Abstract: In 2014, NASA measured that the universe has a Euclidean shape. This discovery suggests that the curvature of space is merely a mathematical description of some more basic physical property of space. By extending the principle of equality of mass and energy to the space occupied by dark energy, a model of gravity was developed, where the gravitational force is due to the variable energy density of dark energy. The more curved the space, the lower the energy density of dark energy. A black hole, like any other stellar object, reduces the energy density of dark energy at its center in proportion to its mass and energy. In the centre of a black hole, the gravitational force is zero, as it is in all stellar objects. There are no wormholes in space, and there is no gravitational singularity at the center of a black hole. Gravity inside black holes follows Newton's physics. Reduced energy density of dark energy inside black holes diminishes the value of the Planck constant, which causes atoms and nuclei to decay. Gravitational collapse is replaced by electric collapse.

Abstract: Microquasars serve as candidate sites for high-energy particle production within our Galaxy. Due to their distances, direct observations are relatively limited, necessitating detailed simulations, in order to connect observations to theory. This work models high-energy particle emission from relativistic magneto-hydrodynamic microquasar jets. The focus is on neutrino production enhanced by an intermittent jet’s plasmoid collisions with ambient photon fields, found in the surrounding medium. An advanced ray-tracing algorithm processes hydrodynamic simulation data to generate synthetic neutrino images from a stationary observer’s perspective. Synthetic spectra and intensity maps are also produced and can be compared with observations from current and future detectors.

Abstract: We construct the strong energy conditions (SECs) for both massive and massless stringy particles in the higher dimensional cosmology (HDC) with dark energy Λ. Exploiting these conditions we find the equation of state (EOS) parameters w ≥ −(D −4)/D for both the massive and massless stringy particles in D dimensional cosmology. We elucidate the relations between the EOS parameter in the HDCwithdarkenergy and that of Hawking-Penrose limit for the massive and massless point particles in the D = 3+1dimensions. Weevaluate the EOS parameters in terms of the contributions from the point particle property, dark energy, and extended object degrees of freedom, respectively. We also investigate the weak energy condition (WEC) and dominant energy condition for the massive and massless stringy particles in the HDC, and those for the massive and massless point particles in the D =3+1dimensions,respectively. We show that the Dark Energy Spectroscopic Instrument (DESI) data satisfies the WEC in the HDC. The high temperature asymptotic behavior of a dilaton-Einstein-Gauss-Bonnet scenario is also shown to be consistent with the corresponding WECs obtained in the HDC.

Abstract: We discuss gravitational concepts and candidate specifications for dark matter that, together, can help explain known ratios of dark-matter effects to ordinary-matter effects and can help explain eras in the rate of expansion of the universe. The ratios pertain to galaxies and galaxy evolution, galaxy clusters, and densities of the universe. The candidate specifications for dark matter reuse, with variations, a set of known elementary particles. Regarding galaxy evolution and the rate of expansion of the universe, we deploy multipole-expansion methods that combine Newtonian gravity, aspects of motions of sub-objects of gravitationally interacting objects, and Lorentz invariance. One outgrowth from our work suggests relationships among some physics constants. Another outgrowth from our work suggests a basis for a candidate specification for quantum gravity.

Abstract: In this review, the formation of the Oort Cloud is illuminated from several aspects. One is the history of the subject with an outline of the fundamental discoveries by Öpik [1], Oort [2] and Hills [3]. It is argued that the basic reason for judging Oort as the real discoverer is that he had access to observational data in the form of original orbits of long period comets. Further landmarks are identified, like the exploration of the role of the Galactic tide in the supply of observable comets by Heisler and Tremaine [4], the clarification of a synergy between tide and stars as the reason for a continued, efficient supply by Rickman et al. [5], the discovery by Kaib and Quinn [6] that inner core comets become observable due to planetary perturbations, disguised as new comets, and the demonstration of how Oort Cloud formation may work in the realm of the Nice Model by Brasser and Morbidelli [7]. It is finally argued that an important Galactic sculpting has occurred since the primordial Oort Cloud was formed by means of global shake-up events resulting from impulses imparted to the Sun by external perturbers like massive stars or Giant Molecular Clouds, and that this may be the real reason for the survival of an outer halo that reveals the existence of the Oort Cloud through the Oort spike.

Abstract: This work does not propose a new cosmological model, nor does it claim to reproduce structure formation, recombination microphysics, or the CMB power spectrum. It instead examines limited, testable consequences of a previously established background level redshift framework in which frequency-independent redshift is described by collisionless Liouville evolution without requiring metric expansion. Treating an illustrative post-recombination relaxation form for the redshift kernel as a concrete hypothesis, this analysis shows that the parameterization predicts reduced cosmic assembly time at z ≳ 10 relative to standard ΛCDM. Observations of early massive galaxies by JWST therefore act as an empirical constraint on the relaxation timescale and initial kernel rate, bounding the allowed post-recombination dynamics rather than resolving timing tensions. The paper further proves that frequency- independent redshift operators preserve angular multipole structure, once present, under collisionless evolution, establishing that the existence of CMB anisotropies alone does not logically discriminate between expansion and non-expansion redshift mechanisms at the level of angular transport. The analysis concludes by clarifying the precise observational content of CMB background and anisotropy data, explicitly delineating which inferences are supported and which require additional dynamical assumptions.

Abstract: In this note, we explain dark energy and the cosmological constant, and present formulas for both. These predictions are part of our exact solution of Einstein’s equation for a universe in which the curvature varies with time, and the vacuum energy acts upon itself. The predicted value of the cosmological constant agrees with the currently accepted value exactly.

Abstract: The two most severe cosmological tensions in the Hubble constant \( H_0 \) and the matter clustering amplitude \( S_8 \) have the same relative discrepancy of 8.3%, which suggests that they may have a common origin. Modifications of gravity and exotic dark fields with numerous free parameters introduced in the Einstein field equations often struggle to simultaneously alleviate both tensions; thus, we need to look for a common cause within the standard \( \Lambda \)CDM framework. At the same time, linear perturbation analyses of matter in the expanding \( \Lambda \)CDM universe have always neglected the impact of comoving peculiar velocities \( \mathbf{v} \) (generally thought to be a second-order effect), the same velocities that in physical space cannot be fully accounted for in the observed late-time universe when the cosmic distance ladder is used to determine the local value of \( H_0 \). We have reworked the linear density perturbation equations in the conformal Newtonian gauge (sub-horizon limit) by introducing an additional drag force per unit mass \( -\Gamma(t)\mathbf{v} \) in the Euler equation with \( \Gamma \equiv \gamma(2 H) \), where \( \gamma\ll1 \) is a positive dimensionless constant and \( 2H(t) \) is the time-dependent Hubble friction. We find that a damping parameter of \( \gamma = 0.083 \) is sufficient to resolve the \( S_8 \) tension by suppressing the growth of structure at low redshifts, starting at \( z_\star\simeq 3.5-6.5 \) to achieve \( S_8\simeq 0.78-0.76 \), respectively. Furthermore, we argue that the physical source causing this additional friction (a tidal field generated by nonlinear structures in the late-time universe) is also responsible for a systematic error in the local determinations of \( H_0 \): the inability to subtract peculiar tidal velocities along the lines of sight when determining the Hubble flow via the cosmic distance ladder. Finally, the dual action of the tidal field on the expanding background—reducing both the matter and the dark-energy sources of the squared Hubble rate \( H^2 \), thereby holding back the cosmic acceleration \( \ddot a \)—is of fundamental importance in resolving cosmological tensions and can also substantially alleviate the density coincidence problem.

Abstract: We present a geometric reinterpretation of cosmic expansion in which expansion is treated as an effective spatial dimension whose projection governs observed distances, time evolution, and physical interactions. By modelling the actual path followed by light through this expanded geometry, we introduce a spiral distance that reproduces observed luminosity and angular-distance relations without requiring accelerated expansion or an additional dark-energy component.Within this framework, gravity emerges as a local suppression of expansion, producing time dilation and curvature consistent with general relativity in the weak-field limit. Expansion is shown to be closely tied to the flow of time itself, with proper time corresponding to progression along the expansion direction and deviations from this trajectory giving rise to gravitational and kinematic time dilation. When applied consistently to both Type Ia supernova luminosity data and the angular scale of the cosmic microwave background, the framework naturally reduces the apparent discrepancy between late- and early-universe determinations of the Hubble constant.Extending the model to the quantum domain, we propose that wave–particle duality, spin, and probabilistic behaviour arise from partial delocalization within a finite temporal window. Electric charge is interpreted as a time-phase asymmetry associated with motion in the expansion dimension, with the electromagnetic coupling strength naturally linked to a dimensionless geometric ratio consistent with the fine-structure constant. Quantum entanglement is reinterpreted as a shared time-phase structure, preserving all experimentally verified predictions of quantum mechanics while providing an intuitive geometric explanation for nonlocal correlations without violating relativistic causality.The framework suggests several testable signatures, including limits on entanglement across extreme temporal separations, time-domain interference effects, and cross-scale correlations between quantum phenomena and gravitational time dilation. While fully compatible with existing observations, this approach offers a unified geometric interpretation connecting cosmology, gravity, time, and quantum behaviour, and motivates further theoretical development and experimental investigation.

Abstract: A novel classical theory of gravity, “gravity shift theory,” assumes absolute flat spacetime and the strong equivalence principle (SEP). Adherence to these postulates necessitates “gravity shifts”—universal fractional length and duration changes—dimensionally perturbing all physical objects and determining gravitational phenomena. Two observer classes emerge. “Natural observers,” using gravity shifted instruments as is, applicable for all presently available observations, perceive a curved “natural metric.” “Absolute observers,” correcting for instrument shifts, measure the absolute flat metric accurately. For a local gravitational system within a negligible-curvature background, the background system’s gravity shifting induces an applied diffeomorphism. Full SEP satisfaction for natural observers is thus ensured—a required critical observational property heretofore predicted by general relativity only. Under the equivalence principle, the natural metric universally couples to matter and nongravitational fields, identifying it as the gravitational metric in physical laws. A unique, parameterless field equation determines gravity shifts and, therefore, the natural metric. The resultant bimetric theory is complete and self-consistent. The field equation yields the observed post-Newtonian natural metric and linearizes to the predictive linearized Einstein equation, which, along with SEP satisfaction, results in successful prediction of a wide variety of observed gravitational phenomena. A supplement is provided that extends the range of prediction verification to include low post-Newtonian order radiation cases, and also the strong-field cases consisting of the properties of black and neutron stars plus nearby matter and light.

Abstract: Based on a unified non-perturbative quantum gravity framework, this paper systematically elaborates on the cross-scale universality of the quantum gravitational correction term containing a logarithmic term. At the microscale of black hole singularities, it dynamically resolves the singularity through a repulsive potential and ensures information conservation; at the macroscale of black hole gravitational fields and galaxies, it maintains the high-speed revolution of stars and the flatness of rotation curves through additional gravity, eliminating the need for assumptions such as dark matter or black hole spin fitting parameters. With quantum vortices (statistical average topological structures of microscopic particles) and nested AdS/CFT duality as the physical core, the framework derives a modified gravitational potential with a logarithmic term: \( Φ(r)=-\frac{GM}{r}-\frac{kG_h M^2 (ln⁡r+1)}{r} \). Among them, the logarithmic term ln⁡r is the core of realizing the cross-scale effect of “repulsion at short distances and attraction at long distances”. Through predicting black hole shadows (Sgr A*, M87*) consistent with EHT observations without introducing additional free parameters (e.g., spin); calculating the “periastron” velocities of high-speed stars (S4714, S62) orbiting black holes; fitting galaxy rotation curve data (Milky Way, Andromeda Galaxy, NGC2974); and further analyzing the mathematical asymptotic behavior of dark matter halos, multiple cross-scale verifications (spanning nearly 30 orders of magnitude from black hole singularities to galaxies) prove that the framework has high consistency with observations in both strong gravitational fields (black holes) and weak gravitational fields (galaxies). It achieves the first unified description of gravity from the microscale to the macroscale, providing observable and reproducible empirical support for quantum gravity theory.

Abstract: We formulate an operational hypothesis—the Synchronization Latency Principle—as a disciplined extension of an “Information Audit” viewpoint within a locality-preserving quantum cellular automaton (QCA) framework. The central claim is scoped so it can be scrutinized: matter-like excitations are auditable images that are not certified at a single-site update, but only after an audit closes over a minimal local neighborhood. In three dimensions, a nearest-neighbor stencil suggests a (1+6) block of cardinality 7; under explicit circuit-locality and audit assumptions, we show a structural lower bound Daudit ≥ 7 on the micro-depth needed to incorporate all neighbor links into a joint certification. We then strengthen the theory beyond narrative plausibility by adding (i) an operational definition of copy time via Helstrom hypothesis testing, (ii) a quantum-speed-limit lower bound on τcopy via QFI/Bures geometry and a stiffness parameter χ, and—crucially for PRA standards—(iii) a minimal explicit translation-invariant QCA class (a 7-layer Floquet-QCA schedule) for which the small-momentum dispersion has an emergent effective mass meff derived from the circuit. In that class we prove a proposition: the certified-sector quasi-energy satisfies E(k) = p (veff∥¯hk∥)2 + (meffc2)2 +O(∥k∥2, θ2, ∥k∥θ), ith veff ∝ 1/Daudit and meffc2 ∝ √ χ/Daudit, both directly testable in QCA simulation. Finally, Planck→electroweak matching is kept as a discussion (not a result): it is presented only as a possible UV boundary-condition narrative, explicitly separated from the structural theorems.

Abstract: We present a comprehensive and pedagogical formulation of Future-Mass Projection (FMP) gravity within two mathematically equivalent but conceptually distinct perspectives: (i) the block-universe perspective, where spacetime exists as a complete four-dimensional geometric entity and gravity responds to a covariant bilocal functional of baryonic stress-energy across a finite future domain, and (ii) the operational (in-time) perspective, where an observer computes identical effects using only present-time fields, their derivatives, and appropriate boundary conditions via the Schwinger-Keldysh closed-time-path formalism. We demonstrate that the apparent "future dependence'' in the block-universe formulation does not violate causality but instead reflects specific boundary conditions analogous to Wheeler-Feynman absorber theory in electrodynamics. The bilocal kernel is rigorously constructed through worldline projection using matter flow, yielding a mathematically tractable one-dimensional convolution along material worldlines. Central to the framework are the zero-DC condition (ensuring background neutrality), finite horizon ∇T ∼ 3-4 Gyr (providing a natural cutoff), and diffeomorphism invariance (guaranteeing covariant conservation \( \nabla_\mu T^{\mu\nu}_{\mathrm{eff}} = 0 \). We derive the explicit kernel form, compute its moments, and establish the equivalence theorem connecting both perspectives under well-defined validity domains. The framework offers several theoretical advantages over the particle dark matter paradigm: it eliminates the need for undetected exotic particles, provides a unified explanation across galactic and cosmological scales with minimal free parameters (4 fundamental parameters versus 6+ for ΛCDM with dark matter), and makes falsifiable predictions testable with current surveys. We discuss observational constraints including gravitational wave speed \( (|c^2_{\mathrm{GW}} - 1| \lesssim 10^{-76}) \), PPN parameters \( (|\gamma - 1| \lesssim 10^{-25}) \), and gravitational slip \( (\Phi = \Psi \) for the trace-adjusted projector). This work synthesizes developments across multiple FMP formulations, presenting a reader-friendly exposition suitable for researchers entering the field.

Abstract: We demonstrate that a broad class of cosmological properties, when expressed in their simplest form, reduce essentially to the reduced Compton wavelength of the Universe. This result follows from the use of the natural unit system (the Planck unit system), together with recent breakthroughs in cosmological thermodynamics. For example, the mass, radius, and Hubble time of the Universe are all simply related to one or two divided by the reduced Comp- ton wavelength of the critical Friedmann mass. The CMB temperature is directly related to the square root of the reduced Compton wavelength of the critical Universe, while the Hubble constant is given by the reduced Compton wavelength of the critical Universe divided by two. These relations not only substantially simplify cosmology, but also significantly increase the precision of many cosmological parameter estimates compared to the Λ-CDM model. The improvement arises because, in recent years, we have derived exact mathematical relations connecting the CMB temperature to other fundamental cosmological properties—relations that have largely gone unnoticed. We hope that increased attention to this framework will reveal the considerable progress that can be achieved along these lines.

Abstract:

This paper proposes a new non-perturbative quantum gravity framework based on quantum topological structures. By introducing "quantum vortices" to characterize the topological order of the statistical average of microscopic particles and embedding them into AdS/CFT holographic duality, the formation of "black hole singularities" is prevented (similar to singularity resolution) without the need for renormalization. Theoretical derivations show that the gravitational potential generated by the quantum vortex field forms a repulsive barrier within the critical radius (), dynamically prohibiting matter from reaching the singularity () and completely avoiding curvature divergence. The constructed Huang's metric (a Schwarzschild metric with quantum gravity corrections) can predict the angular diameter of black hole shadows without free parameters, eliminating the need for post-observation fitting of Kerr black hole spin. Prediction calculations indicate that the theoretical shadow angular diameter of Sgr A* is 53.3 μas, which is highly consistent with the EHT measured value (51.8±2.3 μas); the theoretical shadow angular diameter of M87* is 46.2 μas, falling within the reasonable error range (1.4σ) of the EHT measured value (42±3 μas). This provides a potential solution to the long-standing "parameter degeneracy" flaw of the Kerr black hole model at the theoretical source. For the first time, this theory realizes the unified explanation of singularity resolution, information conservation, and black hole shadows by quantum gravity, offering the first observationally testable physical framework for exploring quantum gravitational effects (rather than purely mathematical theoretical constructions such as string theory or loop quantum gravity).

Abstract: We have collected geomagnetic observations from low and equatorial latitudes during the 19th century to infer the intensity of geomagnetic storms during the years 1841-1877. Daily mean H observations during the above years in Trivandrum, Singapore and Madras is first scaled to Bombay observations and subsequently to the Dst index to infer the intensity of storms in modern units . These results are also compared with the intensity of these storms derived from mid latitudes. Extreme space weather events (ESW) are identified from the list of intense storms inferred during this period. The annual number of ESW events shows the characteristic double peak structure during the sunspot cycles 9-11. Space weather conditions during the sunspot cycle 11 (1867-1877) is found to be exceptional. A discussion on the true intensity of geomagnetic storms is also included.

Abstract: The overlapping spiral galaxies LEDA 2073461 and SDSS J115331.86 form an exceptional system that enables direct examination of spiral‑arm morphology and formation mechanisms. The foreground galaxy, LEDA 2073461, is a well‑defined grand‑design spiral whose inter‑arm regions contain extremely low‑density interstellar material, producing only minimal obscuration of the background galaxy. Such transparency is difficult to reconcile with the expectations of classical Density Wave Theory, which requires substantial interstellar mass to sustain long‑lived density enhancements. Instead, the observations favor a central‑driven emission mechanism for the formation and maintenance of its spiral structure. The background galaxy SDSS J115331.86 exhibits a distinctive morphology defined by an 8‑shaped double‑ring configuration and a chain‑link spiral‑arm crossing pattern, consistent with the crossing behavior previously described by the author. The visibility of multiple arm segments—together with their luminosity gradients, curvature‑extension trends, and geometric relationships—combined with the assumption of central symmetry, enables a robust reconstruction of the galaxy’s intrinsic structure despite partial obscuration by the foreground system. Together, this overlapping pair provides a rare natural laboratory for testing competing models of spiral‑arm formation and for identifying non‑classical spiral morphologies that challenge traditional theoretical frameworks.

Abstract:

Growing evidence for dynamical dark energy challenges the passive cosmological constant paradigm. This perspective article introduces a novel conceptual framework and a minimal, testable benchmark model to probe a fundamental question: is dark energy’s evolution correlated with cosmic structure growth, suggesting it is an intrinsic component of cosmic dynamics rather than a static background? We propose a linear correlation of the form w(a)=−1+η(γ(a)−0.55) between the dark energy equation of state w(a) and the structure growth index γ(a) as a key observational signature of this intrinsic link. This linear relation is the first concrete, testable benchmark framed from the perspective of dark energy as an intrinsic cosmic dynamical component. To provide physical motivation and verify self-consistency, we construct a phenomenological “Dynamic Coupling Model.” In this model, the energy transfer rate between dark energy and dark matter is postulated to be dynamically modulated by cosmic structure growth (traced by γ(a)). This model naturally yields the linear w-γ relation, with a theoretically motivated benchmark slope η=0.25±0.03. The model’s key testable prediction is a deviation at redshift z≈0.5, where w≈−0.89±0.02, in stark contrast to ΛCDM’s w=−1, offering a clear observational target. Future high-precision data will first verify the existence of this correlation. If confirmed, data can further discriminate whether it supports this simple linear parameterization or points to more complex coupling mechanisms. Regardless of the outcome, this w-γ correlation paradigm provides a new, actionable starting point for understanding dark energy’s dynamical role. The proposed framework is consistent with current cosmological data, shows potential to alleviate the Hubble tension, and defines a clear path for observational testing.

Abstract: This new frame work of thermodynamics consists of four parts:（1）The traditional thermodynamics (a brief one), relating to all the thermodynamical processes we meet in our life，work, ordinary research, and so on, covering an extremely immense scope. Numerous and numerous human practices confirm that all these processes are irreversible, and entropy tends to increase, never decreases; (2）The thermodynamics of thermal electrons in a magnetic field. The thermal electrons here are emitted at room temperature from two identical and parallel Ag-O-Cs emitters, A and B (work function 0.8eV) in a vacuum tube. The tube is applied by a static magnetic field parallel to A and B, bending the trajectories of the electrons, resulting in a weak asymmetry in their thermal motion（to left or to right）. Emitter A, losing some net electrons, is charged positively; and emitter B, getting some net electrons, is charged negatively. An electric potential between A and B is formed, enabling the tube outputs a continuous tiny but macroscope current to an exterior load, e.g., a resistor, or a storage battery. (Reverse the direction of the magnetic field, the output current also reverses.) Due to the ceaseless output of electric energy, the internal energy of the tube should decrease slightly, and the whole tube follows to cool down slightly. The slightly cooled tube can automatically absorb waste heat from the ambient air (that is kept at a constant room temperature) to compensate its output electric energy. The experiment converts the waste heat from the ambient air to electric energy, directly violating the Kelvin-Planck statement of the second law. Two short experiment videos are included in this article. (3）Cosmic thermodynamics. The authors approve of the idea that the universe is gravitationally closed, and naturally, there should be an extremely immense ocean of thermal radiation in the central part of the closed universe. The 2.73K microwave background radiation discovered in 1965 should just be this immense heat ocean. Due to the big bang, all the about 2ⅹ1012 galaxies are now flying outward fiercely. When they reach their individual far-most positions in the closed universe，they will turn back one after another, fly towards the central region of the universe, passing through it, until reach their individual far most positions on the other side of the closed universe. Then they keep shuttling with extremely great amplitudes in the closed universe ceaselessly. There are numerous stars and many black holes in every galaxy. A black hole annexes any celestial body that it encounters. The directions of the shuttling of the galaxies are different in the 4p solid angle, so in a long, long duration, the 2×1012 galaxies have numerous chances to meet each other in the central region. When a black hole encounters a star or another black hole in the central region in the shuttling, annexation happens. All the matter scattered to the extremely vast space by the big bang will thus be collected step by step, until finally assemble to be a single extraordinary immense black hole, the central black hole. On the other hand, the big bang and all its subsequent processes are all huge irreversible processes. They produce and eject immense amount of light and thermal radiation into the vast cosmic space. The light and thermal radiation are also impossible to fly off the closed universe, shuttling ceaselessly in the closed universe with much, much greater amplitudes. After a long, long relaxation time, by interchange heat with the rare cosmic atoms, molecules, dusts, rocks, etc., (they are all at 2.73K) in the metagalaxy region, they will finally mingle into the 2.73 heat ocean. The central black hole, containing all the real matter of the universe, has an extraordinary immense event horizon, will take in continuously and monotonically the thermal radiation from the 2.73K heat ocean with an extraordinarily great power, leading eventually to a new big band. A big band followed by a big assembling forms a big cycle. All the matter and an extremely great amount of energy in the universe are involved in the big cycle. (4）The new theoretical system of thermodynamics. The first law of thermodynamics is still energy conservation. Energy is conserved in amount wherever and whenever. It is a law of the universe. The new second law of thermodynamics is energy cycle. All the matter and energy are involved in a big cycle in the closed universe. Entropy may increase, it may also decrease. The general increase and general decrease of entropy match each other in a big cycle. Clausius’ Heat Death is an excessive anxiety.

Abstract: This perspective article proposes and systematically develops a phenomenological framework centered on the correlation between dark energy dynamics and cosmic structure growth. Building upon the foundational linear relation w(a) = -1 + η(γ(a) - 0.55), where w is the dark energy equation of state and γ is the structure growth index, we extend it to allow for redshift-dependent couplings and provide a complete roadmap for empirical testing. We establish its theoretical basis as an interacting dark energy-dark matter model that respects energy-momentum conservation. A key advancement is our complete parameterization w(z)=−1+η(z)[γ(z)− 0.55]+Δw_bg(z), which separates structure-dependent coupling from possible background evolution and allows for redshift-dependent interactions. This work introduces a novel, phenomenologically motivated piecewise parameterization for the coupling strength η(z), designed to capture potential variations across distinct cosmic epochs (z < 0.5, 0.5 ≤ z ≤ 1.5, z > 1.5) based on the history of structure formation.​ We provide a comprehensive testing roadmap using hierarchical Bayesian model comparison, detailing the specific observational data, analysis methods, and systematic error treatments required. Using Fisher matrix forecasts based on detailed survey specifications, we demonstrate that upcoming surveys (DESI, Euclid, Roman Space Telescope) will provide decisive tests, capable of detecting coupling strengths |η| ≳0.05 with strong evidence. This framework offers a unified approach to addressing both the Hubble and S8​ tensions while making distinctive, testable predictions that differentiate it from other proposed solutions. We conclude with specific recommendations for observational teams and theoretical directions for further development.