CP}^n.$ Completeness and indecomposability are derived consequences, not additional axioms. The Standard Model gauge groups arise as natural reductions along the nested shell hierarchy: $U(1)$ from the circular $S^1$ fiber, $SU(2)$ from the $S^3$ shell and $SU(3)$ from the $S^5$ shell. Gravity emerges as the spacetime gauge sector from the K\"ahler geometry of the base and fiber-induced torsion, yielding Einstein--Cartan analogous structure with the Levi--Civita connection recovered in the torsion-free limit. The unified structure group $\mathcal{G}_{\mathrm{total}} = (SU(3) \times SU(2) \times U(1) \times SO(4))/\Gamma$ is intrinsically non-factorable due to the generating role of the universal first Chern class in $H^*(\mathbb{CP}^\infty; \mathbb{Z}) \cong \mathbb{Z}[c_1].$ Applied Topology Results: The Gauge Field Action and Geometric Spectra On each Hopf shell, the generalized Beltrami operator $\mathcal{B} = \star d \big|_{\xi}$ acting on the contact distribution is elliptic, essentially self-adjoint, and possesses a discrete spectrum stable under torsion perturbations by the Kato--Rellich theorem. Fiber winding decomposition yields independent topological sectors whose Gaussian functional determinants, regularized via spectral zeta functions, generate intrinsic mass scales. Fermion mixing (CKM, PMNS) arises from intersection-form overlaps of admissible cycles in $H^*(\mathbb{CP}^4)$, with CP violation induced by fiber holonomy phases. Dynamics emerge from the fluctuation spectrum of the topological action on $S^9$. The electroweak vacuum expectation value $v$ serves as the unit conversion factor between geometric and laboratory scales; given this single identification, the fine-structure constant and all shell-specific mass scales, spectral coefficients, and coupling constants entering the particle spectrum are fixed by the spectral geometry of the complex Hopf fibration. Phenomenology, Physical Interpretations and Numerical Predictions The framework predicts the complete particle mass spectrum and anomalous magnetic moments, with suggested independent experimental tests (torsion-induced phase wobble, absolute neutrino mass scale, and the electron, $\mu$ and $\tau$ $g-2$) providing falsifiability. Fundamental constants arise from topological normalization. Further results include anomaly cancellation, dark sector effects from bundle torsion and holonomy, and the elimination of singularities. The mathematical results stand independently as contributions to the topology of classifying spaces, reductions along nested Hopf shells, and contact spectral geometry.

Abstract: Aqueous two-phase systems (ATPSs) provide a versatile, fully aqueous platform for probing solute–water interactions and protein structure. This review first surveys the diversity and phase behavior of biphasic aqueous systems formed by polymers and salts. We describe how phase diagrams characterize ATPS formation and composition, and how both polymer chemistry and salt identity, more than molecular size alone, govern phase separation by modulating the solvent properties of water. Building on a modified binodal model, we show that phase separation and solute partitioning can be understood in terms of changes in aqueous solvent dipolarity/polarizability, hydrogen-bond donor/acceptor properties, hydrophobicity, and electrostatics, quantified via solvatochromic probes and homologous solute series. These measurements underpin solvent interaction analysis (SIA), in which the partition coefficients of small molecules and proteins across panels of ATPSs are used to generate “structural signatures” that sensitively report on amino acid substitutions, conformational changes, aggregation, ligand binding, osmolyte effects, and post-translational modifications, independent of protein size. We discuss how SIA can be implemented in vial-, plate-, and microfluidic formats and combined with diverse analytical readouts (HPLC, MS, colorimetric and immunoassays), and contrast this structure-focused approach with conventional concentration-only proteomic and biomarker strategies. Particular emphasis is placed on structure-based biomarker discovery, where disease-relevant shifts in proteoform distributions—especially glycosylation changes—are often more informative than bulk protein levels, and where SIA can complement or simplify complex glycomics and top-down proteomics workflows. As a case study, we describe the recently FDA approved isoPSA assay, which applies SIA principles to prostate-specific antigen by measuring cancer-associated structural alterations in circulating PSA via its partition behavior in a proprietary ATPS. IsoPSA generates a single index that discriminates high-grade prostate cancer from benign and low-grade conditions. Prospective, longitudinal, and MRI-integrated clinical studies demonstrate that IsoPSA^® improves pre-biopsy risk stratification, reduces unnecessary biopsies, and provides robust negative and positive predictive characteristics within the PSA “gray zone.” Collectively, the data support aqueous solvent interaction analysis as a broadly applicable, mechanistically grounded technology for protein characterization, drug–protein interaction studies, and structure-centric biomarker development, exemplified by the clinical translation of IsoPSA.