Affine Earth Math Court Remote

verify_shor_witness

QC-001 Shor witness certifier. Presented (N, halfPow, factor, cofactor) as decimal strings. halfPow squared == 1 (mod N), halfPow != 1 or N-1, gcd(halfPow-1,N)=factor, factor*cofactor=N. Does not find a period. Optional q_hex/object is a Q-only Affine expose (no k): returns patoshi_expose + shors_qmt_witness + topological_shear. period_r carries an ECDLP scalar or is empty; the Affine period turn's companion images travel as c1_recon_hex/c3_add_hex inside topological_shear, never as period_r. Verdict on a Q expose is the measured jordan_proven tag. Floats refused.

Input Schema

TableJSON Schema

Name	Required	Description
`N`	No	the modulus, decimal, e.g. 15
`q_hex`	No	optional Affine Q hex; Q-only expose envelope; no k. e.g. 0279be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798
`factor`	No	gcd(halfPow-1, N), decimal, e.g. 3
`object`	No	alias of q_hex. e.g. 0279be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798
`halfPow`	No	the witness a with a^2 == 1 (mod N) and a != 1, N-1, decimal, e.g. 4 for N=15
`cofactor`	No	N / factor, decimal, e.g. 5

Schema Changelog

Changes observed during successful MCP inspections.

Changed7 schema fields changedSep 29, 2026

addedInput schema / anyOf

Added value: +[
+  {
+    "required": [
+      "N",
+      "cofactor",
+      "factor",
+      "halfPow"
+    ]
+  },
+  {
+    "required": [
+      "q_hex"
+    ]
+  },
+  {
+    "required": [
+      "object"
+    ]
+  }
+]

addedInput schema / properties / N / description

Added value: +"the modulus, decimal, e.g. 15"

addedInput schema / properties / cofactor / description
```
Added value: +"N / factor, decimal, e.g. 5"
```

addedInput schema / properties / factor / description

Added value: +"gcd(halfPow-1, N), decimal, e.g. 3"

addedInput schema / properties / halfPow / description

Added value: +"the witness a with a^2 == 1 (mod N) and a != 1, N-1, decimal, e.g. 4 for N=15"

changedInput schema / properties / object / description

Previous value: -"alias of q_hex"New value: +"alias of q_hex. e.g. 0279be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798"

changedInput schema / properties / q_hex / description

Previous value: -"optional Affine Q hex; Q-only expose envelope; no k"New value: +"optional Affine Q hex; Q-only expose envelope; no k. e.g. 0279be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798"

First observedSep 1, 2026

TDQS

A3.6/5.0

Behavior4/5

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

With no annotations, the description carries the full burden and does meaningful work: it declares float inputs are refused, states the tool only certifies rather than searching, and names the returned components. The 'verdict is the measured jordan_proven tag' rule is real behavioral disclosure, though several terms remain unexplained.

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

Conciseness3/5

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

The opening certifier sentence is front-loaded well, but the later sentences are dense chains of internal jargon with low information density for an outside agent. Nothing is padded, yet the structure is hard to parse in one read.

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?

For a six-parameter tool with no annotations and no output schema, the description compensates by naming the required witness quartet, the optional Q expose, the returned components, and the float-rejection rule. Remaining gaps are the cryptic tag names rather than missing call-critical facts.

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 every parameter already carries its own description with the same equations, making the description's restatement of a^2==1 (mod N), gcd, and factor*cofactor=N largely redundant. It adds only the decimal-string presentation and the q_hex/object aliasing, which the schema also already shows.

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 a specific verb (certify/verify) and resource (QC-001 Shor witness) and even explicitly says what the tool does NOT do ('Does not find a period'), which separates it from verify_period. However, the second half collapses into opaque internal vocabulary (patoshi_expose, shors_qmt_witness, topological_shear) that does not sharpen the purpose.

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?

'Does not find a period' implies the sibling verify_period is the alternative for period-finding, but the routing condition is never stated explicitly. No guidance on when to supply (N, halfPow, factor, cofactor) versus the optional q_hex/object envelope.

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

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