Abstract: Given recent advancements in dark matter (DM) search experiments, particularly the latest LUX-ZEPLIN (LZ) direct detection (DD) results, we systematically investigate the light bino–higgsino DM scenario within the natural supersymmetric framework. Requiring the electroweak fine-tuning parameter ΔEW<30 fixes the higgsino mass parameter in the range |μ|∈[100,350] GeV, while we extend the bino mass to M₁∈[10,350] GeV. Incorporating constraints from Higgs physics, rare B decays, LEP limits, and DD experiments, we find that part of the parameter space remains viable. However, the relic density of neutralino DM necessarily lies below the observed Planck value, contributing at most ∼2% of the total DM abundance. Some of the surviving parameter space is already excluded by current 13 TeV LHC searches, while the future 14 TeV HL-LHC with 3000 fb⁻¹ luminosity will probe the remaining region.

Abstract: We prove that the null cone is enough: at every event in Minkowski spacetime, the null cone carries a two-dimensional conformal field theory with spectrum \Delta_{\ell} = \ell + 1 , unifying all massless fields of spin \ell = 0,\frac{1}{2},1,\frac{3}{2},2 through pure geometry. From two postulates—four-dimensional Minkowski spacetime and the Isometric Sampling Condition—the unique Lorentz-invariant propagator is G(x,y) = \mathrm{sinc}(\Omega \sqrt{-\sigma^2 - i\epsilon}) , where the Feynman i\epsilon prescription selects the unique L^2 branch in the spacelike region. The RKHS normalisation K(x,x) = 1 forces G = 1 on the null cone, and the full two-point function is controlled entirely by a 2D CFT on the transverse S^2 , yielding \Delta_{\ell} = \ell + 1 . Fermionic statistics arise from the \mathbb{Z}_2 holonomy of an \mathrm{SL}(2,\mathbb{C}) fibre bundle without any additional postulate. We provide the microscopic foundation for Jacobson's thermodynamic Einstein equation and Verlinde's entropic gravity. We extend the framework to \mathrm{SU}(N) gauge theories and derive asymptotic freedom: b_{\ell} = (12\ell^2 - 1)C_2(G) / (12\pi) > 0 for all \ell \geq 1 , reproducing the Gross-Wilczek-Politzer result for \ell = 1 . We develop the structural correspondence between the sinc kernel and the Riemann zeta function, construct a mathematical bridge to the non-trivial zeros of \zeta (s) , and identify the precise step separating the ISC framework from a proof of the Riemann Hypothesis.It is worth noting that the BSS theorem establishes not merely the unitarity of the sampling map, but a categorical equivalence between \mathrm{PW}_{\Omega} and \ell^2(\mathbb{Z}) — which implies that the ISC is an intrinsic property of the Paley-Wiener space structure, rather than an externally imposed postulate. This observation is crucial for understanding the inevitability of the ISC in its four-dimensional generalization.

Abstract: We present a phenomenological Effective Field Theory (EFT) of the "Warden" field, a massive, colored topological soliton at M_W =8.21±0.4 TeV. Descending from a U(4) unification framework at M_GUT ≈ 3.2 × 10¹⁶ GeV, this EFT explores a dynamical framework for the electroweak scale, color confinement, and the fermion mass hierarchy. We propose that the Standard Model electroweak sector is anchored to a topological Warden condensate characterized by a macroscopic vacuum stiffness of f ≈ 1.1 TeV. By adopting this stiffness and a topological melting threshold of Λ_vac ≈ 259 TeV as UV boundary conditions, we show that the activation of the Warden scalar sector can introduce a stabilizing effect on the Higgs vacuum, consistent with a Higgs pole mass of m_H ≈ 125.19 GeV. Furthermore, this vacuum state is supported by a geometrically conserved U(1) baryon symmetry, offering a mechanism for proton stability. We translate this architecture into collider kinematics, projecting an ≈ 0.85 fb topological gluon fusion production cross-section at √s = 100 TeV, providing a testable signature for the Future Circular Collider (FCC-hh).

Abstract: The ultimate goal of theoretical physics is unifying the microscopic quantum realm with macroscopic general relativity. This paper proposes the 4G Model of Final Unification (having 3+1 interaction dependent gravitational constants) to bridge this gap. Central to this framework is resolving the historical mystery of the gram mole. Rather than an arbitrary chemical convention, the mole is redefined as a fundamental, intrinsic gravitational charge. Consequently, the Avogadro number is physically derived as a structural limit dictated by strong force saturation and nuclear binding energy. By treating the atom as an electromagnetic particle, the model establishes a direct equivalence between microscopic and macroscopic gravitational scales. To formalize this, honouring Einstein, Perrin, Loschmidt, Avogadro and Newton, we introduce the dimensionless EPLAN ratio. This universal scaling factor authenticates the SI-defined magnitude of the Avogadro constant and extends directly into astrophysics. Integrating this ratio with nuclear magic numbers yields a quantized mass spectrum for celestial bodies. This introduces a bottom-up geometric construction of stars, successfully deriving boundaries like the Chandrasekhar mass limit from first principles and suggesting compact objects settle into discrete gravitational orbitals. Finally, the framework reveals that the four fundamental constants corresponding to the strong, weak, electromagnetic, and Newtonian forces are not isolated. Instead, they operate as synchronized gears in a cosmic clockwork. The precise interaction of these quantum gears drives the macroscopic rotation of Newtonian gravity, proving that the subatomic stability of the atom is perfectly interwoven with the grand scale stability of the entire universe. By grounding the pursuit of unification in testable, multi-disciplinary outcomes, this framework offers a practical alternative to highly abstract theoretical models, and we respectfully present it for the physics community’s serious consideration.

Abstract: Electroweak, QCD, and QED radiative corrections to the nucleon low-energy coupling constants gV and gA are enhanced by large perturbative logarithms between the electroweak and hadronic scale, as well as between the hadronic scale and the low-energy MeV scale. Additionally, higher-order pion-mass splitting corrections to the nucleon axial-vector charge might be large. By consistently incorporating these effects, we provide an updated relation between the lattice-QCD and physical gA, finding a total radiative correction of 3.5(2.1)% (5.6(7)%). This leads to an expected lattice-QCD result of gAQCD = 1.265(26) (gAQCD =1.240(9)) when based on a combination of lattice-QCD and data-driven (or only data-driven) inputs, respectively. Future phenomenological, chiral perturbation theory, and lattice-QCD studies can improve both the central value and the uncertainty of this estimate.

Abstract: We present a phenomenological model for nuclear binding energy, termed Field Symmetry Theory (FST), based on an effective nuclear field derived from the Heisenberg uncertainty relation. The model incorporates volume, Coulomb, symmetry, and pairing terms as physical corrections, with the logarithmic term ln A justified through renormalization group arguments. A Lorentzian correction is introduced to account for few-body effects in light nuclei, with a physical justification based on finite-size effects in quantum systems. With only eight adjustable parameters, the model achieves a mean absolute error of 0.0388 MeV per nucleon and R² = 0.99996 when compared to 3554 nuclei from the Atomic Mass Evaluation 2020 (AME2020) dataset. The model performs reasonably well for light nuclei (A < 8: MAE = 1.15 MeV/n, accuracy 65.8\%) and achieves 99.9\% accuracy for heavy nuclei (A > 150), with uranium isotopes reaching 99.9% precision. Cross-validation confirms no overfitting (generalization gap < 10^-6 MeV/n), and correlation analysis reveals expected interdependencies among base parameters while confirming the stability of correction parameters. The complete computational code is provided as supplementary material accompanying this manuscript.

Abstract: We investigate the effects of dark matter on the properties of strange quark stars within the framework of general relativity with two fluids coupled only with gravity. Adopting the color-flavor locked model for strange quark matter and considering both fermionic (free fermion gas) and bosonic (polytropic) equations of state for dark matter, we systematically study the structure and tidal deformability of dark matter admixed strange stars. Our results show that the presence of dark matter significantly modifies the mass-radius relations, with the maximum mass of dark matter admixed strange stars exhibiting a non-monotonic dependence on the dark matter mass fraction χ - a minimum at an intermediate χ. The tidal deformability Λ of dark matter admixed strange stars shows complex behavior depending on both the stellar mass and dark matter fraction, with Λ − β (the compact parameter) relations deviating from the universal relations observed for pure strange stars or dark stars. Our findings demonstrate that dark matter admixed strange stars with different configurations but identical masses and radii can be distinguished by their tidal deformabilities, providing potential observational signatures for detecting dark matter in compact astrophysical objects. The results are compared with current astrophysical constraints from gravitational wave observations and pulsar measurements.

Abstract: The SI Avogadro constant (NA = 6.02214076 ×10²³ per mol) bridges microscopic particle counts to macroscopic masses but its specific scale currently has no widely accepted fundamental physical origin. In this context, we show three independent derivations for the natural kilogram-natural scale of 6.02×10²⁶ atoms/kg: (1) Computational nuclear binding energy analysis yielding precise atomic mass units from QCD saturation (~8 MeV/nucleon peak), (2) Empirical validation through kilogram-scale Faraday constant (F = 9.6435 × 10⁷ C/kg) and (3) Atomic mass number (A) based Dulong-Petit specific heat capacity formula, (25000/A J/kg·K). Notably, 1/F ≅ 1.037×10^-8 kg/C matches Planck mass (M_pl) modulated by electroweak angle (Mpl sinθW), establishing quantum gravity and charged matter unity. By using the Faraday charge, GN = ℏcF²sin²θW emerges from the “QCD-electroweak-gravity cascade” rather than empirical fitting, yielding a theoretically robust universal gravitational constant. These atom-independent origins reposition the Avogadro scale as emergent feature of unification physics. Considering our 4G model of final unification (through which string theory can be made practical), it is possible to show that, ratio of product of short-range gravitational constants and long-range gravitational constants is, [(G_weak*G_nuclear)/(G_electrromag*G_Newton)] ≅ 6.1088×10²³. This ratio plays a crucial role in understanding the hierarchy of fundamental forces. Seeing its fundamental role, we appeal to the science community and concerned authorities to rename SI Avogadro constant (per mole) with ‘Einstein-Perrin-Loschmidt-Avogadro-Newton’ Ratio (EPLAN Ratio).

Abstract: In this work, we present a detailed comparison of the SuSAv2 (SuperScaling Approach version 2) and RDWIA (Relativistic Distorted-Wave Impulse Approximation) models with measurements of charged-current neutrino-induced single-pion production from different experiments (T2K, MINERvA and MiniBooNE), studying the differences between the two theoretical descriptions. The neutrino energy range in these experiments spans from hundreds of MeV to roughly 20 GeV, and the nuclear targets are mainly composed of ¹²C. The SuSAv2 model uses the single-nucleon inelastic structure functions from the ANL-Osaka DCC model, which allows for a separation of pion production channels, distinguishing between the π⁺, π⁻ and π⁰ final states. In the RDWIA approach, the Hybrid model developed by the Ghent group is used for the description of the boson-pion-nucleon vertex.

Abstract: We review recent experimental progress in charmed baryon physics achieved by the Belle and Belle~II experiments, with an emphasis on measurements reported since 2022. Using large $e^{+}e^{-}$ data samples collected at or near the $\Upsilon(4S)$ resonance, Belle and Belle~II have delivered a series of precision results on hadronic weak decays of anti-triplet charmed baryons, providing critical inputs for testing flavor-symmetry approaches and dynamical models. We summarize new and improved branching fraction determinations for $\Xi_c^{0}$, $\Xi_c^{+}$, and $\Lambda_c^{+}$ decays, including channels with neutral hadrons in the final state and the first measurements of several singly Cabibbo-suppressed modes. We also highlight the first determination of the decay asymmetry parameter in $\Xi_c^{0}\to \Xi^{0}\pi^{0}$. In addition, we review the first Belle~II measurements of $CP$ asymmetries in three-body singly Cabibbo-suppressed decays of $\Xi_c^{+}$ and $\Lambda_c^{+}$, and discuss their implications for U-spin sum rules and searches for physics beyond the Standard Model. Finally, we look forward to exploiting the Belle~II data set to perform more stringent tests of decay dynamics.

Abstract: The left-handedness of neutrinos is an undeniable physical phenomenon. Because the first principles of the Standard Model are insufficient to explain this property, the issue is addressed through the chirality postulate, which implies that the weak interaction violates parity. While postulates are acceptable tools in a descriptive theory, they are less satisfactory in a conceptual theory that seeks to eliminate such assumptions. In this article, we show how the left-handedness of neutrinos emerges from first principles within the Structural Model of particle physics.

Abstract: Since the 1950s, nuclear physicists have believed that we have a complete conceptual framework for understanding the low(est)-energy excitations of atomic nuclei. This perspective has persisted in contemporary nuclear structure researches, but it now appears overly optimistic. In this Review, I present two previously unexpected discoveries, one experimental and one theoretical. Although the spherical phonon excitation spectrum has been considered as a typical paradigm of collective excitations in nuclear structure theories, it has not been supported by recent experiments. The result of the experimental discovery reveals a \textit{new} $\gamma$-soft rotational mode which has never been predicted by the previous theories. This mode differs from previous $\gamma$-soft ones and can be described by the newly proposed SU3-IBM theory, a new spherical-like $\gamma$-soft mode representing a specific shape phase.

Abstract: Short-lived nuclear systems with light to medium masses are showing halo phenomena in regions of the nuclear chart that where still unexplored when halo nuclei were discovered 40 years ago. We study these exotic systems with three-body models including nucleon-nucleon correlations with the aim of reproducing measurable properties like radii and electromagnetic transitions strengths.\\ \noindent On the nuclear-rich side, drip-line fluorine isotopes are showing clear signs of a halo structure \cite{Fort20,Casa20,JSin20}: recently we proposed that $^{29}$F is a moderate two-neutron halo nucleus with a large radius and a strong B(E1) response to the continuum. The three-body model place it at the borders of the island of inversion and this is corroborated by new data. According to our models, the next interesting isotope, $^{31}$F, also has large spatial extension due to p-wave components and enhanced B(E1) response, pointing to a speculative halo structure \cite{GSin22}.\\ \noindent On the proton-rich side, we have studied the $^{102}$Sb system, as composed of a $^{100}$Sn core plus a proton-neutron correlated subsystem \cite{Oish25}. We find that the weakening of the proton-neutron correlations with respect to the bare deuteron indicates that this is a one-proton emitter. We have proposed that the presence of resonant state and its decay might provide a crucial benchmark for this system.

Abstract: Critical slowing down and topological freezing in lattice gauge theory can be aggravated by thegauge-redundant link representation, which obscures simpler geometric structure available in al-ternative variables. We introduce Flux-Space Flow Matching (FFM), a generative samplingframework for 2D compact U(1) theory that operates directly on gauge-invariant flux (plaquette-angle) variables. By formulating the dynamics in flux space, the Wilson action is locally factorized,allowing us to train a continuous-time Neural ODE to approximate the equilibrium distributionwithout suffering from the stiff curvature typical of the coupled link formulation. We impose theglobal topological sector constraint via a deterministic “Relax-and-Project” mechanism and applyan independent Metropolis–Hastings accept/reject step as a bias-control procedure. Validated onL∈{48,64}lattices, FFMachievesacceptanceratesof50–70% atL= 48 andreducestheintegratedautocorrelation time of the topological charge by over 500×compared to Hybrid Monte Carlo atβ = 6.0 (on our run lengths). We validate model fidelity against thermodynamic observables, Wilsonloops, and Creutz ratios, finding agreement with the expected non-perturbative confinement scalingwithinthetestedregime. Furthermore, wedemonstratethatSpatialβ-Conditioningenableszero-shot approximation of inhomogeneous thermodynamics, spontaneously nucleating vortex–antivortexpairs in response to spatially varying coupling profiles. These results suggest that identifying theappropriate geometric degrees of freedom can be a more effective path to scalable neural samplingthan architectural complexity alone.

Abstract: Symmetry is a key principle in physics that links basic invariances to the structure of matter and the evolution of the universe. In this review, we use symmetry as a unifying thread connecting nuclear structure, nuclear reactions, and dense matter, and we highlight how symmetry-based arguments connect laboratory observables to astrophysical constraints. We present the essential concepts in a form accessible to a broad physics audience.

Abstract: The Unified Evolution Equation (UEE) provides a common analytical framework that unifies reversible quantum dynamics (unitary evolution), dissipative dynamics of open systems (GKLS), and transport effects induced by boundaries and resonances (zero-area resonance kernels) as a single notion of time evolution of states. The purpose of this paper (UEE_01) is to define the UEE as a mathematically consistent analytical foundation and to establish its well-posedness, including existence, uniqueness, and invariance of states.We formulate the theory by taking the observable algebra as a von Neumann algebra and the state space as its predual, and by characterizing physically admissible time evolutions as preduals of normal, unital, completely positive maps. The UEE is formally expressed as a sum of reversible, dissipative, and resonance-transport generators. Rigorously, solutions are defined in the mild sense as trajectories generated by a strongly continuous completely positive and trace-preserving (CPTP) semigroup.Given the analytical data of the UEE, we construct the reversible, dissipative, and resonance-transport components separately as CPTP group or semigroup evolutions. Using a Chernoff/Trotter-type product formula, we prove that the composite limit evolution exists, forms a CPTP semigroup, and that its generator coincides with the closure of the sum of the individual generators. As a consequence, invariance of the set of normal states and the well-posedness of the UEE are rigorously established.This work provides a solid analytical foundation for the unified GKLS+$R$ representation employed in subsequent papers, ensuring consistency between physical modeling and operator-theoretic dynamics.

Abstract: Background:The Standard Model (SM) has been successful, yet it fails to explain the origin of fermion masses and mixing parameters. Methods: In this study we construct the single-fermion framework “Information Flux Theory (IFT),” derived from the Unified Evolution Equation. IFT preserves gauge symmetry while replacing Standard Model fields with a single fundamental operator, yielding analytic solutions without adjustable parameters. Results: IFT reproduces all SM particle masses—including the 125 GeV Higgs mass—and the CKM matrix within current experimental precision, requiring neither additional particles nor fine-tuning. Conclusion: These results demonstrate that IFT can fully replace the Standard Model with a single-fermion description, providing a conceptually simpler yet phenomenologically complete foundation for particle physics. Supplement: This paper includes proofs for two Clay Millennium Problems: the Yang–Mills mass gap and the Navier–Stokes equations. Note Added: Furthermore, as a result of this series of studies, the origin of gravity has now been clarified.

Abstract: In the present view on neutrinos three flavour states are recognized that are composed by a characteristic mixture of mass eigenstates. The absolute scale of these eigenstates is unknown. So far, observational experiments have revealed numerical values for the squared mass differences. In this article it is shown that mass ratios can be found as well. This enables the assessment of the absolute scale of the neutrino masses.

Abstract: The Plastino-Plastino Equation (PPE) is essential in non-extensive statistics in the study of systems that exhibit anomalous diffusion and do not fit conventional statistics, thus being a nonlinear extension of the Fokker-Planck Equation (FPE). This equation has been applied in various fields of physics (Cosmology, astrophysics and hadrons, specifically in Quark-Gluon Plasma) and other disciplines. In this work, a relativistic approach will be carried out on a system of particles for which the relativistic Boltzmann equation is obtained. Here, grazing collisions are considered to obtain the FPE integrated with special relativity. Subsequently, through fractal derivations, a modification of the FPE is made, resulting in the PPE in a relativistic context.

Abstract: We investigate temperature fluctuations in hot QCD matter using a 3-flavor Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model. The high-order cumulant ratios $R_{n2}$ ($n>2$) exhibit non-monotonic variations across the chiral phase transition, characterized by slight fluctuations in the chiral crossover region and significant oscillations around the critical point. In contrast, distinct peak and dip structures are observed in the cumulant ratios at low baryon chemical potential. These structures gradually weaken and eventually vanish at high chemical potential as they compete with the sharpening of the chiral phase transition, particularly near the critical point and the first-order phase transition. Our results indicate that these non-monotonic peak and dip structures in high-order cumulant ratios are associated with the deconfinement phase transition. This study quantitatively analyzes temperature fluctuation behavior across different phase transition regions, and the findings are expected to be observed and validated in heavy-ion collision experiments through measurements of event-by-event mean transverse momentum fluctuations.