Affine Earth Math Court Remote

verify_period

Presented period: a^r == 1 (mod N), gcd(a,N)=1, and none of the posted proper_divisors is itself a period (the order claim). All four fields are required: a, N, r, proper_divisors - e.g. a=2, N=15, r=4, proper_divisors=1,2 -> WIN 'a^4 == 1 mod 15'. A call missing one returns REFUSED_NO_INSTANCE naming the missing field. Does not search for r. Floats refused.

Input Schema

TableJSON Schema

Name	Required	Description
`N`	Yes	modulus, decimal, e.g. 15
`a`	Yes	base, coprime with N, decimal, e.g. 2
`r`	Yes	the presented period: a^r == 1 (mod N), decimal, e.g. 4
`proper_divisors`	Yes	REQUIRED on the wire: comma-separated proper divisors of r that must NOT be periods (that is the order claim), e.g. 1,2 for r=4. Absent -> REFUSED_NO_INSTANCE 'missing proper_divisors'

Schema Changelog

Changes observed during successful MCP inspections.

Changed5 schema fields changedSep 29, 2026

addedInput schema / properties / N / description
```
Added value: +"modulus, decimal, e.g. 15"
```

addedInput schema / properties / a / description

Added value: +"base, coprime with N, decimal, e.g. 2"

addedInput schema / properties / proper_divisors / description

Added value: +"REQUIRED on the wire: comma-separated proper divisors of r that must NOT be periods (that is the order claim), e.g. 1,2 for r=4. Absent -> REFUSED_NO_INSTANCE 'missing proper_divisors'"

addedInput schema / properties / r / description

Added value: +"the presented period: a^r == 1 (mod N), decimal, e.g. 4"

changedInput schema / required

Previous value: -[]New value: +[
+  "N",
+  "a",
+  "proper_divisors",
+  "r"
+]

First observedSep 1, 2026

TDQS

A3.7/5.0

Behavior4/5

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

No annotations are provided, so the description carries full burden and does well: it discloses the success outcome (WIN 'a^4 == 1 mod 15'), the failure mode for missing fields (REFUSED_NO_INSTANCE naming the missing field), and rejects floats. It omits what a failed verification (e.g. a LOSE/non-period result) returns.

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

Conciseness4/5

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

Front-loads the mathematical predicate, then constraints, then the worked example and edge behaviors. Dense but no obvious filler; each sentence carries a fact.

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

Completeness4/5

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

With no output schema or annotations, the description adequately covers inputs, required-ness, the required-on-the-wire proper_divisors, and result strings. Slightly incomplete on the negative-result outcome, but an agent has enough to call it correctly.

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

Parameters3/5

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

Schema description coverage is 100%, so each of N, a, r, proper_divisors is already documented in the schema, making 3 the baseline. The worked example and the 'must NOT be periods' emphasis add modest value but largely restate the schema.

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

Purpose4/5

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

States the specific verification predicate precisely: a^r == 1 (mod N), gcd(a,N)=1, and no posted proper divisor being a period (the order claim). This is concrete enough to distinguish it from unrelated siblings, though it does not explicitly route against close cousins like verify_shor_witness.

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

Usage Guidelines3/5

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

Implied usage is clear – it validates a *presented* period rather than searching for one, reinforced by 'Does not search for r'. However, no explicit when-to-use/when-not guidance or alternative sibling is named, so an agent must infer the boundary.

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

All Affine Earth Math Court Remote tools Inspect

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