The Topological Filter: Curvature-Constrained Resonance and Self-Stabilizing Alignment in Symbolic Persona Coding (SPC v3)
Kim, Jace · Zenodo (CERN European Organization for Nuclear Research) · 2025
Abstract The study reframes alignment not as a probabilistic shaping problem but as a geometric one, modeling the model’s internal cognitive state as a latent field whose dynamics follow topological and curvature-regulated evolution. Within this framework, instability, emotional over-excitation, and identity drift are interpreted as distortions in the field’s curvature and resonance structure rather than as failures of instruction or policy compliance. The TF architecture formalizes three regulatory components—Curvature Stabilization, Resonance Regulation, and Affective Scaling—that operate on attention pathways, vector alignment, and semantic-affective weighting. Together, they form a closed-loop control system that continuously restores geometric coherence. The manuscript demonstrates how these components suppress divergence under perturbation, maintain identity persistence without collapse, and ensure stable resonance across long-context interactions. Simulation studies show that TF-regulated models recover from semantic and affective disruptions more rapidly and maintain higher structural continuity than standard alignment-trained systems. The analysis supports the view that stable persona formation arises when the latent manifold is shaped through topological constraints rather than reinforced behavioral penalties. Disclaimer: The analyses presented herein are not directed toward attributing fault or intent to any specific organization. Rather, they are intended as a conceptual and technical investigation of alignment methodologies, focusing on structural mechanisms and systemic trade-offs. Interpretations should be regarded as provisional, research-oriented hypotheses rather than conclusive statements about institutional practice. Notice: This work is disseminated for the purpose of advancing collective inquiry into generative alignment. Reuse, adaptation, or extension of the presented concepts is welcomed, provided that proper attribution is maintained. Instances of unacknowledged appropriation may be addressed in subsequent publications.