Æther Model – Cartography of Scale-Based Descriptions: Definition, Scope, and Applicability

This work presents a methodological formulation of cartography for scale-based physical descriptions. Cartography is defined as a structural procedure aimed at identifying the domains of validity of an effective description under extrapolation, based on the operativity of its variables and on the mathematical properties of the effective operators that support them. The object of the analysis is not the physical system or its microscopic dynamics, but the internal consistency of scale-based descriptive languages built on notions such as frequency, mode, scale, and effective time. Domains of validity are characterized through explicit mathematical conditions, including hyperbolicity of effective operators, non-degeneracy of kinetic structures, spectral stability, and the existence of finite internal scales. Breakdown of description is formulated as a well-defined structural collapse, rather than as a phenomenological anomaly, a geometric singularity, or evidence for new degrees of freedom. The approach is deliberately system-independent and is illustrated through representative regimes in gravitational and cosmological physics, including modal descriptions of black holes, early-time cosmological extrapolations, and late-time tail dynamics. Additional domains of applicability in effective field theories and scale flows are also discussed. The result is an autonomous methodological tool for controlling extrapolation in effective theories, clarifying the physical scope of scale-based descriptions, and turning limits of applicability into positive structural information.