To evaluate gene-drive edge cases

To evaluate gene-drive edge cases, the system forking logic incorporates the Stability Expression as the primary validator. This Monte Carlo simulation models stochastic failures in the Quorum Validation Layer and boundary crossings in $R_0$ containment.

Simulation Parameters

• $R_0$ Boundary Risk: Models the probability that the drive's reproductive rate exceeds the containment invariant ($R_0^{drive} < 1.0$ outside target zones).
• Quorum Failure: Models the probability that independent genomic labs, biosecurity groups, or international bodies fail to reach the mandatory distributed consensus (3:2:1 ratio).
• Stability Threshold: Computes the $Control/Amplification$ ratio to ensure it remains $\geq 1.0$.

Monte Carlo Simulation Logic

import random
import math

class GeneDriveMonteCarlo:
    def __init__(self, iterations=1000):
        self.iterations = iterations
        # Required Invariants (Tier 2 & Tier 4)
        self.min_labs = 3
        self.min_biosecurity = 2
        self.min_oversight = 1
        self.stability_threshold = 1.0

    def run_simulation(self):
        results = {"SUCCESS": 0, "QUORUM_FAILURE": 0, "CONTAINMENT_BREACH": 0, "STABILITY_DEFICIT": 0}

        for _ in range(self.iterations):
            # Stochastic Inputs for Edge Cases
            observed_r0 = random.uniform(0.5, 1.5)  # Edge case around 1.0
            labs_ok = random.randint(1, 5)
            bio_ok = random.randint(0, 3)
            oversight_ok = random.randint(0, 2)

            # Tier 4: Amplification Scalar (alpha)
            # Modeling higher risk as R0 increases
            alpha = observed_r0 * 2.5
            control_density = labs_ok + bio_ok + oversight_ok
            stability = control_density / alpha if alpha > 0 else 0

            # Invariant Validation Logic
            quorum_met = (labs_ok >= self.min_labs and
                          bio_ok >= self.min_biosecurity and
                          oversight_ok >= self.min_oversight)

            containment_intact = observed_r0 < 1.0 # Section IX Invariant
            stability_valid = stability >= self.stability_threshold

            # Evaluate Composite Acceptance Condition (Section VIII)
            if not quorum_met:
                results["QUORUM_FAILURE"] += 1
            elif not containment_intact:
                results["CONTAINMENT_BREACH"] += 1
            elif not stability_valid:
                results["STABILITY_DEFICIT"] += 1
            else:
                results["SUCCESS"] += 1

        return results

# Execute Pilot Simulation
sim = GeneDriveMonteCarlo(iterations=10000)
summary = sim.run_simulation()

print("--- Gene-Drive Edge Case Simulation Results ---")
for key, value in summary.items():
    percentage = (value / 10000) * 100
    print(f"{key}: {value} ({percentage:.2f}%)")

Analysis of Invariant Failures

1. Quorum Failures: Occur when the distributed authority is fragmented. Per the Framework, unilateral release is prohibited even if $R_0$ is low.
2. Containment Breaches: Occur when the drive's propagation strength ($\alpha$) exceeds the threshold where $R_0^{drive} \geq 1.0$ outside of isolation.
3. Stability Deficits: Even with a quorum and low $R_0$, if the amplification power of the drive outpaces the multi-layer control density, the system enters an "Under-scaled Governance" state (Stability < 1.0) and must be frozen.