Abstract

Current Artificial Intelligence (AI) systems, including Large Language Models (LLMs) and neuro-symbolic Automated Theorem Provers (ATPs), face severe limitations regarding semantic preservation and out-of-distribution reasoning. When attempting to transfer inferential logic across heterogeneous mathematical domains, these systems frequently suffer from "semantic hallucinations" and catastrophic forgetting. This vulnerability stems from an underlying axiomatic blindness: neural architectures process mathematical structures purely extensionally (as quantitative weights), ignoring their intrinsic ordinal structures. Drawing upon recent advancements in set-theoretic multiverse theory, this paper proposes a novel framework for machine learning architectures: Skeleton-Aware Artificial Intelligence. By integrating the Axiom of Structural Identity (ASI) and the Methodological Principle of Operational Integrity (MPOI), we formalize mathematical objects as dual-invariant tensors ⟨Card, Ord⟩. Furthermore, we replace traditional heuristic loss functions with a Boolean-valued Entropic Dispersion metric. This ensures that the structural negentropy of a proof skeleton is mathematically bounded, penalizing syntactical mutations during cross-domain transfers. The result is a mathematically rigorous inference engine capable of extracting Hegel’s "Concrete Universal" across shifting axiomatic models without generating set-theoretic paradoxes.