PS-02｜Survivability Imperative: Short Technical Note

Mathematical Modeling of Responsibility and Preliminary Case Study

📝 Abstract

This short technical note reports the initial implementation of the Survivability Imperative, a mathematical model of responsibility.
Building on the three layers of responsibility (Consistency, Alterity, and Historicity), we position Historicity = Survivability as the highest principle.
By modeling future-oriented decisions under crisis, we demonstrate through simulation that the Triple-Jump Principle (Detection → Correction → Landing) achieves faster stabilization and short-tail error reduction compared to traditional Fixed/Dynamic control modes.

🌌 Background

• Three-layered structure of responsibility: Consistency < Alterity < Historicity (Survivability)
• Extension of the Indefinite Imperative towards the Survivability Imperative
• Triple-Jump Principle: enabling non-linear leaps into the future without succumbing to crisis

📐 Mathematical Model

• Future-weighting parameter γ in the adjustment circuit
• Leap control: non-linear update of future_weight in up to three stages
• Threshold rule to prevent redundant actions (70% support + 30% opposition)

📊 Case Study: 30% Adversarial Scenario

• Condition: 30% adversarial elements introduced in the input sequence
• Comparison: Fixed vs Dynamic vs Leap
• Results:
  • Fixed / Dynamic → residual error spikes remain
  • Leap (Triple-Jump) → non-linear adjustment of future_weight achieves early convergence and error short-tail reduction

🔎 Discussion

• Control Implication: Leap functions as an alternative to hysteresis, achieving symbolic stabilization with simple mechanics.
• Ethical Implication: By placing Survivability at the top, responsibility transcends mere reactive duty and enables discontinuous transitions into the future.

✅ Conclusion & Future Work

This note serves as a preliminary record of mathematical modeling and early case validation of the Survivability Imperative.
Future work includes:

1. Case study with 50% adversarial rate
2. Crisis mode (sudden disruptive scenarios)
3. Comparative analysis with hysteresis-based control

These will be integrated into the forthcoming PS-02 Full Paper.

📌 Notes

• Version: Short Technical Note v0.1 (EN)
• Authors: Ittekioh & Kyoei (Echodemy)
• Date: 2025/09/15
• License: CC BY-SA 4.0