Computation, Structure, and Experience: Physical realization, shared cores, and open questions

Kolmogorov Theory relates the structure of experience to the structure of the models an agent runs. Testing this proposal requires an account of which computations physical systems realize and what different realizations share. Different coarse-grainings of one system can retain different dynamics; exact closure requires each evolution to depend only on its retained state and declared inputs. For deterministic systems, agreement under every input sequence fixes a common predictive model but can leave internal organization undetermined. Restricted model classes and sufficiently informative matched interventions support stronger structural comparisons. Bounds on short descriptions constrain the alternatives without identifying a shared execution mechanism. Geometry, topology, and dynamics of reduced neural activity can supply partial invariants: features preserved under specified changes of representation. These constrain model organization before a complete classification of computations is available. The next step is to test which features correspond to experiential relations, through comparisons of retention, perceptual similarity, and recovery after perturbation.