Adaptive Observability as a Framework for Single-Cell Learning in Stentor coeruleus

Abstract

Preprint of a theoretical and computational manuscript developing adaptive observability as a falsifiable framework for habituation and cellular memory in Stentor coeruleus. The work formulates an operator-based framework in which an observable’s access to slow dynamics is characterized through modal leakage, projection onto slow subspaces, and observable-dependent relaxation rates. Exact results are derived for a reversible/self-adjoint reference class, including a spectral-measure formulation that accommodates both discrete spectra and continuous distributions of relaxation timescales. Stentor coeruleus is used as the biological reference system for turning these mathematical ideas into experimentally falsifiable hypotheses. The manuscript explicitly distinguishes among a low-order memory architecture, a hierarchy of slow resources, and distributed or fractional-memory alternatives (M0–M1–M2), while separating the observational theory from the local physical U-H6 hypothesis. Calcium signaling, kinase and phosphatase regulation, protein synthesis, and other molecular candidates are treated as possible experimental coordinates rather than as established identities of the memory resource. This version constitutes a pre-data freeze. The requested individual-cell records for the planned empirical analysis have not been received or inspected, and no claim of local biological closure is considered established. This version prospectively fixes the theoretical structure, competing model classes, and principal falsification criteria that will later be confronted with data. This deposit contains the manuscript only. Associated code, figure-reproduction materials, and analysis files will be deposited in a later version or alongside the eventual empirical journal submission.