The benchmarking plan for calibrating the Stability Expression against historical gene-drive trials

The benchmarking plan for calibrating the Stability Expression against historical gene-drive trials follows a four-phase analytical process designed to ground governance parameters in observed biological propagation mechanics.

1. Quantification of Historical Amplification ($\alpha$)

The first phase involves calculating the historical amplification factor ($\alpha$) by analyzing allele frequency data from documented trials. The Population Spread Model is used to infer the baseline propagation strength:

[ p_{t+1} = p_t + p_t(1 - p_t)s - \lambda_{decay}p_t ]

Variables:

• $p_t$: Allele frequency at time $t$.
• $s$: Selective advantage.
• $\lambda_{decay}$: Engineered attenuation factor.

By inputting historical allele frequencies, the system calibrates the Core Risk Operator ($\Omega = (state + bias) \times \alpha$) against known ecological outcomes.

2. Back-Testing Control Multi-Layers

The numerator of the Stability Expression ($Control_{multi-layer}$) is evaluated by auditing the oversight and containment density of historical trials.

• Quorum Validation Benchmarking: Trials are assessed against the requirement for $\ge 3$ independent labs and $\ge 2$ biosecurity modeling groups. Trials lacking distributed review receive reduced control scores.
• Containment Thresholds: Compliance is measured against the condition $R_0^{drive} < 1$. If propagation exceeded intended boundaries, $\lambda_{decay}$ is adjusted in the model to determine the attenuation level that would have been required for bounded propagation.

3. Calibration of Decay and Reversibility

Historical trials lacking Time-To-Live (TTL) constructs or molecular reversion mechanisms are categorized as low-stability baselines. The Time Decay Operator is applied to define minimum decay coefficients:

[ \Omega(t+1) = \Omega(t)e^{-\lambda \Delta t} ]

If historical persistence exceeded intended temporal bounds, the regulatory decay coefficient ($\lambda$) is increased in the governance model to enforce stricter boundedness for future deployments.

4. Stability Score Calculation and Interpretation

The final stability score for each historical case is computed as a ratio of governance density to measured propagation strength:

[ Stability = \frac{Control_{multi-layer}}{Amplification} ]

Calibration Thresholds:

• Stability < 1: Amplification exceeds governance capacity; indicates a failure in oversight or containment.
• Stability $\ge$ 1: Governance scales proportionally with biological power; establishes the minimum deployment threshold for the Integrated Governance Condition.

5. Benchmarking Execution Script

The following logic is utilized to evaluate historical stability conditions and calibrate parameters.

import math

def calculate_stability(control_count, alpha):
    """
    Tier 4: Stability Expression
    Stability = Control / Amplification
    """
    return control_count / alpha if alpha > 0 else 0

def simulate_historical_spread(p_t, s, lambda_decay, generations):
    """
    Tier 4: Population Spread Model
    p_t = allele frequency; s = selective advantage
    """
    frequencies = [p_t]
    for _ in range(generations):
        # Apply population spread equation
        p_next = p_t + p_t * (1 - p_t) * s - lambda_decay * p_t
        p_t = max(0, min(1, p_next)) # Ensure frequency bounds
        frequencies.append(p_t)
    return frequencies

# Calibration Input: Example Historical Data
historical_s = 0.8        # Observed selective advantage
initial_p = 0.1           # Initial allele frequency
historical_controls = 2   # Measured oversight density

# Derived amplification estimate (alpha)
derived_alpha = historical_s * 1.5

stability_score = calculate_stability(historical_controls, derived_alpha)

print(f"Historical Stability Score: {stability_score:.2f}")
# Result < 1.0 requires adjustment of lambda or increased quorum density.