Presented period: a^r == 1 (mod N), gcd(a,N)=1. Optional proper_divisors must not themselves be periods. Does not search for r. Floats refused.
| Name | Required | Description | Default |
|---|---|---|---|
| N | No | ||
| a | No | ||
| r | No | ||
| proper_divisors | No |
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations, the description carries the full burden and it discloses the key behaviors: the congruence condition, the gcd condition, the proper-divisor minimality check, the fact that r is not searched for, and that floats are refused. It does not state return type or invalid-input handling, but the core behavior of a pure verification tool is well specified.
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?
Three short sentences convey the formula, the proper-divisor constraint, the no-search caveat, and an input restriction without filler. The most important semantic is front-loaded and every clause 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 tool with no annotations, no output schema, and zero parameter descriptions in the schema, the description covers the normal verification logic but leaves significant gaps: return behavior, invalid-input handling, and whether N/a/r are mandatory. An agent can construct a typical call but is undersupplied for edge cases and expected responses.
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?
The formula maps N, a, and r to their roles in the verification and gives proper_divisors clear meaning as the minimality-check input. It also marks proper_divisors as optional. However, string formats and the requiredness of N/a/r are left ambiguous, especially since the schema lists no required parameters.
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 specifies an exact mathematical predicate: verify that r is a presented period satisfying a^r == 1 (mod N) with gcd(a,N)=1, and that optional proper divisors are not themselves periods. It clearly identifies the action (verify) and the resource (a period candidate), and explicitly distinguishes itself from searching for r.
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 phrase 'Presented period' and 'Does not search for r' make clear this tool is for validating a supplied candidate exponent, not for discovering one. It does not name an explicit alternative tool, but the usage context is sufficiently clear.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Add one secure layer between your agents and this server.
Many verify_* tools are distinct, but there are overlapping clusters: math_court duplicates execute_2local_hamiltonian, route_spin_glass_manifold, and the quantum verifiers; project_affine_key, expose, verify_presented_pair, and the optional affine exposes in other tools blur together; weather and geometry tools also overlap. The detailed descriptions help a human, but an agent would likely struggle to choose between equivalent-seeming entry points.
Naming is mostly snake_case but otherwise inconsistent: some tools use dotted prefixes (atc.*, twin.robotics.*, weather.*), some use bare verbs (expose, lattice_op, math_court), some use noun phrases (corpus_bonds, feeds_catalog), and others mix prefixes with verbs (ide_rebuild_mesh, umc_resume). The verify_* family is consistent, but the overall set has no single predictable verb_noun pattern.
49 tools is far above the typical well-scoped server size and includes multiple near-duplicate paths to the same law (math_court, execute_*, route_*, verify_*). While not quite 50+, the count still feels like a sprawling kitchen-sink rather than a deliberate minimal surface.
The toolset covers a surprisingly wide range: QC verifiers, QMA laws, affine projections, corpus reads, weather, UMC state, and robotics IK. However, there are notable gaps for such a broad surface: no general court case lifecycle beyond expose/seal, no corpus content search, and no way to manage or update sealed artifacts; several areas have only entry-point coverage.