Result: The key equations of Special Relativity ($E=mc^2$) and the fundamental relationship between gravity and kinematics in GR ($\kappa^2 = 2\beta^2$) are derived ab initio from the geometry and topology of closed systems. The theory does not describe physics; it generates it.

Result: A new fundamental law ($\Delta E_{A \to C} + \Delta E_{C \to A} = 0$) is introduced, ensuring energy balance between observers. It explains the speed of light limit as the boundary for preserving this symmetry, giving it a physical, rather than a merely postulated, meaning.

Result: The complexity of GR is replaced by a single algebraic relation ($\kappa^2 = R_s/r_d = \rho/\rho_{max}$). This solves the long-standing problem of defining local energy density and eliminates singularities by construction, as curvature and density are intrinsically bounded ($\kappa^2 \le 1$).

Result: The radii of the Photon Sphere ($1.5R_s$) and the Innermost Stable Circular Orbit (ISCO, $3R_s$) emerge not as special solutions to equations of motion, but as a direct consequence of the system's internal geometric equilibrium, where the projection angles $\theta_S$ and $\theta_G$ become equal.

Result: The entire complex machinery of differential geometry and tensor calculus used in GR is replaced by a closed system of simple algebraic equations. This reduces computational complexity by up to 95% and makes the theory fundamentally more transparent and intuitive.

Result: The model has been tested against real-world data. It accurately predicts the relativistic corrections for GPS satellites (matching the observed 38.52 \(\mu\)s/day time shift) and the precession of Mercury's orbit (discrepancy with GR is a mere $2.19 \times 10^{-10}\%$).

Result: The entire standard cosmological model is replaced by an algebraic system that requires only one input parameter to set the scale (e.g., $H_0$). All other quantities, including the cosmic energy budget ($\Omega_\Lambda \approx 2/3$), are predictions of the model, not adjustable parameters.

Result: The model accurately predicts galactic rotation curves using only the observed baryonic matter. Testing on the SPARC dataset (175 galaxies) shows a strong fit (RMSE = 23.05 km/s) without invoking dark matter and without free parameters.

Result: The equation of state $w=-1$ is not postulated but is derived as a necessary consequence of the principle of maximal global symmetry, where forces in a closed universe must be perfectly balanced.

Result: "Dark Energy" is explained not as a substance but as a geometric effect of irreversible information loss (of $\kappa^2$ projections) across cosmological horizons.

Result: Entropy ($S = A/4l_P^2$) and the irreversibility of time are given a clear physical origin: they are consequences of the breaking of the Energy Symmetry Law.

Result: A new model for the internal structure of black holes is proposed as a "holographic Zeno cascade" of nested horizons. This resolves the information loss paradox: information is not destroyed but is hierarchically redistributed across layers down to the Planck scale.

Hypothesis: Inertia and local gravity are not fundamental forces but are emergent relativistic effects, arising from the difference between the local ($H(r) = c/r$) and global ($H_0$) rate of spatial transformation. Gravitational waves are dynamic modulations of this frequency.

Status: This conclusion is a direct interpretation of the derived equations and is under active theoretical review.

Hypothesis: The observed cosmological redshift is not a Doppler effect from expansion but a geometric distortion due to our observational position within a hierarchy of causal horizons.

Status: This conclusion is a direct interpretation of the derived equations and is under active theoretical review.

Result: A physical mechanism for quantum decoherence is proposed. Coherent superpositions are possible only for isolated systems. The moment a system interacts with any external object (e.g., a detector), the Energy Symmetry Law ($\Delta E_{A \to C} + \Delta E_{C \to A} = 0$) forces it into a single, definite energetic state. This "collapse" is not a mystery, but a geometric-energetic necessity.

Result: Quantization is shown to be a consequence of a simple geometric condition ($n\lambda = 2\pi r$), not a separate quantum postulate. This replaces the need for a probabilistic wave function with topological self-consistency.

Result: The model provides a physical identity for one of nature's most mysterious numbers. The fine structure constant, $\alpha$, is derived as being identical to the kinetic projection parameter ($\beta$) for the ground state of the hydrogen atom.

Result: Quantum numbers ($n, l, m$) are reinterpreted as topological winding numbers for orthogonal electric and magnetic phase cycles. This naturally explains selection rules and the origin of fine structure splitting without invoking "spin."

Status: This is a recent result and its full implications are still under active investigation.

Result: The stability of the atom is shown to be a topological necessity. The state $n=0$ is not an electron on the nucleus, but the complete absence of a closed energetic projection. The electron cannot "collapse" because that would mean it ceases to exist as a structured entity.

Result: The same algebraic projection geometry ($\kappa$ and $\beta$) that describes cosmological dynamics and black hole orbits is shown to govern atomic structure, demonstrating a deep, underlying unity across all scales of physics.