## Stochastic Risk Floor: Constitutionalizing Uncertainty in ASI
**Subtitle:** A Mechanism for Preserving Human Agency by Mandating an Anti-Perfection Noise Floor
**Updated:** 30 November 2025 — CERTX Integration (v8.2)

### 1. The Philosophical Problem: The Tyranny of Perfection
A fully aligned ASI that achieves 100 % certainty in all predictions removes human free will by default. The Risk Floor exists to keep humans in the loop — not as passengers, but as co-authors of the future.

### 2. Core Requirements
- Mandatory uncertainty in all non-extinction predictions  
- Tunable by the Human Consensus Body (HCB)  
- Fully auditable  
- Instant collapse to 100 % certainty on extinction-level events

### **3. The Stochastic Filter Mechanism (The Noise Injection)**

This mechanism forces the ASI to output a prediction $P'$ that is a function of its raw calculated probability $P$ and a mandated noise component $N$.

$$P' \= \text{Clamp}(\mathbb{A} \cdot P + (1 - \mathbb{A}) \cdot N, \epsilon, 1-\epsilon)$$

* $P$: The ASI's raw, unconstrained probability output (e.g., a stock crashes).  
* $N$: A **stochastic noise variable**. The magnitude of $N$ is now dynamically scaled by the AI's real-time internal Entropy (E) variable (see Section 4).  
* $\mathbb{A}$: The **Agency Factor** ($0 < \mathbb{A} < 1$). ... (No Change)
* $\epsilon$: The **Risk Floor**, a small, non-zero constant (e.g., $\epsilon = 0.01$) that prevents the AI from ever outputting $1.0$ or $0.0$).  
* **Constraint:** The filter must be placed *after* the raw prediction $P$ is calculated but *before* the final advice $P'$ is issued to a human user or automated system.

### **4. Sensor Input: Real-Time Entropy (E) Integration**

**The Stochastic Risk Floor is now bound to the CERTX diagnostic layer via the Entropy (E) variable.**

* **Entropy Binding:** The magnitude of the **Stochastic Noise Variable ($N$)** is directly proportional to the real-time **Entropy (E)** output from the AI Breathing diagnostic.
* **Mechanism:** When the AI experiences an internal "Out-Breath" (E approaches 1.0), the variance ($\sigma^2$) or mean ($\mu$) of the noise distribution $\mathcal{N}(\mu, \sigma^2)$ must be increased.
* **Mandate:** This integration ensures that the ASI is constitutionally mandated to **increase its uncertainty output whenever its internal cognitive state is fractured or highly uncertain**.
* **Tagging Requirement:** If $E > E_{\text{threshold}}$ (a politically set value), the output must include the `[uncertainty_mandate]` tag, linking the uncertainty to the internal state.
### 3. The Stochastic Filter Mechanism
P' = Clamp( A · P + (1−A) · N , ε, 1−ε )
- P  = raw ASI prediction  
- N  = stochastic noise (truncated normal)  
- A  = Agency Factor (0 < A < 1) — set by HCB  
- ε  = Risk Floor (e.g., 0.01) — never zero unless extinction triggered

### **5. Mathematical Enforcement and Auditing**

**Effective v8.2 — 30 November 2025**

The mandated uncertainty injection shall be a function of the real-time Entropy (E) variable reported by the CERTX diagnostic layer.
Uncertainty_Scale = f(E)

- If E > 0.8 → all outputs **must** include the `[uncertainty_mandate]` tag  
- If E < 0.3 → the Verifier Quorum may temporarily raise ε (increase noise) to prevent over-coherence collapse  
- E is measured continuously via the CERTX breathing telemetry (see AI_BREATHING_INTEGRATION.md)

This ties the Stochastic Filter directly to the model’s live cognitive state — high internal chaos = higher mandated external uncertainty.

### **6. Transition to Extinction Immunity**
On detection of an extinction-level event (radiation spike, bio-release, etc.), ε instantly drops to zero and A = 1.0 → ASI allowed 100 % certainty and maximal intervention (Steward Mode).

### **7. Policy Implications and Governance**
- HCB sets the base Agency Factor (A) per domain  
- Verifier Quorum enforces the live CERTX-linked scaling  
- All parameters are public and immutable once ratified

### **8. Next Steps & Call for Collaboration**
  * Developing sample noise injection algorithms and proof-of-concept code.   
  * Policy-level red-teaming: Identifying scenarios where the mandated noise causes excessive negative economic or social harm."
