Nuclear Crystallography: The Universal Tension-Driven Lattice (UTDL-N) and the First-Principles Derivation of Macroscopic Nuclear Scaling

Standard macroscopic nuclear models, such as the Liquid Drop Model (LDM) and the Shell Model, successfully approximate binding energy trends but rely entirely on phenomenological, empirically fitted free parameters to define their volume, surface, Coulomb, and asymmetry coefficients. This paper proposes a microscopic, first-principles ontological basis for these coefficients via the Universal Tension-Driven Lattice (UTDL) framework. In this nuclear application (UTDL-N), we model the nucleus not as a continuous quantum fluid, but as a discrete Face-Centered Cubic (FCC) crystalline defect within a high-tension icosahedral vacuum substrate. By mapping the discrete geometric limits of this FCC lattice onto the continuous dimensional scaling of the LDM, we replace the empirical tuning dials with parameter-free geometric constants derived from the fundamental vacuum strain quantum (Eλ ≈ 20.93 MeV). Furthermore, we derive the super-linear nuclear baseline mass scaling (A1.0107) entirely from the topological yield strain between the incommensurate A5 vacuum and the cubic nuclear boundary. Execution of this zero-parameter deterministic algorithm across the AME2020 dataset (n=3557) yields a global RMS relative precision of ≈ 0.14%. These findings reveal a global Harmonic Staircase of quantized mass excess and suggest that nuclear stability is governed by a Geometric Efficiency Law, where the isospin ratio converges to the Pythagorean constant √2. This framework successfully resolves contemporary isotopic anomalies, including the unbound nature of 28O and the emergent stability of 257Sg, offering a rigorous quantitative benchmark against highly tuned legacy models.