The exponent-range precision barrier (validated in FP32-BF16 LMC transitions) will constrain the optimal context window size for agentic AI systems (AgentSafe/TRACE) managing long-horizon ML research (AiScientist), where coalition-based deviations in tool-use equilibria emerge as memory costs exceed 10M-token thresholds.

In agentic AI systems performing long-horizon ML research tasks (e.g., autonomous experiment design/execution loops of the AiScientist/AgentSafe/TRACE class), there exists a critical context-memory threshold — predicted near 10M tokens of cumulative working/episodic memory — beyond which the numerical precision ceiling of FP32 accumulation (and the exponent-range mismatch introduced when mixed FP32/BF16 representations are used for state, embeddings, or gradient-like coordination signals) causes measurable degradation in multi-tool coordination equilibria. Specifically: (a) as effective context/memory size M (in tokens) increases past a threshold M* ≈ 10^7, the probability of "coalition-like" deviations — defined as subsets of tool-calling agents/modules converging on locally-stable but globally suboptimal repeated tool-use patterns — increases discontinuously (a phase transition, not a smooth degradation); and (b) this transition is mechanistically attributable to floating-point exponent-range/precision limits in the representations used to track long-horizon state (attention scores, KV-cache summaries, reward/value accumulators), such that the transition point shifts predictably (by a quantifiable ΔM*) when precision is changed (FP32 vs BF16 vs FP16 vs FP8) holding architecture and task constant.

This is falsifiable: if no discontinuity in coordination-failure rate is observed as a function of M across precision settings, or if the location/existence of any observed discontinuity is statistically independent of numerical precision (i.e., identical M* under FP32, BF16, FP16), the hypothesis is disproven.

Minimum viable test (MVT): a controlled multi-agent tool-use simulation harness where N=4 tool-calling sub-agents coordinate on a synthetic long-horizon ML research task (hyperparameter search + result logging + hypothesis revision loop), with artificially inflated "memory cost" via a controllable context-compression module. Sweep (a) effective memory size M ∈ {10^4, 10^5, 10^6, 5×10^6, 10^7, 2×10^7, 5×10^7} and (b) numeric precision ∈ {FP8, FP16, BF16, FP32, FP64-control}, in a fully-crossed design (7 × 5 = 35 conditions × ≥20 seeds = 700 runs minimum). Measure coordination-failure/coalition-deviation rate as the dependent variable; fit changepoint models per precision condition; compare M* across precisions via bootstrap CI overlap.

# Pseudocode: Precision x Memory-Scale Agentic Coalition Sweep

for precision in [FP8, FP16, BF16, FP32, FP64_control]:
    configure_accumulation_precision(memory_pathway, precision)  # weights fixed at BF16
    for M in [1e4, 1e5, 1e6, 5e6, 1e7, 2e7, 5e7]:
        for seed in range(N_SEEDS):
            env = LongHorizonAgentEnv(task=synthetic_ml_research_loop,
                                       target_memory_tokens=M,
                                       compression_schedule=adaptive_summarize)
            agents = spawn_tool_agents(n=4, framework="AgentSafe/TRACE-proxy")
            trace = run_episode(env, agents, max_steps=STEP_BUDGET, seed=seed)

            failure_rate = compute_coalition_deviation_score(trace, epsilon=EPS)
            fp_error = measure_exponent_saturation_events(trace.memory_pathway_log)
            log_result(precision, M, seed, failure_rate, fp_error, trace.task_reward)

# Analysis
for precision in precisions:
    model = fit_changepoint(failure_rate ~ log(M), method="bayesian_segmented")
    M_star[precision], CI[precision] = model.changepoint_estimate()

compare_M_star_across_precisions(M_star, CI, method="bootstrap+permutation")
mediation_result = mediation_analysis(M -> fp_error -> failure_rate)