Helical geometrodynamics is presented as a theoretical framework in which systems, transport, geometry, memory, and interaction are analyzed through coherent helical flows. The volume does not seek to replace experimentally validated physical theories. Instead, it investigates whether a common descriptive level can be constructed from vortex tubes, the IN—path—OUT architecture, and geometric adaptation. It introduces the Preda descriptors Cc = dQ/dt, Cf = rvt², and Ce = r³f², together with the independent rotational descriptor Cr, the helical ratio η = va/vt, axial direction, chirality, and phase. The relation Cf = 4π²Ce is treated as an algebraic identity when vt and f refer to the same local rotation, whereas α = CeCf/Cc² remains a derived ratio and a hypothetical filter rather than a sufficient coupling criterion. On this basis, the volume formulates four candidate interaction kernels and develops the concepts of geometrodynamic memory, the Fundamental Torsion Wave (F.T.W.), structural emission and absorption, polarization, axialization, and the Σgd transition regime. Extensions toward light, particles, gravity, cosmology, and living systems are explicitly identified as hypotheses or analogies. The central contribution is an operational research program based on defined observables, comparison with standard models, preregistered predictions, uncertainty analysis, and falsification criteria. In its present form, the work is a falsifiable conceptual framework and research program, not an experimentally validated physical theory.