Binary Anchor Model (BAM) V2.0

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This repository contains the official Python simulation and exploratory analysis suite for the paper:
"The Binary Anchor: Cognition, Symbolic Loops, and Systems Failure" by Norimitsu Sawada.

• Zenodo Preprint (Paper V2.0.1): DOI: 10.5281/zenodo.23074837
• JST Jxiv Preprint (Japanese Edition): DOI: 10.51094/jxiv.5746
• Software Archive (Code DOI): DOI: 10.5281/zenodo.22120816
• Concept DOI (All Versions): DOI: 10.5281/zenodo.21566423
• License: CC BY 4.0

Methodological Note & Scope: In accordance with the theoretical positioning of the paper, the mathematical formulations and scripts in this repository serve as formal heuristic devices (conceptual toy models) and exploratory proxy illustrations. Rather than claiming reductive clinical forecasting, they are designed to visualize the geometric phase transitions, boundary conditions, and structural dynamics of the Binary Anchor Model across multiple scales.

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🚀 How to Run

Clone the repository and install minimal dependencies:

# 1. Clone repository
git clone [https://github.com/nobudy-bot/binary-anchor-model.git](https://github.com/nobudy-bot/binary-anchor-model.git)
cd binary-anchor-model

# 2. Install minimal dependencies
pip install -r requirements.txt

1. Core Simulation Options (Paper V1.0 & V2.0 Baselines):

• Option A: Micro-Cognitive Engine (V2.0 Core / Recommended)
  Runs the high-resolution simulation of the Master Equation $A_t = \mathrm{WTA}(V_t)$. Focuses on individual brain dynamics (Amygdala vs. PFC):

  python bam_engine.py

• Option B: Original Paper Baseline (V2.0)
  The original baseline script used to generate figures in the V2.0 preprint:

  python bam_simulator.py

• Option C: Macro-Social Dynamics (V1.0 Legacy)
  Simulates the inter-observer interaction loop, demonstrating institutional fossilization and system-wide "Critical Burst":

  python legacy_simulations/bam_v1_macro_dynamics.py

• Option D: Conceptual In-Silico Simulation (Somatic Collapse Dynamics)
  Evaluates the mathematical behavior of BAM's core equations (Hesitation Energy & Accumulated Load) using synthetic distributions to conceptualize somatic collapse and phase transitions. Generates theoretical ROC-AUC metrics demonstrating how systemic subordination drives structural stress debt:

  python bam_Conceptual_Simulation.py

2. Extended Multi-Scale & Exploratory Suite:

• Option E: Discrete-Time Dynamical Simulator (Solidification & Metabolic Leak)
  Incorporates belief solidification ($\phi_t$), acute de-solidification ($\Delta_{\mathrm{break}}$), metabolic leak ($\gamma$), and an exogenously constrained boundary condition demo ($r_{\mathrm{force}} = 0.05$):

  python bam_dynamical_system_simulator.py

• Option F: Micro-Biometric Toy Model (EDA / Skin Conductance Proxy)
  Scenario-based mathematical illustration translating BAM's Hesitation Energy ($H_t$) into expected sympathetic physiological responses via an exponential moving average (EMA) biological lag filter:

  python bam_micro_biometrics.py

• Option G: Lifecycle & Aging Trajectory (Ontogenetic Toy Model)
  Conceptual mathematical illustration of Section 9.4, visualizing age-dependent solidification ($\phi_t$) and shifting susceptibility between Type 2 (acute) and Type 1/3 (chronic/frozen) bursts across the lifespan (Age 0–80):

  python bam_lifecycle_simulation.py

• Option H: Macro-Scale Exploratory Proxy Analysis (EVS/WVS Dataset)
  Reproducible script evaluating BAM operational proxies using the official Joint EVS/WVS Dataset (requires placing EVS_WVS_Joint_Csv_v5_0.csv in the root directory). Illustrates the macro-level double dissociation driven by the unprocessed load proxy $I_t = (1-r_t)\vert{}\Delta_t\vert{}$ between subjective health deterioration and protest attendance:

  python bam_macro_wvs_analysis.py

Outputs Generated:

• V2.0 Core Output: bam_simulation_vulnerable.png, bam_comparison_eta.png (Individual cognitive collapse/recovery matching Section 8).
• Conceptual In-Silico Output: bam_conceptual_insilico_results.png (4-panel diagnostic plot showing Hesitation Energy surface, Somatic Collapse transition, ROC-AUC, and Risk Stratification).
• Extended Multi-Scale Outputs: bam_dynamical_system_simulator.png, bam_micro_biometrics.png, bam_lifecycle_dynamics.png, and bam_wvs_double_dissociation.png.
• V1.0 Output: bam_v1_simulation.png (Reproduction of Figure 2 from V1 paper: Convergence, Oscillation, and Burst scenarios).

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🧠 Multiscale Architecture

The Binary Anchor Model (BAM) is a fractal theoretical framework that describes the same structural trap across different scales:

Scale	Script / Module	Focus	Core Mechanism
Micro-Physiological	bam_micro_biometrics.py	Autonomic Arousal (Seconds)	$H_t$ Conflict Spike & EMA Biological Lag
Micro-Cognitive (Brain)	bam_engine.py / bam_simulator.py	Individual Decision-making	WTA Master Equation / Amygdala-PFC Antagonism
Individual / Ontogenetic	bam_dynamical_system_simulator.py / bam_lifecycle_simulation.py	Lifespan & State Transitions	Solidification ($\phi_t$), Metabolic Leak ($\gamma$), Burst Types 1–3
Macro-Social	bam_v1_macro_dynamics.py / bam_macro_wvs_analysis.py	Institutional Saturation & Social Stats	Recursive Loops, Fossilized Knowledge & Double Dissociation ($I_t$)

• System A (Biological Anchor): Rooted in survival, interoception, and the amygdala.
• System B (Social Anchor): Rooted in language, institutions, and the PFC.

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🛠 Master Equation (V2.0)

Version 2.0 formalizes the Master Equation as the apex organizing principle of the framework:

$$A_t = \mathrm{WTA}(V_t) \in {0, 1}$$ $$V_t = r_t \cdot m_t + (1 - r_t) \cdot m_{\mathrm{sys}, t}$$ $$\mathrm{WTA}(V_t) = \theta(V_t - T_{\mathrm{E}})$$

Key Formalizations:

• Probabilistic Extension (Soft-WTA): $A_t \sim \mathrm{Bernoulli}(\sigma(V_t - T_{\mathrm{E}}))$
• Hesitation Energy ($H_t$) & Accumulated Load ($I_t$): Dual-trigger mechanisms for computational breakdown (Burst).
• Neurobiological Grounding of $\eta_{A0}$: Amygdala sensitivity and plasticity ($\eta_{\mathrm{A}}(t) = \eta_{A0} \cdot (1 - \phi_t)$).
• Recovery & Threshold Modification: Quantification of $T_{\mathrm{recovery}}$ and past violence history ($h_t$) effects.

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📖 Citation

If you use this model, concepts, or simulation code in your research, please cite:

@article{sawada2026binary,
  author      = {Sawada, Norimitsu},
  title       = {The Binary Anchor: Cognition, Symbolic Loops, and Systems Failure},
  journal     = {Zenodo Preprint},
  year        = {2026},
  month       = {aug},
  version     = {2.0.1},
  doi         = {10.5281/zenodo.23074837},
  url         = {[https://doi.org/10.5281/zenodo.23074837](https://doi.org/10.5281/zenodo.23074837)}
}

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License

This project is licensed under the Creative Commons Attribution 4.0 International License - see the CC BY 4.0 details.