We propose a dual‑tier fractal‑recursive framework that unifies social homeostasis and individual consciousness under a common mathematical and empirical basis. The Social FPOM models collective regulation through recursive feedback, oscillatory synchrony, and nonlinear phase transitions, enabling falsifiable predictions about social stability. Complementarily, the Detailed Consciousness FBCM provides a biologically grounded model of recursive cognition through coupled differential equations, mapping higher‑order (Reflective Manager) and lower‑order (Probabilistic Default) processes onto measurable neural dynamics. Both formulations share core metrics—multiscale entropy, Hurst exponent, box‑counting fractal dimension—and offer pathways for empirical validation.

Consciousness and social homeostasis are phenomena that emerge from complex, self‑organizing systems. Drawing inspiration from philosophical traditions (phenomenology, process philosophy, enactivism) and leveraging advances in fractal geometry and nonlinear dynamics, our framework proposes that both individual cognition and collective regulation arise from nested, recursive feedback loops. The original Fractal‑Based Consciousness Model (FBCM) laid the groundwork for understanding consciousness as a dynamic fractal process. Here, we extend this vision to encompass social systems, offering a dual‑tier model with two complementary formulations:

1. Social FPOM: A simplified, scalable model for social integration and homeostasis, ideal for applications such as harmonized contributions in socio‑economic systems.
2. Detailed Consciousness FBCM: A full dynamic model of individual cognition that utilizes coupled differential equations to capture the interplay between reflective (RM) and automatic (PD) processes.

By uniting these formulations, we show how fractal‑recursive dynamics underlie both neural and social systems, providing measurable and falsifiable predictions.

Social systems function through distributed feedback and recursive communication. Similar to neural oscillations, synchronized collective behavior (e.g., coordinated public discourse) stabilizes the system. When external perturbations (e.g., economic shocks or political unrest) disrupt this balance, corrective feedback via leadership and policy interventions restores homeostasis. Social interactions display self‑similar, fractal patterns that can be quantified using established metrics.

The simplified Social FPOM is expressed as:

$$ C_s(t) = \Bigl[S_{MSE}(t) \cdot PLV(t) \cdot \Bigl(1 + \alpha, C_s(t-\tau)\Bigr)\Bigr]^{H(t)} + \beta_L, L(t) + \sigma,\xi(t) $$

Where:

• $(C_s(t)$ is the overall “social consciousness” or homeostatic state at time (t).
• $(S_{MSE}(t)$ represents the multiscale entropy of socio‑economic data (e.g., diversity of opinions, economic indicators).
• $PLV(t)$ denotes the phase‑locking value, reflecting synchrony in social communications and public engagement.
• $(\alpha$ and $(\tau$ capture the strength and delay of feedback within the social network (e.g., the lag between policy implementation and public response).
• $(H(t)$ is the Hurst exponent, indicating the predictability and long‑range correlations in social dynamics.
• $(\beta_L, L(t)$ models sudden “Lévy jumps” in social behavior—rapid shifts triggered by crises or major events.
• $(\sigma,\xi(t)$ represents random fluctuations or noise in the system.

This formulation yields several testable hypotheses:

• Feedback-Induced Stability: Effective policy interventions (high $\alpha)$ should lead to a rise in $H$ toward 0.7, reflecting enhanced stability.
• Crisis-Induced Fractal Disruption: During acute social stress, the box‑counting fractal dimension (inferred from variability in $C_s(t)$ should spike, indicating a phase transition.
• Restorative Synchronization: Coordinated public messaging and harmonized contributions should increase PLV, correlating with improved social stability.
• Delayed Feedback Effects: Shorter feedback delays $\tau$ correlate with more rapid restoration of homeostasis, measurable via cross‑correlation analyses of policy and public response data.

These predictions can be validated using time‑series analyses of social media data, economic indicators, and public sentiment surveys.

The Detailed Consciousness FBCM models individual cognition as a recursive, self‑organizing process. Consciousness emerges from the dynamic interplay between higher‑order reflective processes (Reflective Manager, RM) and lower‑order automatic processes (Probabilistic Default, PD). This interaction is characterized by continuous‑time dynamics, nonlinear feedback, and fractal self‑similarity. The model builds on philosophical and empirical insights, providing a framework that yields measurable predictions via EEG/fMRI.

$$ \frac{dZ}{dt} = \gamma_{RM},\tanh\bigl(Z^2 + \mu M + A\bigr) + \gamma_{AP},Z + \lambda E + \beta_L L + \sigma\xi $$

• $(Z = R + iA)$:** Combined cognitive state (with $(R)$ as RM and $(A)$ as PD).
• $(\gamma_{RM})$, $(\gamma_{AP})$:** Gain parameters for RM and PD, respectively.
• $(\lambda E)$:** External perturbations from sensory or social inputs.
• $(\beta_L L)$:** Lévy‑distributed jumps capturing sudden cognitive shifts.
• $(\sigma\xi)$:** Stochastic noise representing random neural fluctuations.

To capture the distinct contributions of RM and PD, we further decompose the system:

$$ \frac{dR}{dt} = \gamma_{RM},\tanh\bigl(R^2 + \mu M + \eta A\bigr) + \beta_L L + \lambda E + \sigma \xi $$

$$ \frac{dA}{dt} = \gamma_{AP},A + \alpha_M M + \tanh(\Delta A) - \eta R $$

These equations model the bidirectional feedback between reflective and automatic processes, ensuring that the dynamics of each component influence and modulate the other. This coupling is critical for generating fractal properties (e.g., specific Hurst exponent values) that are observable in neural data.

The Consciousness FBCM yields explicit hypotheses that can be tested through neurophysiological experiments:

• RM‑Dominance vs. PD‑Dominance: RM‑dominated states should exhibit higher Hurst exponent values (around 0.7), whereas PD‑dominated states should show lower values (around 0.5). This can be verified with EEG during tasks requiring reflective versus automatic processing.
• Phase Transitions: Sudden shifts in cognitive state (e.g., during insight or trauma) will be accompanied by marked increases in fractal dimension $(D_B)$, observable via real‑time EEG fractal analysis.
• Feedback Delays: The time lag $(\tau)$ between RM and PD interactions should correlate with the rapidity of cognitive adjustments, measurable through ERP latency studies.

• Data Sources: Social media sentiment, economic time series, public opinion surveys.
• Experimental Approach: Analyze changes in fractal metrics (e.g., $(H)$ and inferred $(D_B))$ before and after major policy interventions or during crisis events.
• Expected Outcome: Increased synchrony (higher PLV) and elevated $(H)$ in response to effective policy feedback; sudden spikes in fractal measures during crises.

• Data Sources: EEG, fMRI, and ERP recordings during cognitive tasks.
• Experimental Approach: Use multiscale entropy and fractal analysis to differentiate between RM‑ and PD‑dominated states.
• Expected Outcome: Distinct neural signatures (e.g., differences in $(H)$ and $(D_B))$ corresponding to reflective versus automatic processing, along with observable Lévy‑style jumps during cognitive transitions.

• Social Policy: Guide the design of interventions (e.g., Universal Basic Income) by predicting the impact on collective stability and adaptive capacity.
• Neuropsychiatry: Inform therapeutic strategies for conditions like PTSD or depression by restoring fractal dynamics through targeted interventions (e.g., neurofeedback).
• AI and Cognitive Architectures: Inspire the development of systems that balance exploration (reflective processing) and exploitation (default heuristics) via fractal‑recursive algorithms.

This dual‑tier white paper demonstrates that fractal‑recursive dynamics provide a robust framework for both social and individual systems. The Social FPOM offers a simplified yet empirically grounded approach to modeling social homeostasis, with clear, falsifiable predictions that can be tested using existing socio‑economic data. In parallel, the Detailed Consciousness FBCM offers a comprehensive model of neural consciousness, capturing the interplay of reflective and automatic processes with measurable fractal signatures.

By integrating these perspectives, our framework bridges the gap between collective regulation and individual cognition, offering new insights into how complex systems self‑organize and adapt in both social and biological contexts.

(Please refer to the full reference list provided in the original FBCM paper for detailed bibliographic information.)