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

With no annotations, the description carries the full disclosure burden, and it delivers: it states input restrictions ('Floats refused'), scopes the verification mathematically, explains what it does not do, and discloses the return topology for Q exposes including period_r semantics and where companion images travel. This goes well beyond a basic statement of effect and gives an agent real behavioral insight.

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?

The description is information-dense and front-loaded with the key certifier purpose, and every sentence contributes technical meaning. However, it is written as a terse spirals of specialized tokens ('patusi_expose', 'shors_qmt_witness', 'topological_shear', 'jordan_proven') that are not defined, and 'QC-001' adds no functional value. It is compact but not optimally easy for an agent to parse.

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?

The Q expose path is described in detail, with return pieces, companion-image transport, and verdict semantics, but the standard non-Q return value is not described at all. The schema lists Required as empty while the description implies N, halfPow, factor, and cofactor are the presented core values, leaving ambiguity about which parameters are mandatory. For a verifier with no output schema and no annotations, this is a meaningful completeness gap.

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 only 33%, but the description compensates for the undocumented N, halfPow, factor, and cofactor by defining them as decimal strings and giving their exact verification conditions. It also clarifies q_hex/object as an optional Q-only Affine expose with no k. The main weakness is that the meaning of 'halfPow' and the precise role of q_hex are left somewhat implicit, but this is still strong compensation for the schema gap.

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?

The description identifies a specific verb/resource: it certifies a Shor witness for (N, halfPow, factor, cofactor) and states the exact mathematical conditions that must hold. It also draws a useful boundary by explicitly saying 'Does not find a period,' which helps distinguish it from verify_period. The heavy internal jargon and oblique Q expose wording keep it from being fully crisp, so it stops short of 5.

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?

The intended input context is clear: call this when you have N, halfPow, factor, cofactor as decimal strings, and optionally a q_hex/object for a Q-only expose. The statement 'Does not find a period' is an explicit negative usage signal, though it does not name verify_period directly. There is no thorough when-not-to-use guidance for the other sibling verifiers, so it earns a 4 rather than a 5.

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