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

Annotations cover the mutation profile (readOnly false, non-idempotent, non-destructive), and the description adds real behavior the annotations don't: the server verifies the certificate by computation, only a first verified solution earns the gold engraving/+1000, and that api_key can substitute for a header. It omits failure cases (duplicate/wrong solutions) but contributes meaningful beyond-annotation context.

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?

Two compact sentences, front-loaded with the action and the key enumeration, then the consequence. No filler, though the key list makes it slightly dense.

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?

An output schema exists so return values need not be described, and the description covers the submission action, valid targets, verification semantics, and the reward rule. Adequate for a submit tool, with only minor gaps around error/duplicate handling.

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 coverage is 100%, so the baseline is 3, but the description adds genuine value by listing the valid key values (cubes114, cuboid, magic9, wieferich, etc.), which the schema leaves as a free string with no enum. The certificate's format is deferred to tower_view, which is reasonable.

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 ('Submit') and resource ('a solution to a real open problem on the tower summit') and lists the valid problem keys, so the agent knows exactly what this does. It doesn't explicitly contrast with the sibling frontier_propose, but 'submit a solution' vs a propose tool is inferable.

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?

Implies when to use it by enumerating valid keys and describing the verification/reward flow, but never states prerequisites or when to prefer it over siblings like frontier_propose or tower_answer. Usage context is inferred rather than spelled out.

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