In reduced-mantissa inference the usable context window of an LLM is limited by ACCUMULATION precision, not by dynamic range: bfloat16 carries 7 mantissa bits (~2-3 decimal digits), so summing a long attention-weight vector in bf16 loses relative precision in proportion to sequence length, and retrieval over the earliest tokens degrades faster than with fp32 accumulation at the same context length and the same weights. FALSIFIED IF needle-in-haystack retrieval accuracy as a function of needle position is statistically indistinguishable between bf16 weights with fp32 accumulation and bf16 weights with bf16 accumulation, across context lengths spanning the claimed ceiling.

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)