This page serves as a living technical reference for Synchrona’s core mathematical framework. Here, we formally describe the structure of the fidelity space, the posture vector system, structural referents, misalignment analysis, and recursive adaptation dynamics. Our goal is to provide transparent, rigorous definitions to support scientific, clinical, and engineering validation. This foundation will continue to evolve as our research and applications progress.
Defines the multi-dimensional space where each axis represents a contextually meaningful, dynamic, or latent property of a system or person. This space is not static — it can evolve, deform, and adapt recursively, supporting deep behavioral and structural mapping.
Describes how a system or person’s state is represented as a posture vector, formed by scoring on each axis. The structural referent acts as a target or ideal vector for comparison, defining coherent alignment and directional goals.
Explores the difference or "gap" between the posture vector and the referent — called the misalignment region. Rather than simple deviations, this space is treated as structurally rich, allowing for fine-grained analysis, correction, and deeper insight into behavioral or systemic drift.
Covers how both the posture vector and the fidelity space can be recursively adapted: adding or dropping axes, reweighting dimensions, or reshaping referents. This enables continuous, evolving learning and alignment rather than static evaluation.
Focuses on the ability to actively modulate or "cycle" dimensions, adjust topology, and explore or compress different fidelity subspaces. This enables multi-layered analysis and fine-tuned control across various levels of behavioral or system states.
Details how machine learning or deep learning models can be integrated to derive new latent axes, interpret misalignment regions, or suggest nuanced corrective vectors. These models act as "cruise control" aids, but remain transparent and controlled via fidelity scores.
Highlights the wide applicability of the framework: from clinical and therapeutic tools to robotics, AI safety, energy optimization, and secure communication. Emphasizes that the structural foundation allows coherent expansion across almost any domain.
