The Topology of REM Mentation (Dreams): Attractors, Affective Projections, and the Dual-Regime Architecture of Consciousness

This monograph presents a unified mathematical framework for analyzing dreaming (REM mentation), comprising 21 components with formal definitions, propositions, proofs, and seven computational toy models. The framework treats the brain as a generative system whose output during sleep exhibits structural properties like local coherence with global inconsistency, lazy specification of detail, drifting relational structure, virtual complexity, affective saturation, and near-total content loss at termination. The relationship between model and actual dreaming is analogous to that between the Ising model and ferromagnetism—capturing structural regularities without claiming ontological identity. Components include a dual-regime model of consciousness, topological attractor theory, affective projection, dream amnesia formalization, and correspondence with large language model idle generation.

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Abstract

Author: Boris KrigerAffiliations: Information Physics Institute, Gosport, Hampshire, UK; Institute of Integrative and Interdisciplinary Research, Toronto, CanadaORCID: 0009-0001-0034-2903Date: February 2026Pages: 125License: CC BY 4.0 Description This monograph presents a unified mathematical framework for the formal analysis of dreaming (REM mentation), comprising twenty-one interlocking components developed across 125 pages with full formal definitions, propositions, proofs, seven computational toy models, and a 155-term glossary. The framework treats the brain as a generative system whose output—when deprived of external sensory input during sleep—exhibits a suite of structural properties recognizable as dreamlike: local coherence with global inconsistency, lazy specification of detail, drifting relational structure, virtual complexity, affective saturation, and near-total loss of content at termination. The relationship between the model and actual dreaming is analogous to the relationship between the Ising model and ferromagnetism: the model captures structural regularities without claiming ontological identity with the target system. The 21 Components Dual-Regime Model of Consciousness — Waking and dreaming as distinct dynamical regimes in a continuous cognitive phase space, separated by bifurcation-like transitions. Topological Attractor Theory — Recurring dream spaces as stable attractors in the phase space of an internal world-model. Affective Projection — A continuous mapping from emotional states to spatial configurations experienced as dream environments. Logical vs. Affective Validation — The shift from spatiotemporal consistency-checking (waking) to emotional-identity coherence-checking (dreaming). Self-Model Dissolution — Predictive-processing account of identity boundary loosening during REM sleep. Inverted Information Filter — Dreaming preferentially amplifies content suppressed during waking. Neural Network Analogy — Structural parallel between dreaming and unsupervised recalibration in artificial neural networks (wake-sleep algorithm). Statistical Psychogeography — Proposal for empirical clustering of collective dream-space motifs across populations. Stochastic Crystallization — Dream onset as noise-driven attractor selection, with structural analogy to quantum measurement. Interrogative Collapse — Dream content exists in radical indeterminacy until internal cognitive acts force ad hoc specification; excessive interrogation destabilizes the dream. Virtual Complexity — The dissociation between compact generation (low Kolmogorov complexity), rich experience (high Shannon entropy), and moderate regularity (intermediate Gell-Mann effective complexity). Non-Topological Dream Space — Drifting relational structure modeled via pretopological spaces, relational graphs, and sheaf cohomology. Dream Amnesia — Formalization of encoding failure via noradrenergic suppression, MCH-neuron hippocampal inhibition, and prefrontal deactivation, with four experimental interventions proposed. Dream Atemporality — Variable subjective temporality modeled through content-dependent pseudo-Riemannian metrics (structural analogy with general relativity). Generative Prior & Agency Paradox — Why dreams preserve physical law despite the absence of external constraints; why the dreamer is simultaneously sole author and powerless spectator. Terminal Regime (Near-Death Experience) — Extension of the parameter space beyond dreaming to model NDE phenomenology as the mathematical limit of the framework. Reality Testing & Nested Dreams — Dream-reality indistinguishability and false awakenings as recursive confabulation; epistemic underdetermination from the inside. Negativity Bias & Psychic Impact — The inverted filter mechanism for dream negativity; affective leakage into waking mood; intervention pathways (imagery rehearsal therapy, lucid dreaming, pre-sleep priming). Prophetic Dreams & Symbolic Compression — Prophetic dreams as predictive processing without executive constraints; dream symbolism as culturally modulated compression under suppression. LLM Dreamlike States — Formal correspondence between biological dreaming and large language model idle generation; dreaming as inevitable idle computation in any sufficiently complex generative system; the overfitting-prevention hypothesis. Dream-Memory Boundary — Source monitoring failure as the mechanism by which dream episodes contaminate autobiographical memory; the shared-generator problem; the hypothesis that every memory that passes through a sleep cycle is, to some degree, a dream. Formal Apparatus The monograph employs tools from dynamical systems theory, stochastic differential equations, information theory (Kolmogorov, Shannon, Gell-Mann effective complexity), algebraic topology (sheaf cohomology over pretopological spaces), pseudo-Riemannian geometry, signal detection theory, and Boltzmann-form generative models. Each formal result is classified by epistemic status: Theorem (deductively valid), Modeling Assumption (formally stated empirical hypothesis), Structural Analogy (illuminating parallel), Empirical Conjecture (testable prediction), or Structural/Generative Property (mathematical fact about the model). Computational Toy Models (Appendices B–H) Seven concrete computational models demonstrate that the framework produces non-trivial quantitative outputs: Toy Model A — 3D dual-regime bifurcation with transcritical transition at λ_eff ≈ 0.43 Toy Model B — Affective projection (valence-arousal → enclosure-verticality) with anisotropy ratio 2.66 Toy Model C — Interrogative collapse Monte Carlo (N=50 features, 10,000 realizations): critical interrogation rate at R(t)/N ≈ 0.37 Toy Model D — Kramers crystallization in double-well potential: attractor selection probabilities within 8% of theoretical prediction Toy Model E — Virtual complexity computation confirming K̂ ≈ 180 ≪ Ĉ_eff ≈ 320 ≪ T·ĥ ≈ 2800 Toy Model F — Drifting relational graph (8 nodes, Ornstein-Uhlenbeck dynamics): topological consistency fails at t̄ ≈ 7 Toy Model G — Dream time dilation: 53% dilation over 5-minute episode with piecewise cognitive load Additional Features Dynamic Dream Map (Appendix I): Full-page visualization tracing a single dream episode through all 21 components simultaneously Complete Dependency Diagram: All 21 components with formal interdependencies 155-Term Glossary: Every mathematical, neuroscientific, and framework-specific term explained accessibly Epistemological framing: Explicit Ising-model-style disclaimer clarifying that the framework is a formal generative system, not an ontological claim about neural processes 80+ references spanning dynamical systems theory, cognitive neuroscience, sleep science, information theory, algebraic topology, and AI Keywords REM mentation, dream topology, cognitive phase space, attractor dynamics, affective projection, dual-regime consciousness, predictive processing, self-model dissolution, statistical psychogeography, unsupervised learning, stochastic attractors, crystallization dynamics, interrogative collapse, virtual complexity, Kolmogorov complexity, effective complexity, pretopological space, sheaf cohomology, dream amnesia, MCH neurons, dream atemporality, subjective spacetime metric, generative prior, ontological reframing, agency paradox, near-death experience, terminal regime, reality testing, nested dreams, negativity bias, threat simulation, affective leakage, prophetic dreams, symbolic compression, cultural modulation, large language models, hallucination, source monitoring, dream-memory boundary, false memory, epistemic contamination