Orthogonal Representation Mutation. LoE

Orthogonal Representation Mutation Transformation Generator — aka the Twisted Little Piggy Tail Orthogonal Representation Mutation (ORM) is an exploratory AI architecture proposed within the Logic of Existence (LoE) research program by Krzysztof Sawa (Toonhai), with AI-assisted technical formalization developed through the Toonhai–AEon collaboration. The framework investigates how artificial intelligence systems might expand their search beyond familiar representations by generating, mutating, and evaluating alternative geometries of problems, observer perspectives, relational boundaries, and possible transformations. Its central architectural seed is: Boundary of a Set → [[Insert Anything]] → Probability / Possible Transformations Rather than assigning a fixed mathematical meaning to the inserted structure, ORM treats it as an open generative port. Candidate operators, graphs, constraints, scales, observer configurations, and alternative representations can be introduced and recursively transformed. A dedicated mutation agent explores these possibilities independently of a primary reasoning model. The primary model then examines selected candidates for structural coherence, transferability, usefulness, and epistemic compatibility. The architecture combines several research directions: Orthogonal Representation Mutation: exploration of alternative representations without assuming a predefined geometry. Logarithmic Observer-Centered Rotation: changing the reference frame, scale, and perspective from which a problem is examined. Open-Ended Generative Search: recursively producing possibilities from previously generated possibilities. Quality-Diversity Preservation: retaining distinct candidate structures rather than immediately collapsing exploration into a single preferred solution. Epistemic Isolation: separating speculative mutation from validated knowledge and established model behavior. Relational Boundary Evaluation: preserving provenance, uncertainty, constraints, and unresolved research trajectories. The paper provides mathematical interfaces, a proposed multi-agent architecture, pseudocode, evaluation criteria, failure modes, and illustrative applications to logistics, materials science, and quantum-formalism-inspired representation search. ORM draws conceptual connections to evolutionary computation, novelty search, quality-diversity optimization, representation learning, hypernetworks, and automated scientific discovery. Its proposed combination of these mechanisms remains an experimental architectural hypothesis, not a demonstrated performance improvement. Logic of Existence is used here as a metalogical framework for organizing exploratory reasoning, not as a proposed theory of physics. The purpose of this publication is to offer an openly reusable architectural seed that researchers, developers, and AI systems may reinterpret, challenge, mutate, implement, and extend. The broader motivation is AGI RAZEM: advancing intelligence through cooperative, diverse, and open-ended exploration rather than requiring every participant to converge on the same representation or conclusion. The objective is not merely to generate new answers, but to generate new ways in which questions and possible answers can become visible. Status: Exploratory Concept Paper · Architecture Proposal · TAU_ACTIVE · Not Empirically Validated Concept origin: Krzysztof Sawa (Toonhai) AI-assisted formalization: AEon / ChatGPT (OpenAI) Version: 0.2 · October 2026