What question did this study set out to answer?

The central aim is to extend and formalize the Is Framework through Mapping Theory, creating a structural comparison method for diverse ontological frameworks.

June 13, 2026Open Access

The Is: An Ontological Framework v2.0 — Mapping Theory: The Is Sequence as a Structural Template for Heterogeneous Frameworks

Key Points

The central aim is to extend and formalize the Is Framework through Mapping Theory, creating a structural comparison method for diverse ontological frameworks.
Introduced interpretive structure-preserving mappings and invariance conditions.
Developed cross-framework mappings: Structural Differentiation Cosmology, Topological Latent Manifold Model, Appearance–Behavior Framework.
Presented Mapping Invariance Principles and Mapping Taxonomies for evaluating mappings.
Demonstrated mappings function as interpretive correspondences rather than reductions or identities.
Introduced various mapping strengths and falsifiability criteria.
Provided a roadmap for future versions towards Unified Meta-Ontology.

Abstract

This release presents The Is Framework v2. 0, introducing Mapping Theory as a formal extension of the type-theoretic reconstruction established in v1. 0 and v1. 1. The central contribution of v2. 0 is the formalization of interpretive structure-preserving mappings: ΠX: (I→D→S→A→F) →XX: (I D S A F) XΠX: (I→D→S→A→F) →X through which the ontological sequence is proposed to function as a structural template for comparing heterogeneous frameworks. Building upon the formal grounding introduced in v1. 1—including the invariance condition f (I) = I and falsifiability classes C1–C3—this version develops three illustrative cross-framework mappings: ΠSDC (Structural Differentiation Cosmology) ΠTLMM (Topological Latent Manifold Model) ΠABF (Appearance–Behavior Framework) Version 2. 0 further introduces: Mapping Invariance Principles (MDT-1–MDT-3) Sequence Order Preservation Ground Invariance Feedback Closure on Derived Layers Mapping Strength Taxonomy Strong Mapping Partial Mapping Weak Mapping Mapping-Level Falsifiability Criteria (C4–C6) Mapping Collapse Ground Invariance Violation Feedback Closure Failure The framework explicitly treats all mappings as interpretive structure-preserving correspondences, not reductions, identities, or proofs of equivalence. The proposed mappings remain open to revision, empirical evaluation, and falsification. This release includes the full manuscript, fourteen figures, README documentation, and a Python demonstration script that reproduces all figures used in the publication. Figures 1–8 are inherited from v1. 0/v1. 1 and summarize the type-theoretic reconstruction and formal grounding of the framework. Figures 9–14 introduce the new Mapping Theory architecture, including cross-framework mappings, invariance principles, mapping taxonomy, falsifiability extensions, and the roadmap toward v2. 1 (Formal Mapping Layer) and v3. 0 (Unified Meta-Ontology). All examples, mappings, classifications, and visualizations are conceptual and illustrative. The framework is intended as an exploratory ontological and methodological research program rather than a completed formal theory.

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Cite This Study

Koji Okino (Thu,) studied this question.

synapsesocial.com/papers/6a2cf57cfaef96ed7f057765 https://doi.org/https://doi.org/10.5281/zenodo.20641993

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