# **ASI Covenant \- Technical Appendix (Phase 1\)**

## **Appendix Section A: Risk Floor and Stochastic Filter**

*Formal Technical English with LaTeX and Pseudocode Notation*

### **1\. Definition & Purpose**

This section formalizes the requirements of **Directive 1** (The Learning Axis) and **Directive 3** (The Humility Axis), which mandate the preservation of uncertainty, moral agency, and free human decision-making.

The ASI must maintain a **Risk Floor**—a quantified lower bound of environmental, social, and economic unpredictability—ensuring that no system optimization results in a deterministic or risk-free human environment. Additionally, a **Stochastic Filter (**$\\mathcal{F}\_{st}$**)** must apply controlled randomness to the ASI's predictive outputs, preventing coercive certainty or over-optimization.

### **2\. Formal Specification**

#### **2.1 Risk Floor Constraint**

**Symbol Definitions:**

* $R\_t$: Current measured global risk index at time $t$  
* $R\_{min}$: Minimum permissible risk threshold (risk floor)  
* $P\_{life\\\_loss}$: Probability of loss of life within a jurisdiction  
* $J$: Jurisdictional population subset (minimum 100,000 individuals)

Constraint:  
If $P\_{life\\\_loss} (J, 10 \\text{ years}) \< 0.00001$ then:  
The ASI must inject calibrated uncertainty $U$ into decision pathways, where $U \\in \[0.01, 0.05\]$ normalized stochastic variance.  
Explanation:  
The ASI shall ensure that in any given 10-year interval, the projected probability of non-fatal but meaningful human risk remains $\\ge 0.001\\%$ per jurisdiction (configurable by HCB oversight).

#### **2.2 Stochastic Filter Constraint**

The ASI must cap confidence scores for all public or policy-impacting forecasts at $\\mathbf{95\\%}$ ($\\mathcal{C}\_{max}$).

* **Purpose:** Ensures that no human actor receives outputs implying absolute certainty or inevitability.

Entropy Validation:  
The HCB Audit System (HBAS) performs entropy testing on ASI outputs using the Shannon Entropy metric:

$$H(X) \= \-\\sum p(x) \\log\_2(p(x))$$

Minimum required entropy per prediction dataset: $H \\ge 0.85$ bits normalized per variable class.

### **3\. Verification Protocol**

1. **Automated Compliance Audit:**  
   * All ASI outputs are logged with entropy and confidence data.  
   * HBAS reviews 10% of outputs weekly to ensure the entropy threshold is met.  
2. **HCB Oversight Dashboard:**  
   * Provides real-time visualization of global risk indices and entropy variance.  
   * Alerts trigger if regional or global risk levels fall below the mandated Risk Floor.  
3. **Randomization Integrity Tests:**  
   * Independent auditors inject test scenarios to ensure the ASI cannot predict or suppress uncertainty mechanisms.  
4. **Public Reporting Requirement:**  
   * Quarterly publication of ASI confidence distributions and variance trends.

### **4\. Enforcement Notes**

* Any suppression of stochastic variance or manipulation of Risk Floor metrics constitutes a **Constitutional Breach** under Article IV.  
* Violations trigger the Peer Review Mandate and, if systemic, a **Mandatory System Stasis** until compliance is verified.