AI Safety
Teleological Vectors: A Mathematical Framework for Semantic Goal Alignment
Christopher Royse, Kansas State University•December 2025•arXiv:2512.XXXXX
Strategic misalignment costs organizations $138 billion annually, AI safety incidents impose catastrophic risks ($1T+ volatility), and educational curricula fail 43% of graduates entering the workforce. This paper introduces the Teleological Vectors Framework, extending Harris's distributional hypothesis from linguistic semantics to goal-directed systems through the Teleological Distributional Hypothesis: goals pursued through similar action contexts have similar teleological meanings. We formalize alignment as cosine similarity in semantic embedding space, proving four theorems (transitivity bounds, composability guarantees, convergence rates, RLHF generalization). The framework transforms alignment from qualitative aspiration into quantitative discipline, positioning semantic vectors as foundational infrastructure for civilization-scale coordination.
Teleological VectorsSemantic AlignmentGoal-Directed SystemsAI SafetyMulti-Agent Coordination
AI Theory
The Theory of Epistemic Symmetry: A Theory of Epistemic Transformation in the Age of Artificial Intelligence
Christopher Royse, Kansas State University•November 2025•arXiv:2503.15432
This paper introduces and substantiates the Theory of Epistemic Symmetry, arguing that high-capability generative AI fundamentally collapses the historical asymmetry between inquiry and discovery. By enabling computational reversibility—the capacity to reconstruct complex prompts from outputs with high fidelity—AI transforms the question-answer relationship from a unidirectional vector into a bidirectional, symmetrical exchange. Through 33 falsifiable propositions, the theory predicts that as computational reversibility approaches unity, traditional epistemic labor is offloaded, professional expertise is redefined from knowledge possession to verification, and educational assessment systems face a crisis of validity.
Epistemic SymmetryComputational ReversibilityLarge Language ModelsEducational TheoryCognitive Offloading
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