**Agentic AI systems governed by dual-helix lifecycle architectures (e.g., WebGIS) will exhibit coalition-based equilibrium deviations in their tool-use policies when subjected to persistent Brownian noise in their context memory buffers, measurable as a power-law increase in cross-session forgetting rates proportional to the exponent-range precision barrier of their underlying LLM weights.**

In agentic AI systems built on "dual-helix" lifecycle architectures (two coupled control loops — e.g., a long-horizon planning/state-management strand and a short-horizon execution/tool-invocation strand, as exemplified by WebGIS-style orchestration), injecting persistent Brownian (Wiener-process) perturbations into the context-memory buffer will cause: (a) systematic, non-random drift in tool-selection policy distributions away from a task-optimal equilibrium ("coalition-based equilibrium deviation," operationalized as KL-divergence between perturbed and unperturbed tool-choice distributions across repeated sessions), and (b) a cross-session forgetting rate F(t) that grows as a power law F(t) ∝ t^α, where the exponent α is a monotonic function of the effective mantissa/exponent precision (bit-width) of the underlying LLM's weight representation (e.g., fp32 vs bf16 vs fp8/int4). The falsifiable claim: α measured empirically at 3+ precision levels will differ by more than measurement noise (>2σ across ≥5 seeds) and will correlate with representational precision with Pearson |r|≥0.6, p<0.05.

Minimum viable test (MVT): single open-weight LLM (e.g., Llama-3.1-8B or Qwen2.5-7B) wrapped in a minimal dual-helix agent (planner loop + executor/tool-call loop) with a vector-store context buffer. Run N=100 sessions per condition across a 2×4 design: {Brownian noise, i.i.d. control} × {fp32, bf16, fp8, int4 weight precision}, each session performing a fixed multi-step tool-use task (e.g., a synthetic WebGIS-style spatial query workflow: geocode → buffer → intersect → report). Measure per-session tool-choice distribution and cross-session recall of prior task state.

class DualHelixAgent:
    def __init__(self, planner_llm, executor_llm, memory_store, noise_mode):
        self.planner = planner_llm       # Strand A
        self.executor = executor_llm     # Strand B
        self.memory = memory_store       # shared vector buffer
        self.noise_mode = noise_mode     # 'brownian' | 'iid' | 'none'
        self.cum_drift = np.zeros(embed_dim)

    def write_memory(self, embedding):
        if self.noise_mode == 'brownian':
            self.cum_drift += np.random.normal(0, sigma*sqrt(dt), embed_dim)
            embedding = embedding + self.cum_drift
        elif self.noise_mode == 'iid':
            embedding = embedding + np.random.normal(0, sigma, embed_dim)
        self.memory.add(embedding)

    def run_session(self, task):
        plan = self.planner.generate_plan(task, self.memory.retrieve(task))
        for step in plan:
            tool_choice = self.executor.select_tool(step, self.memory.retrieve(step))
            result = execute_tool(tool_choice)
            self.write_memory(embed(result))
            log(tool_choice, result)

# Experiment driver
for precision in [fp32, bf16, fp8, int4]:
    model = load_quantized(base_model, precision)
    for noise_mode in ['brownian', 'iid']:
        agent = DualHelixAgent(model, model, VectorStore(), noise_mode)
        for chain in range(100):
            for session in range(10):
                agent.run_session(sample_task())
        compute_KL(tool_choice_dist(noise_mode), baseline_dist)
        fit_forgetting_curve(retrieval_accuracy_over_sessions)

alpha_by_precision = {p: fit_power_law(...)['alpha'] for p in precisions}
correlation = pearsonr(list(alpha_by_precision.values()), mantissa_bits)