The Is: An Ontological Framework v2.1 — Formal Mapping Layer

This release presents The Is Framework v2.1, introducing the Formal Mapping Layer, a systematic extension of the ontological framework established in v2.0. Building on the five foundational axioms (T1–T5), the ontological ordering I → D → S → A → F (The Is → Difference → Structure → Appearance → Feedback), derived theorems, and the falsifiability architecture (C1–C11), v2.1 formalizes interpretive mappings (ΠX) that connect the ontological sequence to three domain frameworks: Structural Differentiation Cosmology (SDC), the Topological Latent Manifold Model (TLMM), and the Appearance-Based Framework (ABF). The release introduces three Mapping Invariance Principles (MDT-1 to MDT-3) governing structure preservation, appearance dependence, and feedback closure across framework mappings. It further extends the falsifiability architecture through the introduction of C12 (Mapping Invariance Test), which evaluates whether interpretive mappings preserve the ontological ordering of the framework. A taxonomy of mapping fidelity is proposed through Strong, Partial, and Weak Mapping Classes, providing a structured approach for assessing correspondence quality between ontological constructs and domain-specific models. The framework also develops the concept of structural completeness without terminal completeness, arguing that coherent structures may remain valid without requiring a final or complete endpoint. This idea is illustrated through formal mapping examples and the π analogy, motivating the next stage of development toward a Unified Meta-Ontology (v3.0). All figures, mappings, and examples are conceptual and illustrative. The proposed correspondences are interpretive rather than identity relations and are intended to support theoretical analysis, cross-framework comparison, and future empirical investigation. The framework is presented as an exploratory ontological and methodological research program rather than a validated scientific theory of reality.