Hierarchics: A Proposed Quantitative Framework for Hierarchical Organization

Hierarchics is a proposed quantitative framework for measuring hierarchical organization across biological, ecological, engineered, physical, and social systems. The framework introduces two complementary domains: Systems Relativity, the applied measurement protocol, and Quantitative Philosophy, the theoretical search for hierarchical invariants. Its operational engine combines the Compass Lens, which measures causal coupling and coordination strength, with the Nest Lens, which measures hierarchical depth and structural efficiency. The framework also introduces observer-dependent measurement, a four-part Validity Gate, and the ln(4) attractor hypothesis as a falsifiable candidate invariant of efficient hierarchical organization. This manuscript presents the conceptual architecture, mathematical primitives, and proposed validation pathway for future empirical testing.