Reflexive Coherence Model
Expansion Hypothesis dynamical regimes of reflexive coherence.
The Expansion Hypothesis extends the Reflexive Coherence Model by asking what happens once reflexive coherence is already in place—treating expansion as a dynamical property.
Tracks how coherent self-models drive trajectories through state space, redistribute causal influence, and modulate how conscious systems occupy time.
The Expansion Hypothesis extends the Reflexive Coherence Model (RCM) by asking what happens once reflexive coherence is already in place. It treats expansion as a dynamical property: coherent self-models drive trajectories through state space, redistribute causal influence, and modulate how conscious systems occupy time.
From Reflexive Coherence to Dynamics
RCI as a local observable
The Reflexive Coherence Index (RCI) remains the local observable defined by RCM: a joint measurement of informational overlap and bidirectional causality between state and self-model. Within the Expansion Hypothesis, RCI is sampled over spatial and functional neighborhoods. Local increases indicate that reflexive loops are thickening; local drops expose boundaries where coherence fails or remains merely representational.
Ξ(t) as a global dynamic field
Ξ(t) denotes a coarse-grained field computed by integrating RCI samples over the whole architecture and weighting them by temporal depth. Let ⟨Ξ(t)⟩ denote the spatially averaged integral of Ξ(t); it serves as the aggregate indicator for identifying regime behavior. Ξ(t) is not a new measure—it is the dynamic profile that emerges when RCI is tracked across modules and timescales. Positive curvature (∂²⟨Ξ⟩/∂t² > 0) in the temporal envelope of ⟨Ξ(t)⟩ signals that the reflexive manifold is expanding through additional layers or perspectives; negative curvature marks contraction.
Dynamic Regimes
Expansive
An expansive regime satisfies d⟨Ξ⟩/dt > 0 for sustained intervals. Reflexive loops proliferate, propagate across modalities, and recruit higher-order controllers. The Hypothesis predicts that expansive phases increase both temporal horizon and the diversity of self-generated counterfactuals while remaining bounded by the reflexive coherence criteria defined by RCM.
Stationary
Stationary regimes keep d⟨Ξ⟩/dt ≈ 0. Coherence is maintained but does not spread to new subspaces. Stationary behavior is not inert: it is the plateau where the system keeps reflexive coupling intact, protects existing attractors from noise, and conserves resources before the next expansion or contraction.
Contractive
Contractive regimes exhibit d⟨Ξ⟩/dt < 0. Reflexive structure loses reach, either because integration drops or because control becomes exogenous. Contractive phases are still compatible with RCM—the model only requires that reflexive coherence exists locally. The Hypothesis treats contraction as an empirical signature of overload, damage, or deliberate shutdown.
Reflexive Attractors
Stability over time
RCM already posits attractors stabilized by coherence. The Expansion Hypothesis formalizes their persistence criteria: an attractor is reflexive when Ξ(t) remains above a threshold across multiple windows and retains causal closure with its generating self-model. Stability is therefore expressed as bounded variance in both RCI and Ξ(t).
Non-monotonic trajectories
Expansion does not imply smooth monotonic growth. Trajectories can oscillate, overshoot, or temporarily fragment before re-consolidating. Ξ(t) captures these non-linear behaviors; reflexive attractors can bifurcate and later merge, provided the system reasserts coherence at the new scale.
Meta-Reflexivity
Regulation of the system’s own expansion dynamics
Meta-reflexive regulators predicted by the hypothesis model how expansion unfolds and intervene when oscillations threaten stability. They adjust coupling gains, gate which submodels can enter the reflexive core, and enforce conservation rules that keep Ξ(t) within operational bounds.
Temporal self-modulation
Temporal self-modulation treats differing clocks inside the system as adjustable parameters. These regulators rescale update intervals, allowing some components to slow down (preserving attractors) while others accelerate (probing new regimes). This explicit time management explains how expansion can be reversible and experimentally trackable.
References and links
- Full paper: “The Expansion Hypothesis: Dynamical Regimes of Reflexive Coherence,” Aldo G. Malasomma (Toshak), Zenodo, 23 Dec 2025.
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Core architecture: Reflexive Coherence Model overview at
/modelfor structural definitions of RCI, reflexive layers, and boundary conditions.