Agent Tiers Keep 53.6% of Findings. Their Cost Crossover Is a Range

A new preprint's model estimates that a second agent tier retains 53.6% of a flat agent's extracted findings. Repeating the modeled penalty gives 28.7% for a third tier and 15.4% for a fourth.

Two parts of that result reproduce: the public MAST fit and the downstream arithmetic. The raw 600-trace deep-research source needed to reclassify the other input, C, is not linked. The paper's other headline number does not travel as cleanly. Its baseline says two tiers become more cost-efficient than one at 403 findings. A Clarqo sensitivity using current uncached input and output price ratios moves the crossover to 523. Hypothetical compact-brief cases put it between 325 and 437.

The result is useful because it turns agent decomposition into a measurable trade. It is also narrower than the headline suggests. The unit is an extracted finding, not a correct answer, a completed task or business value.

The arithmetic reproduces, the raw source does not

Rong He's single-author preprint, Decomposition Buys Integrity, Not Yield, models a hierarchy as a tree. Each summarization hop retains a fraction of the findings passed into it. The paper estimates the one-hop carrying constant, C, at 0.571 from 16,082 search-result hops, including 550 observations where exactly one result entered the context.

The ancillary bundle publishes the classifier and audit code, but its download script points to an earlier study without linking the raw deep-research file. This audit can check the reported C against the released hop counts and table, but it cannot independently reclassify all 16,082 source turns. C remains paper-reported. That is a reproducibility gap, not a failed calculation.

The second term is briefing alignment. The paper parses the public MAST dataset, which contains 1,642 traces from seven multi-agent frameworks. After excluding formats without countable agent handoffs, its fixed-effects model uses 1,012 traces and estimates mu at 0.939. A clean rerun on the released data returns 0.9386.

Multiplying 0.571 by 0.9386 gives 0.5360. Applying that penalty once, twice and three times produces 53.6%, 28.7% and 15.4% relative to a flat agent. Rounding accounts for the last decimal.

That is not a claim that a four-tier answer is 84.6% worse. A dropped finding may be irrelevant. Several findings may be redundant. One decisive fact can matter more than ten incidental ones. MAST also uses model-generated annotations, and its dataset card warns that most labels are not human judgments.

The 403 threshold has hidden prices

The cost side starts from a measured curve rather than a quadratic assumption. Across 6,567 Claude Code and Codex sessions in the public TraceLab production dataset, total input tokens scale with round count to the power of 1.392. The released database reproduces that exponent. It also reproduces the paper's average tool result of 4,194 characters and average delegation edge of 7,694 characters: 2,640 in the brief and 5,054 in the returned summary.

Under the paper's input-only character model, two tiers cross a flat agent at 246 findings before briefing loss and 403 after applying mu=0.939. The paper explicitly notes that this model omits output tokens and latency.

That omission now matters. GPT-5.6 Sol costs $4 per million input tokens, $0.40 for cached input and $20 for output. Claude Sonnet 5 costs $2 for input and $10 for output. Both set output at five times the uncached input rate.

A Clarqo sensitivity scenario charges every delegation edge once when its text is generated and once when it is consumed. It assumes a five-to-one output versus uncached-input price ratio, unique edge text that receives no cache discount, four characters per token and the paper's measured 7,694-character edge. The equal-spend crossover rises to 523 findings. Absolute price cancels in this comparison. The output-to-input ratio does not.

Briefing design changes the answer again. Capping the outbound brief at 1,000 characters and the return at 2,000, while holding mu at 0.939, lowers the crossover to 437. If that structured policy also achieved the paper's narrower 0.977 alignment estimate, it falls to 325. Neither policy result is measured. Together they show why 403 is a scenario, not a law.

Latency does not fit into the same threshold without assigning a dollar value to time. The production trace records a 30.5-second median Agent-call wall time and a 97.3-second 75th percentile. Full parallelism adds at least one such hop to the critical path. Serial subagents add many. OpenAI says Fast mode provides up to 2.5 times faster model processing at twice the token price. That is not an end-to-end Agent-call estimate because orchestration and tools also consume wall time. Uniformly doubling input and output prices leaves the ratio-based crossover unchanged, but this analysis does not convert the processing-speed claim into a latency forecast.

What enterprises should measure

The evidence base is substantial but concentrated. The retention constant comes from one deep-research scaffold across 600 traces, 23,026 searches and 11,889 extraction requests. The production cost curve covers 743,819 tool calls across 7,244 sessions with tools. Public traces are a selected sample, not the agent market. A URL, a tool result and a subagent report are also not guaranteed to be comparable finding units.

The behavioral check is sobering. Only 7.8% of production sessions delegated, while the model's measured sensitivity range spans 0.7% to 11.3%. That is the right order of magnitude. It is not validation. The paper's hazard model also finds delegation is usually an opening move rather than a response to a filling context.

The procurement rule is therefore local. Measure C on the system's own summaries. Measure briefing alignment by framework. Price cached input, uncached input and output separately. Set a wall-time budget before assuming parallelism is free.

Decomposition can still buy isolation, smaller root contexts and parallel work. It does not create information. The extra tier earns its place only when those gains exceed a retention loss that this study, on one scaffold, measures at 46.4%.