Spacetime Curvature Identity:Euler's Formula, Riemann Zeros, and the Unified Dark Sectors

Energy conservation is the only principle in physics that admits no exception.Building on this, author introduce the UFED Theory --- Unified Field of Existential Density, which posits that energy is the sole substrate: continuous, differentiable, and endowed with a constant modulus. Under this premise, time, space, and electromagnetism are not independent ontological entities but curvature projections of the same underlying substrate in different directions. Within the minimal UFED structure, the electromagnetic and geometric curvatures arise as two orthogonal projections of a unified complex-phase wavefunction. Owing to the Euler structure, these two projections correspond to opposite phases of the same modulus. Because their magnitudes are identical, their product is naturally a constant. Author note that this constant may bear a close numerical relation to the fine-structure constant (approximately 1/137), although this connection is only structural and not required by the theory. When the two curvature projections coincide, the system reaches a symmetry state. The structural manner in which this symmetry arises is identical to that of the nontrivial zeros of the Riemann zeta function on the critical line: both correspond to nodes where the phase difference vanishes. In this sense, Riemann zeros appear naturally as symmetry points within the unified curvature structure, rather than as independent mathematical accidents. Extending the dual structure to a three-component form, author introduce a ''temporal curvature'' and obtain the spacetime curvature identity, in which geometric, electromagnetic, and temporal sectors become the three orthogonal components of the same unified wavefunction. Under this identity, dark matter, dark energy, and black holes correspond respectively to the positive, negative, and divergent limits of temporal curvature; meanwhile, SR, GR, and EM emerge as distinct projections of the same underlying curvature identity. This preprint presents only the structural identity and its implications, without technical derivations or observational predictions.