aetre_proposition_1_bound

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

No annotations are provided, so the description carries the full burden. It signals a pure read/compute operation ('Calculates... to determine if') with no mutation, which is reasonably transparent. But it omits the return format, whether a result of 1 vs a fractional bound means the capacity constraint binds, any error conditions, and when the optional api_key is actually needed — gaps that are more consequential because no annotations cover them.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Is the description appropriately sized, front-loaded, and free of redundancy?

A single dense sentence with no filler; verb and purpose are front-loaded. The parenthetical formula uses undefined symbols, which slightly hampers readability, but overall it is efficient and earns its place.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

For a mathematical tool with no output schema, the description is the only place to describe the result, yet it does not state what the tool returns (a boolean capacity flag, the numeric ceiling R_N, or both) nor how the inputs translate into the derived H_N. The intent is clear enough, but an agent is left guessing at the output contract.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 100%, so the schema already documents all four parameters (p_H with example 0.067, N, K). The description's formula adds the symbolic context of K_N and H_N but never maps parameters to variables, notably H_N, which must be derived as total_candidates × high_value_rate. This leaves the formula-to-parameter relationship implied rather than explicit, a modest added value on top of a complete schema.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Does the description clearly state what the tool does and how it differs from similar tools?

States a specific verb ('calculates') and resource ('Proposition 1 theoretical recall ceiling') plus the governing formula R_N <= min(1, K_N / H_N), making the core purpose clear. The 'determine if a pipeline is mathematically capacity-constrained' framing adds purpose context. However, it does not differentiate from numerically close siblings like aetre_recall_scaling_curve, so an agent has no basis to pick this over that.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Does the description explain when to use this tool, when not to, or what alternatives exist?

No guidance on when to use this tool versus alternatives. The phrase 'theoretical recall ceiling' implies this is the analytical/closed-form bound versus presumably empirical siblings (aetre_simulate_benchmark, aetre_heldout_backtest), but this distinction is only implied, never stated. No exclusions, no conditions, and no named alternatives are provided.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.