On the Discrete Derivation of Structural Closure via Radix-Dependent Integer Mappings

This record presents an investigation into radix-translation frameworks and discrete structural closure, utilizing the integer 360 as a primary architectural target. By analyzing how operational indices like 19 undergo sparse-to-dense quaternary reinterpretation (yielding 261), the study documents an exact internal integer identity: 261 + 99 = 360. Rather than relying on continuous spatial paradigms or modifying classical constants, the framework serves as an independent investigation within the overarching binary-base 4-base 10 framework, demonstrating how multi-base syntax forces precise architectural boundaries.