Kolmogorov Theory

2007 – Information, complexity, brains, and reality (Kolmogorov Manifesto) (arXiv) · Zenodo

Proposes that cognition can be understood as the search for programs approaching the Solomonoff–Kolmogorov–Chaitin complexity limit. Introduces “reality” as a mental model constructed by compressing and interpreting coherent sensory inputs.

2009 – Reality as Simplicity (arXiv) · Zenodo

Argues that all human experience is built from algorithmic models seeking simplicity. Develops a hierarchy of processing levels where the brain selects the simplest model consistent with data, illustrating applications in mismatch negativity and Presence research.

2016 – MODELS, NETWORKS AND ALGORITHMIC COMPLEXITY (arXiv) · Zenodo

Demonstrates that models, classification functions, invariances, and datasets are algorithmically equivalent. Shows how neural networks implement these models and fall into a descriptive power hierarchy aligned with recursive‑function theory.

2017 – An algorithmic information theory of consciousness (Neuroscience of Consciousness) · Zenodo

Presents an AIT framework for quantifying structured experience from neurophysiological data. Hypothesizes that compressive generative models by recurrent networks underlie phenomenal structure and self‑awareness; reviews methods such as ERP paradigms, spontaneous state analysis, stimulation, and behavioral measures. Annotated version

2021 – The 2D Ising model, criticality and AIT (bioRxiv) · Zenodo

Uses the 2D Ising model to link phase‑transition phenomena (correlation length, susceptibility) with algorithmic complexity metrics (LZW compression, information rate). Shows how sparse long‑range couplings shift critical temperature and discusses implications for neural criticality.

2022 – AIT Foundations of Structured Experience (Journal of Artificial Intelligence and Consciousness) preprint

Unifies consciousness under AIT by defining structured experience (𝒮) as the match between data and succinct generative programs. Associates model length with qualitative aspects of experience and predicts empirical markers via dimensionality reduction and criticality.

2022 – Algorithmic structure of experience and the unfolding argument (PsyArXiv)

Examines how the “unfolding argument” and falsification criteria challenge AIT‑based consciousness theories. Analyzes computational hierarchies and resource limits to propose refinements for causal‑structure models.

2023 – LSD‑induced increase of Ising temperature and algorithmic complexity of brain dynamics (PLOS Computational Biology)

Compares fMRI‑derived Ising models under placebo vs. LSD, showing LSD raises system temperature and algorithmic complexity. Personalized models reveal homotopic connectivity decreases and complexity metrics (LZW, BDM) correlate with temperature.

2023 – Neural geometrodynamics, complexity, and plasticity: a psychedelics perspective (Entropy)

Introduces “neural geometrodynamics,” linking fast neural dynamics and slow (meta)plasticity. Shows psychedelics flatten the neural landscape, increasing entropy and complexity, and discusses how plasticity processes consolidate new dynamics.

2024 – The Algorithmic Agent Perspective and Computational Neuropsychiatry: From Etiology to Advanced Therapy in Major Depressive Disorder (Entropy)

Applies the KT framework to model Major Depressive Disorder as low‑valence states in algorithmic agents. Maps cognitive, affective, and executive deficits to brain circuits and biotypes; proposes personalized interventions combining stimulation, psychotherapy, and pharmacology.

2024 – Navigating Complexity: How Resource‑Limited Agents Derive Probability and Generate Emergence (PsyArXiv) · Zenodo · Preprints.org

Shows that finite data access and computational resources naturally generate probabilistic reasoning, Bayesian inference, and a formal notion of emergence via coarse‑graining and algorithmic complexity; connects to Free Energy and Active Inference frameworks.

2025 – Structured Dynamics in the Algorithmic Agent (Entropy)

Formalizes generative models via Lie‑group symmetry and demonstrates that data‑tracking constrains an agent’s dynamical repertoire to mirror world symmetries, supporting structured experience and the manifold hypothesis. Examines how compressive models and symmetry constraints shape an agent’s structural and dynamical repertoire, bridging AIT, group theory, and dynamical conservation laws.

2025 – Compositional Symmetry as Compression: Lie Pseudogroup Structure in Algorithmic Agents (arXiv) · Zenodo

Proposes that agents make sense of sensory data by exploiting compositional symmetry—modeling the world using geometric transformations (Lie pseudogroups). They demonstrate that for a neural system to track the world accurately, it must mirror these external symmetries internally (equivariance). This constraint forces the agent's neural dynamics onto efficient, low-dimensional manifolds, providing a geometric explanation for why deep learning works ("the blessing of compositionality") and suggesting a predictive coding model where layers process unresolved residual transformations.

2025 – The Algorithmic Regulator (arXiv) · Entropy · Zenodo

Reinterprets the classic Good Regulator Theorem through the lens of Algorithmic Information Theory, modeling agents and environments as interacting Turing machines. The author proves that a successful regulator acts as a compressor that reduces the Kolmogorov complexity of the world’s output, thereby minimizing the algorithmic cost of survival. This mathematical framework demonstrates that effective regulation requires high mutual algorithmic information, confirming that agents must structurally mirror the environments they seek to control. Ultimately, the paper bridges control theory and the Free Energy Principle by defining intelligence as the capacity to model and compress environmental data

2026 – Pattern, Persist! (Perspective Paper) (Zenodo) · Preprints.org

A substrate-independent account of agency: an algorithmic agent is a persistent pattern that regulates its own bounded code through a thin, thermodynamically costly boundary, built from a Modeling Engine, a scalar Objective Function, and a Planning Engine. Derives the ME/OF/PE structure from algorithmic persistence via the Algorithmic Regulator Theorem, prices regulation with a Landauer cost, and reframes the free-energy principle and alignment as an objective-distribution problem.

2026 – When Patterns Persist: Reach, Regulation, and Death in the Game of Life (Zenodo)

Uses Conway's Game of Life as a fully computable laboratory for the KT account of persistence (companion to Pattern, Persist!). Shows that persistence is ensemble-relative through a measurable reach set—holding identity and region fixed, an evolved local rule lifts reach from 0.000 (a passive block) to 0.892—and that the effective regulator compresses to a single minimal threshold rule: reach is set by the program, not the substrate.

2026 – From "More Is Different" to Algorithmic Emergence: Regularity, Compression, and the Limits of Discovery (Zenodo) · Preprints.org · Code and examples · accepted in Entropy (October 2026)

Studies why knowing microscopic laws does not guarantee a short description of a retained history, a terminating method that finds one whenever it exists, or a uniformly near-optimal code. Defines algorithmic emergence through an observer's acquisition of a reusable compressive model, with implementation cost and subsequent coding gains counted. The public companion provides glider and cellular-automaton examples with a single-command numerical verifier.

2026 – Telehomeostasis: Nicotine Parasitic Manipulation (Zenodo)

Casts the tobacco plant's nicotine as a telehomeostatic manipulation factor in the KT sense: a single alkaloid that sustains the plant's persistence by remotely rewriting primate decision-making, achieving a "triple lock" on the agent's Objective Function, Modeling Engine, and Planning Engine. Places nicotine on a continuum with classic parasitic manipulators (Toxoplasma, Ophiocordyceps) and traces the same persistence program up through trade, plantation, and lobbying scales.

2026 – A Lean 4 Formalization of Kolmogorov Theory (KT-LEAN) (Zenodo)

Builds KTAIT, a Lean 4 + Mathlib formalization that machine-checks that the KT corollaries follow from an explicit AIT axiom layer, with the KT ontology typed so structural errors (e.g. comparing a whole pattern to its own part) cannot silently compile. Classical AIT results are taken as a clearly delimited axiom layer; every KT corollary is then proved with no sorry, and a toy model witnesses that the axiom layer is jointly satisfiable. (Collaboration open.)

2026 – Algorithmic Experiential Structural Platonism: The Philosophical Stance of Kolmogorov Theory (Zenodo)

Sets out KT's philosophical stance — Algorithmic Experiential Structural Platonism (KT-ESP): experience is taken as ontologically primitive, with mathematics as the structural aspect of that same base. Worlds are structured patterns on pure experience; agents are persistent, model-running programs with modeling, objective, and planning (M,O,P) modules whose structured experience carries agent-level valence.

2026 – From Structured Experience to Algorithmic Agency (Zenodo)

Reads Kolmogorov Theory as the latest station of one long argument about persistent form — from Pythagoras and Plato, through Aristotle's entelechy and Kant, to Turing and Kolmogorov — tracing the path from structured experience to algorithmic agency.

2026 – Formas persistentes: de Pitágoras a la Teoría de Kolmogorov (Zenodo)

(In Spanish.) A structured framework for understanding mind, agency, and experience through algorithmic information theory, tracing the philosophical lineage from Pythagoras and Aristotle through Kant and Turing to Kolmogorov (KT-ESP).

2026 – The Good Algorithmic Regulator Theorem: Model It, Transmit It, or Leave It in the World (Zenodo) · Preprints.org · under review at Entropy

Grounds the Algorithmic Regulator Theorem in a conservation statement: the complexity gap between the unregulated and the regulated world must be paid from four ledgers — model content shared by world and regulator, the realized action transcript, retained regulator memory, or a record left hidden in the world. "Every good regulator is a model" becomes one corner of a balance: a regulator can model it, transmit it, or leave it in the world.

2026 – What Flows When Information Is Conserved? Algorithmic Localization, Materialization, and Persistence (Zenodo)

Closed computable reversible dynamics preserve the Kolmogorov complexity of a complete finite state up to a coding constant, while the description lengths of its parts can change. Introduces localization coordinates (the complexity private to each part and the mutual algorithmic information between them, summing to the joint complexity), separates profile-level dependence from a materialized common description that is recoverable from a subsystem, and shows that recurrent recoverability of an identity description lower-bounds persistence across time. The paper stops at this kinematic boundary; the regulation and persistence companions add the directed ledger and the agency synthesis.

2026 – Pattern, Persist! Algorithmic Persistence, Telehomeostatic Closure, and the Graded Architecture of Agency (Zenodo)

Review article (with Francesca Castaldo) on the persistence-first account of agency: an observer identifies a pattern by the continued reuse of a compressed description, and a bounded pattern that stays identifiable must keep identity-relevant novelty from accumulating without bound. The Algorithmic Persistence Balance tracks that novelty across later self-code, model update, retained state, action, and the record left in the world; a bounded self-code cannot also be an indefinitely growing memory; a constructive counterexample shows that persistence need not produce a positive ART complexity gap. Telehomeostasis names the organization that closes these operations onto the pattern's own continuation, and agency is graded by mode, reach, model depth, explicitness, and internalization.

2026 – From Kolmogorov to Free Energy: Data Compression as a Common Problem for AIT, MDL, Bayes, and the FEP (Zenodo)

Organizes algorithmic information theory, minimum description length, Bayesian inference, and variational free energy around one question: how to construct a compressor for the observed data. AIT asks for the shortest program in a universal class; MDL restricts the admissible programs and selects by model-plus-residual codelength; Bayes replaces hard selection by a mixture of probabilistic compressors; variational free energy replaces exact mixture inference by optimization over a tractable distribution. With the latent variable indexing candidate compressors, a point-mass posterior recovers two-part MDL, the exact posterior recovers the Bayesian mixture code, and a restricted posterior gives its variational approximation.

2026 – The algorithmic agent: mathematical foundations (in prep)

Develops rigorous definitions for algorithmic agents grounded in Turing‑machine pairs and AIT. Analyzes computational degeneracy and argues that high‑level program structure must manifest in observable dynamics; discusses identification of agent modules.