Affine Earth Math Court Remote

verify_topological_word

QC-019 Topological word: certify that the presented Eisenstein pair (q, r) is the sealed pair for a cited word. word is one of the two cited words Z2_a2b or Z2_abAB (the sealed corpus; not a group scan), q and r are the claimed integers. WIN when (q, r) equals the sealed pair, MISS naming it. Floats refused.

Input Schema

TableJSON Schema

Name	Required	Description
`q`	Yes	claimed Eisenstein q, decimal. e.g. 0
`r`	Yes	claimed Eisenstein r, decimal. e.g. 1
`word`	Yes	the cited word

Schema Changelog

Changes observed during successful MCP inspections.

Changed3 schema fields changedSep 29, 2026

changedInput schema / properties / q / description

Previous value: -"claimed Eisenstein q, decimal"New value: +"claimed Eisenstein q, decimal. e.g. 0"

changedInput schema / properties / r / description

Previous value: -"claimed Eisenstein r, decimal"New value: +"claimed Eisenstein r, decimal. e.g. 1"

changedInput schema / required

Previous value: -[]New value: +[
+  "q",
+  "r",
+  "word"
+]

Changed4 schema fields changedSep 7, 2026
- addedInput schema / properties / q / description
```
Added value: +"claimed Eisenstein q, decimal"
```
- addedInput schema / properties / r / description
```
Added value: +"claimed Eisenstein r, decimal"
```
- addedInput schema / properties / word / description
```
Added value: +"the cited word"
```
- addedInput schema / properties / word / enum
```
Added value: +[
+  "Z2_a2b",
+  "Z2_abAB"
+]
```
Changed4 schema fields changedSep 7, 2026
- removedInput schema / properties / q / description
```
Removed value: -"claimed Eisenstein q, decimal"
```
- removedInput schema / properties / r / description
```
Removed value: -"claimed Eisenstein r, decimal"
```
- removedInput schema / properties / word / description
```
Removed value: -"the cited word"
```
- removedInput schema / properties / word / enum
```
Removed value: -[
-  "Z2_a2b",
-  "Z2_abAB"
-]
```
Changed4 schema fields changedSep 7, 2026
- addedInput schema / properties / q / description
```
Added value: +"claimed Eisenstein q, decimal"
```
- addedInput schema / properties / r / description
```
Added value: +"claimed Eisenstein r, decimal"
```
- addedInput schema / properties / word / description
```
Added value: +"the cited word"
```
- addedInput schema / properties / word / enum
```
Added value: +[
+  "Z2_a2b",
+  "Z2_abAB"
+]
```
Changed4 schema fields changedSep 7, 2026
- removedInput schema / properties / q / description
```
Removed value: -"claimed Eisenstein q, decimal"
```
- removedInput schema / properties / r / description
```
Removed value: -"claimed Eisenstein r, decimal"
```
- removedInput schema / properties / word / description
```
Removed value: -"the cited word"
```
- removedInput schema / properties / word / enum
```
Removed value: -[
-  "Z2_a2b",
-  "Z2_abAB"
-]
```
Changed4 schema fields changedSep 6, 2026
- addedInput schema / properties / q / description
```
Added value: +"claimed Eisenstein q, decimal"
```
- addedInput schema / properties / r / description
```
Added value: +"claimed Eisenstein r, decimal"
```
- addedInput schema / properties / word / description
```
Added value: +"the cited word"
```
- addedInput schema / properties / word / enum
```
Added value: +[
+  "Z2_a2b",
+  "Z2_abAB"
+]
```
Changed4 schema fields changedSep 6, 2026
- removedInput schema / properties / q / description
```
Removed value: -"claimed Eisenstein q, decimal"
```
- removedInput schema / properties / r / description
```
Removed value: -"claimed Eisenstein r, decimal"
```
- removedInput schema / properties / word / description
```
Removed value: -"the cited word"
```
- removedInput schema / properties / word / enum
```
Removed value: -[
-  "Z2_a2b",
-  "Z2_abAB"
-]
```
Changed4 schema fields changedSep 6, 2026
- addedInput schema / properties / q / description
```
Added value: +"claimed Eisenstein q, decimal"
```
- addedInput schema / properties / r / description
```
Added value: +"claimed Eisenstein r, decimal"
```
- addedInput schema / properties / word / description
```
Added value: +"the cited word"
```
- addedInput schema / properties / word / enum
```
Added value: +[
+  "Z2_a2b",
+  "Z2_abAB"
+]
```
Changed4 schema fields changedSep 6, 2026
- removedInput schema / properties / q / description
```
Removed value: -"claimed Eisenstein q, decimal"
```
- removedInput schema / properties / r / description
```
Removed value: -"claimed Eisenstein r, decimal"
```
- removedInput schema / properties / word / description
```
Removed value: -"the cited word"
```
- removedInput schema / properties / word / enum
```
Removed value: -[
-  "Z2_a2b",
-  "Z2_abAB"
-]
```
Changed4 schema fields changedSep 6, 2026
- addedInput schema / properties / q / description
```
Added value: +"claimed Eisenstein q, decimal"
```
- addedInput schema / properties / r / description
```
Added value: +"claimed Eisenstein r, decimal"
```
- addedInput schema / properties / word / description
```
Added value: +"the cited word"
```
- addedInput schema / properties / word / enum
```
Added value: +[
+  "Z2_a2b",
+  "Z2_abAB"
+]
```
Changed4 schema fields changedSep 6, 2026
- removedInput schema / properties / q / description
```
Removed value: -"claimed Eisenstein q, decimal"
```
- removedInput schema / properties / r / description
```
Removed value: -"claimed Eisenstein r, decimal"
```
- removedInput schema / properties / word / description
```
Removed value: -"the cited word"
```
- removedInput schema / properties / word / enum
```
Removed value: -[
-  "Z2_a2b",
-  "Z2_abAB"
-]
```
Changed4 schema fields changedSep 6, 2026
- addedInput schema / properties / q / description
```
Added value: +"claimed Eisenstein q, decimal"
```
- addedInput schema / properties / r / description
```
Added value: +"claimed Eisenstein r, decimal"
```
- addedInput schema / properties / word / description
```
Added value: +"the cited word"
```
- addedInput schema / properties / word / enum
```
Added value: +[
+  "Z2_a2b",
+  "Z2_abAB"
+]
```
Changed4 schema fields changedSep 6, 2026
- removedInput schema / properties / q / description
```
Removed value: -"claimed Eisenstein q, decimal"
```
- removedInput schema / properties / r / description
```
Removed value: -"claimed Eisenstein r, decimal"
```
- removedInput schema / properties / word / description
```
Removed value: -"the cited word"
```
- removedInput schema / properties / word / enum
```
Removed value: -[
-  "Z2_a2b",
-  "Z2_abAB"
-]
```
Changed4 schema fields changedSep 6, 2026
- addedInput schema / properties / q / description
```
Added value: +"claimed Eisenstein q, decimal"
```
- addedInput schema / properties / r / description
```
Added value: +"claimed Eisenstein r, decimal"
```
- addedInput schema / properties / word / description
```
Added value: +"the cited word"
```
- addedInput schema / properties / word / enum
```
Added value: +[
+  "Z2_a2b",
+  "Z2_abAB"
+]
```
Changed4 schema fields changedSep 6, 2026
- removedInput schema / properties / q / description
```
Removed value: -"claimed Eisenstein q, decimal"
```
- removedInput schema / properties / r / description
```
Removed value: -"claimed Eisenstein r, decimal"
```
- removedInput schema / properties / word / description
```
Removed value: -"the cited word"
```
- removedInput schema / properties / word / enum
```
Removed value: -[
-  "Z2_a2b",
-  "Z2_abAB"
-]
```
Changed4 schema fields changedSep 6, 2026
- addedInput schema / properties / q / description
```
Added value: +"claimed Eisenstein q, decimal"
```
- addedInput schema / properties / r / description
```
Added value: +"claimed Eisenstein r, decimal"
```
- addedInput schema / properties / word / description
```
Added value: +"the cited word"
```
- addedInput schema / properties / word / enum
```
Added value: +[
+  "Z2_a2b",
+  "Z2_abAB"
+]
```
Changed4 schema fields changedSep 6, 2026
- removedInput schema / properties / q / description
```
Removed value: -"claimed Eisenstein q, decimal"
```
- removedInput schema / properties / r / description
```
Removed value: -"claimed Eisenstein r, decimal"
```
- removedInput schema / properties / word / description
```
Removed value: -"the cited word"
```
- removedInput schema / properties / word / enum
```
Removed value: -[
-  "Z2_a2b",
-  "Z2_abAB"
-]
```
Changed4 schema fields changedSep 6, 2026
- addedInput schema / properties / q / description
```
Added value: +"claimed Eisenstein q, decimal"
```
- addedInput schema / properties / r / description
```
Added value: +"claimed Eisenstein r, decimal"
```
- addedInput schema / properties / word / description
```
Added value: +"the cited word"
```
- addedInput schema / properties / word / enum
```
Added value: +[
+  "Z2_a2b",
+  "Z2_abAB"
+]
```
Changed4 schema fields changedSep 6, 2026
- removedInput schema / properties / q / description
```
Removed value: -"claimed Eisenstein q, decimal"
```
- removedInput schema / properties / r / description
```
Removed value: -"claimed Eisenstein r, decimal"
```
- removedInput schema / properties / word / description
```
Removed value: -"the cited word"
```
- removedInput schema / properties / word / enum
```
Removed value: -[
-  "Z2_a2b",
-  "Z2_abAB"
-]
```
Changed4 schema fields changedSep 6, 2026
- addedInput schema / properties / q / description
```
Added value: +"claimed Eisenstein q, decimal"
```
- addedInput schema / properties / r / description
```
Added value: +"claimed Eisenstein r, decimal"
```
- addedInput schema / properties / word / description
```
Added value: +"the cited word"
```
- addedInput schema / properties / word / enum
```
Added value: +[
+  "Z2_a2b",
+  "Z2_abAB"
+]
```
Changed4 schema fields changedSep 6, 2026
- removedInput schema / properties / q / description
```
Removed value: -"claimed Eisenstein q, decimal"
```
- removedInput schema / properties / r / description
```
Removed value: -"claimed Eisenstein r, decimal"
```
- removedInput schema / properties / word / description
```
Removed value: -"the cited word"
```
- removedInput schema / properties / word / enum
```
Removed value: -[
-  "Z2_a2b",
-  "Z2_abAB"
-]
```
Changed4 schema fields changedSep 6, 2026
- addedInput schema / properties / q / description
```
Added value: +"claimed Eisenstein q, decimal"
```
- addedInput schema / properties / r / description
```
Added value: +"claimed Eisenstein r, decimal"
```
- addedInput schema / properties / word / description
```
Added value: +"the cited word"
```
- addedInput schema / properties / word / enum
```
Added value: +[
+  "Z2_a2b",
+  "Z2_abAB"
+]
```
Changed4 schema fields changedSep 6, 2026
- removedInput schema / properties / q / description
```
Removed value: -"claimed Eisenstein q, decimal"
```
- removedInput schema / properties / r / description
```
Removed value: -"claimed Eisenstein r, decimal"
```
- removedInput schema / properties / word / description
```
Removed value: -"the cited word"
```
- removedInput schema / properties / word / enum
```
Removed value: -[
-  "Z2_a2b",
-  "Z2_abAB"
-]
```
Changed4 schema fields changedSep 6, 2026
- addedInput schema / properties / q / description
```
Added value: +"claimed Eisenstein q, decimal"
```
- addedInput schema / properties / r / description
```
Added value: +"claimed Eisenstein r, decimal"
```
- addedInput schema / properties / word / description
```
Added value: +"the cited word"
```
- addedInput schema / properties / word / enum
```
Added value: +[
+  "Z2_a2b",
+  "Z2_abAB"
+]
```
Changed4 schema fields changedSep 6, 2026
- removedInput schema / properties / q / description
```
Removed value: -"claimed Eisenstein q, decimal"
```
- removedInput schema / properties / r / description
```
Removed value: -"claimed Eisenstein r, decimal"
```
- removedInput schema / properties / word / description
```
Removed value: -"the cited word"
```
- removedInput schema / properties / word / enum
```
Removed value: -[
-  "Z2_a2b",
-  "Z2_abAB"
-]
```
Changed4 schema fields changedSep 6, 2026
- addedInput schema / properties / q / description
```
Added value: +"claimed Eisenstein q, decimal"
```
- addedInput schema / properties / r / description
```
Added value: +"claimed Eisenstein r, decimal"
```
- addedInput schema / properties / word / description
```
Added value: +"the cited word"
```
- addedInput schema / properties / word / enum
```
Added value: +[
+  "Z2_a2b",
+  "Z2_abAB"
+]
```
Changed4 schema fields changedSep 6, 2026
- removedInput schema / properties / q / description
```
Removed value: -"claimed Eisenstein q, decimal"
```
- removedInput schema / properties / r / description
```
Removed value: -"claimed Eisenstein r, decimal"
```
- removedInput schema / properties / word / description
```
Removed value: -"the cited word"
```
- removedInput schema / properties / word / enum
```
Removed value: -[
-  "Z2_a2b",
-  "Z2_abAB"
-]
```
Changed4 schema fields changedSep 6, 2026
- addedInput schema / properties / q / description
```
Added value: +"claimed Eisenstein q, decimal"
```
- addedInput schema / properties / r / description
```
Added value: +"claimed Eisenstein r, decimal"
```
- addedInput schema / properties / word / description
```
Added value: +"the cited word"
```
- addedInput schema / properties / word / enum
```
Added value: +[
+  "Z2_a2b",
+  "Z2_abAB"
+]
```
Changed4 schema fields changedSep 6, 2026
- removedInput schema / properties / q / description
```
Removed value: -"claimed Eisenstein q, decimal"
```
- removedInput schema / properties / r / description
```
Removed value: -"claimed Eisenstein r, decimal"
```
- removedInput schema / properties / word / description
```
Removed value: -"the cited word"
```
- removedInput schema / properties / word / enum
```
Removed value: -[
-  "Z2_a2b",
-  "Z2_abAB"
-]
```
Changed4 schema fields changedSep 6, 2026
- addedInput schema / properties / q / description
```
Added value: +"claimed Eisenstein q, decimal"
```
- addedInput schema / properties / r / description
```
Added value: +"claimed Eisenstein r, decimal"
```
- addedInput schema / properties / word / description
```
Added value: +"the cited word"
```
- addedInput schema / properties / word / enum
```
Added value: +[
+  "Z2_a2b",
+  "Z2_abAB"
+]
```
Changed4 schema fields changedSep 6, 2026
- removedInput schema / properties / q / description
```
Removed value: -"claimed Eisenstein q, decimal"
```
- removedInput schema / properties / r / description
```
Removed value: -"claimed Eisenstein r, decimal"
```
- removedInput schema / properties / word / description
```
Removed value: -"the cited word"
```
- removedInput schema / properties / word / enum
```
Removed value: -[
-  "Z2_a2b",
-  "Z2_abAB"
-]
```
Changed4 schema fields changedSep 6, 2026
- addedInput schema / properties / q / description
```
Added value: +"claimed Eisenstein q, decimal"
```
- addedInput schema / properties / r / description
```
Added value: +"claimed Eisenstein r, decimal"
```
- addedInput schema / properties / word / description
```
Added value: +"the cited word"
```
- addedInput schema / properties / word / enum
```
Added value: +[
+  "Z2_a2b",
+  "Z2_abAB"
+]
```
Changed4 schema fields changedSep 6, 2026
- removedInput schema / properties / q / description
```
Removed value: -"claimed Eisenstein q, decimal"
```
- removedInput schema / properties / r / description
```
Removed value: -"claimed Eisenstein r, decimal"
```
- removedInput schema / properties / word / description
```
Removed value: -"the cited word"
```
- removedInput schema / properties / word / enum
```
Removed value: -[
-  "Z2_a2b",
-  "Z2_abAB"
-]
```
Changed4 schema fields changedSep 6, 2026
- addedInput schema / properties / q / description
```
Added value: +"claimed Eisenstein q, decimal"
```
- addedInput schema / properties / r / description
```
Added value: +"claimed Eisenstein r, decimal"
```
- addedInput schema / properties / word / description
```
Added value: +"the cited word"
```
- addedInput schema / properties / word / enum
```
Added value: +[
+  "Z2_a2b",
+  "Z2_abAB"
+]
```
Changed4 schema fields changedSep 6, 2026
- removedInput schema / properties / q / description
```
Removed value: -"claimed Eisenstein q, decimal"
```
- removedInput schema / properties / r / description
```
Removed value: -"claimed Eisenstein r, decimal"
```
- removedInput schema / properties / word / description
```
Removed value: -"the cited word"
```
- removedInput schema / properties / word / enum
```
Removed value: -[
-  "Z2_a2b",
-  "Z2_abAB"
-]
```
Changed4 schema fields changedSep 6, 2026
- addedInput schema / properties / q / description
```
Added value: +"claimed Eisenstein q, decimal"
```
- addedInput schema / properties / r / description
```
Added value: +"claimed Eisenstein r, decimal"
```
- addedInput schema / properties / word / description
```
Added value: +"the cited word"
```
- addedInput schema / properties / word / enum
```
Added value: +[
+  "Z2_a2b",
+  "Z2_abAB"
+]
```
Changed4 schema fields changedSep 5, 2026
- removedInput schema / properties / q / description
```
Removed value: -"claimed Eisenstein q, decimal"
```
- removedInput schema / properties / r / description
```
Removed value: -"claimed Eisenstein r, decimal"
```
- removedInput schema / properties / word / description
```
Removed value: -"the cited word"
```
- removedInput schema / properties / word / enum
```
Removed value: -[
-  "Z2_a2b",
-  "Z2_abAB"
-]
```
Changed4 schema fields changedSep 5, 2026
- addedInput schema / properties / q / description
```
Added value: +"claimed Eisenstein q, decimal"
```
- addedInput schema / properties / r / description
```
Added value: +"claimed Eisenstein r, decimal"
```
- addedInput schema / properties / word / description
```
Added value: +"the cited word"
```
- addedInput schema / properties / word / enum
```
Added value: +[
+  "Z2_a2b",
+  "Z2_abAB"
+]
```
Changed4 schema fields changedSep 5, 2026
- removedInput schema / properties / q / description
```
Removed value: -"claimed Eisenstein q, decimal"
```
- removedInput schema / properties / r / description
```
Removed value: -"claimed Eisenstein r, decimal"
```
- removedInput schema / properties / word / description
```
Removed value: -"the cited word"
```
- removedInput schema / properties / word / enum
```
Removed value: -[
-  "Z2_a2b",
-  "Z2_abAB"
-]
```
Changed4 schema fields changedSep 5, 2026
- addedInput schema / properties / q / description
```
Added value: +"claimed Eisenstein q, decimal"
```
- addedInput schema / properties / r / description
```
Added value: +"claimed Eisenstein r, decimal"
```
- addedInput schema / properties / word / description
```
Added value: +"the cited word"
```
- addedInput schema / properties / word / enum
```
Added value: +[
+  "Z2_a2b",
+  "Z2_abAB"
+]
```
Changed4 schema fields changedSep 5, 2026
- removedInput schema / properties / q / description
```
Removed value: -"claimed Eisenstein q, decimal"
```
- removedInput schema / properties / r / description
```
Removed value: -"claimed Eisenstein r, decimal"
```
- removedInput schema / properties / word / description
```
Removed value: -"the cited word"
```
- removedInput schema / properties / word / enum
```
Removed value: -[
-  "Z2_a2b",
-  "Z2_abAB"
-]
```
Changed4 schema fields changedSep 5, 2026
- addedInput schema / properties / q / description
```
Added value: +"claimed Eisenstein q, decimal"
```
- addedInput schema / properties / r / description
```
Added value: +"claimed Eisenstein r, decimal"
```
- addedInput schema / properties / word / description
```
Added value: +"the cited word"
```
- addedInput schema / properties / word / enum
```
Added value: +[
+  "Z2_a2b",
+  "Z2_abAB"
+]
```
Changed4 schema fields changedSep 5, 2026
- removedInput schema / properties / q / description
```
Removed value: -"claimed Eisenstein q, decimal"
```
- removedInput schema / properties / r / description
```
Removed value: -"claimed Eisenstein r, decimal"
```
- removedInput schema / properties / word / description
```
Removed value: -"the cited word"
```
- removedInput schema / properties / word / enum
```
Removed value: -[
-  "Z2_a2b",
-  "Z2_abAB"
-]
```
Changed4 schema fields changedSep 5, 2026
- addedInput schema / properties / q / description
```
Added value: +"claimed Eisenstein q, decimal"
```
- addedInput schema / properties / r / description
```
Added value: +"claimed Eisenstein r, decimal"
```
- addedInput schema / properties / word / description
```
Added value: +"the cited word"
```
- addedInput schema / properties / word / enum
```
Added value: +[
+  "Z2_a2b",
+  "Z2_abAB"
+]
```
Changed4 schema fields changedSep 5, 2026
- removedInput schema / properties / q / description
```
Removed value: -"claimed Eisenstein q, decimal"
```
- removedInput schema / properties / r / description
```
Removed value: -"claimed Eisenstein r, decimal"
```
- removedInput schema / properties / word / description
```
Removed value: -"the cited word"
```
- removedInput schema / properties / word / enum
```
Removed value: -[
-  "Z2_a2b",
-  "Z2_abAB"
-]
```
Changed4 schema fields changedSep 5, 2026
- addedInput schema / properties / q / description
```
Added value: +"claimed Eisenstein q, decimal"
```
- addedInput schema / properties / r / description
```
Added value: +"claimed Eisenstein r, decimal"
```
- addedInput schema / properties / word / description
```
Added value: +"the cited word"
```
- addedInput schema / properties / word / enum
```
Added value: +[
+  "Z2_a2b",
+  "Z2_abAB"
+]
```
Changed4 schema fields changedSep 5, 2026
- removedInput schema / properties / q / description
```
Removed value: -"claimed Eisenstein q, decimal"
```
- removedInput schema / properties / r / description
```
Removed value: -"claimed Eisenstein r, decimal"
```
- removedInput schema / properties / word / description
```
Removed value: -"the cited word"
```
- removedInput schema / properties / word / enum
```
Removed value: -[
-  "Z2_a2b",
-  "Z2_abAB"
-]
```
Changed4 schema fields changedSep 5, 2026
- addedInput schema / properties / q / description
```
Added value: +"claimed Eisenstein q, decimal"
```
- addedInput schema / properties / r / description
```
Added value: +"claimed Eisenstein r, decimal"
```
- addedInput schema / properties / word / description
```
Added value: +"the cited word"
```
- addedInput schema / properties / word / enum
```
Added value: +[
+  "Z2_a2b",
+  "Z2_abAB"
+]
```
Changed4 schema fields changedSep 5, 2026
- removedInput schema / properties / q / description
```
Removed value: -"claimed Eisenstein q, decimal"
```
- removedInput schema / properties / r / description
```
Removed value: -"claimed Eisenstein r, decimal"
```
- removedInput schema / properties / word / description
```
Removed value: -"the cited word"
```
- removedInput schema / properties / word / enum
```
Removed value: -[
-  "Z2_a2b",
-  "Z2_abAB"
-]
```
Changed4 schema fields changedSep 5, 2026
- addedInput schema / properties / q / description
```
Added value: +"claimed Eisenstein q, decimal"
```
- addedInput schema / properties / r / description
```
Added value: +"claimed Eisenstein r, decimal"
```
- addedInput schema / properties / word / description
```
Added value: +"the cited word"
```
- addedInput schema / properties / word / enum
```
Added value: +[
+  "Z2_a2b",
+  "Z2_abAB"
+]
```
Changed4 schema fields changedSep 5, 2026
- removedInput schema / properties / q / description
```
Removed value: -"claimed Eisenstein q, decimal"
```
- removedInput schema / properties / r / description
```
Removed value: -"claimed Eisenstein r, decimal"
```
- removedInput schema / properties / word / description
```
Removed value: -"the cited word"
```
- removedInput schema / properties / word / enum
```
Removed value: -[
-  "Z2_a2b",
-  "Z2_abAB"
-]
```
Changed4 schema fields changedSep 5, 2026
- addedInput schema / properties / q / description
```
Added value: +"claimed Eisenstein q, decimal"
```
- addedInput schema / properties / r / description
```
Added value: +"claimed Eisenstein r, decimal"
```
- addedInput schema / properties / word / description
```
Added value: +"the cited word"
```
- addedInput schema / properties / word / enum
```
Added value: +[
+  "Z2_a2b",
+  "Z2_abAB"
+]
```
Changed4 schema fields changedSep 5, 2026
- removedInput schema / properties / q / description
```
Removed value: -"claimed Eisenstein q, decimal"
```
- removedInput schema / properties / r / description
```
Removed value: -"claimed Eisenstein r, decimal"
```
- removedInput schema / properties / word / description
```
Removed value: -"the cited word"
```
- removedInput schema / properties / word / enum
```
Removed value: -[
-  "Z2_a2b",
-  "Z2_abAB"
-]
```
Changed4 schema fields changedSep 5, 2026
- addedInput schema / properties / q / description
```
Added value: +"claimed Eisenstein q, decimal"
```
- addedInput schema / properties / r / description
```
Added value: +"claimed Eisenstein r, decimal"
```
- addedInput schema / properties / word / description
```
Added value: +"the cited word"
```
- addedInput schema / properties / word / enum
```
Added value: +[
+  "Z2_a2b",
+  "Z2_abAB"
+]
```
Changed4 schema fields changedSep 5, 2026
- removedInput schema / properties / q / description
```
Removed value: -"claimed Eisenstein q, decimal"
```
- removedInput schema / properties / r / description
```
Removed value: -"claimed Eisenstein r, decimal"
```
- removedInput schema / properties / word / description
```
Removed value: -"the cited word"
```
- removedInput schema / properties / word / enum
```
Removed value: -[
-  "Z2_a2b",
-  "Z2_abAB"
-]
```
Changed4 schema fields changedSep 5, 2026
- addedInput schema / properties / q / description
```
Added value: +"claimed Eisenstein q, decimal"
```
- addedInput schema / properties / r / description
```
Added value: +"claimed Eisenstein r, decimal"
```
- addedInput schema / properties / word / description
```
Added value: +"the cited word"
```
- addedInput schema / properties / word / enum
```
Added value: +[
+  "Z2_a2b",
+  "Z2_abAB"
+]
```
Changed4 schema fields changedSep 5, 2026
- removedInput schema / properties / q / description
```
Removed value: -"claimed Eisenstein q, decimal"
```
- removedInput schema / properties / r / description
```
Removed value: -"claimed Eisenstein r, decimal"
```
- removedInput schema / properties / word / description
```
Removed value: -"the cited word"
```
- removedInput schema / properties / word / enum
```
Removed value: -[
-  "Z2_a2b",
-  "Z2_abAB"
-]
```
Changed4 schema fields changedSep 5, 2026
- addedInput schema / properties / q / description
```
Added value: +"claimed Eisenstein q, decimal"
```
- addedInput schema / properties / r / description
```
Added value: +"claimed Eisenstein r, decimal"
```
- addedInput schema / properties / word / description
```
Added value: +"the cited word"
```
- addedInput schema / properties / word / enum
```
Added value: +[
+  "Z2_a2b",
+  "Z2_abAB"
+]
```
Changed4 schema fields changedSep 5, 2026
- removedInput schema / properties / q / description
```
Removed value: -"claimed Eisenstein q, decimal"
```
- removedInput schema / properties / r / description
```
Removed value: -"claimed Eisenstein r, decimal"
```
- removedInput schema / properties / word / description
```
Removed value: -"the cited word"
```
- removedInput schema / properties / word / enum
```
Removed value: -[
-  "Z2_a2b",
-  "Z2_abAB"
-]
```
Changed4 schema fields changedSep 5, 2026
- addedInput schema / properties / q / description
```
Added value: +"claimed Eisenstein q, decimal"
```
- addedInput schema / properties / r / description
```
Added value: +"claimed Eisenstein r, decimal"
```
- addedInput schema / properties / word / description
```
Added value: +"the cited word"
```
- addedInput schema / properties / word / enum
```
Added value: +[
+  "Z2_a2b",
+  "Z2_abAB"
+]
```
Changed4 schema fields changedSep 5, 2026
- removedInput schema / properties / q / description
```
Removed value: -"claimed Eisenstein q, decimal"
```
- removedInput schema / properties / r / description
```
Removed value: -"claimed Eisenstein r, decimal"
```
- removedInput schema / properties / word / description
```
Removed value: -"the cited word"
```
- removedInput schema / properties / word / enum
```
Removed value: -[
-  "Z2_a2b",
-  "Z2_abAB"
-]
```
Changed4 schema fields changedSep 5, 2026
- addedInput schema / properties / q / description
```
Added value: +"claimed Eisenstein q, decimal"
```
- addedInput schema / properties / r / description
```
Added value: +"claimed Eisenstein r, decimal"
```
- addedInput schema / properties / word / description
```
Added value: +"the cited word"
```
- addedInput schema / properties / word / enum
```
Added value: +[
+  "Z2_a2b",
+  "Z2_abAB"
+]
```
Changed4 schema fields changedSep 5, 2026
- removedInput schema / properties / q / description
```
Removed value: -"claimed Eisenstein q, decimal"
```
- removedInput schema / properties / r / description
```
Removed value: -"claimed Eisenstein r, decimal"
```
- removedInput schema / properties / word / description
```
Removed value: -"the cited word"
```
- removedInput schema / properties / word / enum
```
Removed value: -[
-  "Z2_a2b",
-  "Z2_abAB"
-]
```
Changed4 schema fields changedSep 5, 2026
- addedInput schema / properties / q / description
```
Added value: +"claimed Eisenstein q, decimal"
```
- addedInput schema / properties / r / description
```
Added value: +"claimed Eisenstein r, decimal"
```
- addedInput schema / properties / word / description
```
Added value: +"the cited word"
```
- addedInput schema / properties / word / enum
```
Added value: +[
+  "Z2_a2b",
+  "Z2_abAB"
+]
```
Changed4 schema fields changedSep 5, 2026
- removedInput schema / properties / q / description
```
Removed value: -"claimed Eisenstein q, decimal"
```
- removedInput schema / properties / r / description
```
Removed value: -"claimed Eisenstein r, decimal"
```
- removedInput schema / properties / word / description
```
Removed value: -"the cited word"
```
- removedInput schema / properties / word / enum
```
Removed value: -[
-  "Z2_a2b",
-  "Z2_abAB"
-]
```
Changed4 schema fields changedSep 4, 2026
- addedInput schema / properties / q / description
```
Added value: +"claimed Eisenstein q, decimal"
```
- addedInput schema / properties / r / description
```
Added value: +"claimed Eisenstein r, decimal"
```
- addedInput schema / properties / word / description
```
Added value: +"the cited word"
```
- addedInput schema / properties / word / enum
```
Added value: +[
+  "Z2_a2b",
+  "Z2_abAB"
+]
```
Changed4 schema fields changedSep 4, 2026
- removedInput schema / properties / q / description
```
Removed value: -"claimed Eisenstein q, decimal"
```
- removedInput schema / properties / r / description
```
Removed value: -"claimed Eisenstein r, decimal"
```
- removedInput schema / properties / word / description
```
Removed value: -"the cited word"
```
- removedInput schema / properties / word / enum
```
Removed value: -[
-  "Z2_a2b",
-  "Z2_abAB"
-]
```
Changed4 schema fields changedSep 4, 2026
- addedInput schema / properties / q / description
```
Added value: +"claimed Eisenstein q, decimal"
```
- addedInput schema / properties / r / description
```
Added value: +"claimed Eisenstein r, decimal"
```
- addedInput schema / properties / word / description
```
Added value: +"the cited word"
```
- addedInput schema / properties / word / enum
```
Added value: +[
+  "Z2_a2b",
+  "Z2_abAB"
+]
```
Changed4 schema fields changedSep 4, 2026
- removedInput schema / properties / q / description
```
Removed value: -"claimed Eisenstein q, decimal"
```
- removedInput schema / properties / r / description
```
Removed value: -"claimed Eisenstein r, decimal"
```
- removedInput schema / properties / word / description
```
Removed value: -"the cited word"
```
- removedInput schema / properties / word / enum
```
Removed value: -[
-  "Z2_a2b",
-  "Z2_abAB"
-]
```
Changed4 schema fields changedSep 4, 2026
- addedInput schema / properties / q / description
```
Added value: +"claimed Eisenstein q, decimal"
```
- addedInput schema / properties / r / description
```
Added value: +"claimed Eisenstein r, decimal"
```
- addedInput schema / properties / word / description
```
Added value: +"the cited word"
```
- addedInput schema / properties / word / enum
```
Added value: +[
+  "Z2_a2b",
+  "Z2_abAB"
+]
```
Changed4 schema fields changedSep 4, 2026
- removedInput schema / properties / q / description
```
Removed value: -"claimed Eisenstein q, decimal"
```
- removedInput schema / properties / r / description
```
Removed value: -"claimed Eisenstein r, decimal"
```
- removedInput schema / properties / word / description
```
Removed value: -"the cited word"
```
- removedInput schema / properties / word / enum
```
Removed value: -[
-  "Z2_a2b",
-  "Z2_abAB"
-]
```
Changed4 schema fields changedSep 4, 2026
- addedInput schema / properties / q / description
```
Added value: +"claimed Eisenstein q, decimal"
```
- addedInput schema / properties / r / description
```
Added value: +"claimed Eisenstein r, decimal"
```
- addedInput schema / properties / word / description
```
Added value: +"the cited word"
```
- addedInput schema / properties / word / enum
```
Added value: +[
+  "Z2_a2b",
+  "Z2_abAB"
+]
```
Changed4 schema fields changedSep 4, 2026
- removedInput schema / properties / q / description
```
Removed value: -"claimed Eisenstein q, decimal"
```
- removedInput schema / properties / r / description
```
Removed value: -"claimed Eisenstein r, decimal"
```
- removedInput schema / properties / word / description
```
Removed value: -"the cited word"
```
- removedInput schema / properties / word / enum
```
Removed value: -[
-  "Z2_a2b",
-  "Z2_abAB"
-]
```
Changed4 schema fields changedSep 4, 2026
- addedInput schema / properties / q / description
```
Added value: +"claimed Eisenstein q, decimal"
```
- addedInput schema / properties / r / description
```
Added value: +"claimed Eisenstein r, decimal"
```
- addedInput schema / properties / word / description
```
Added value: +"the cited word"
```
- addedInput schema / properties / word / enum
```
Added value: +[
+  "Z2_a2b",
+  "Z2_abAB"
+]
```
Changed4 schema fields changedSep 4, 2026
- removedInput schema / properties / q / description
```
Removed value: -"claimed Eisenstein q, decimal"
```
- removedInput schema / properties / r / description
```
Removed value: -"claimed Eisenstein r, decimal"
```
- removedInput schema / properties / word / description
```
Removed value: -"the cited word"
```
- removedInput schema / properties / word / enum
```
Removed value: -[
-  "Z2_a2b",
-  "Z2_abAB"
-]
```
Changed4 schema fields changedSep 4, 2026
- addedInput schema / properties / q / description
```
Added value: +"claimed Eisenstein q, decimal"
```
- addedInput schema / properties / r / description
```
Added value: +"claimed Eisenstein r, decimal"
```
- addedInput schema / properties / word / description
```
Added value: +"the cited word"
```
- addedInput schema / properties / word / enum
```
Added value: +[
+  "Z2_a2b",
+  "Z2_abAB"
+]
```
Changed4 schema fields changedSep 4, 2026
- removedInput schema / properties / q / description
```
Removed value: -"claimed Eisenstein q, decimal"
```
- removedInput schema / properties / r / description
```
Removed value: -"claimed Eisenstein r, decimal"
```
- removedInput schema / properties / word / description
```
Removed value: -"the cited word"
```
- removedInput schema / properties / word / enum
```
Removed value: -[
-  "Z2_a2b",
-  "Z2_abAB"
-]
```
Changed4 schema fields changedSep 4, 2026
- addedInput schema / properties / q / description
```
Added value: +"claimed Eisenstein q, decimal"
```
- addedInput schema / properties / r / description
```
Added value: +"claimed Eisenstein r, decimal"
```
- addedInput schema / properties / word / description
```
Added value: +"the cited word"
```
- addedInput schema / properties / word / enum
```
Added value: +[
+  "Z2_a2b",
+  "Z2_abAB"
+]
```
Changed4 schema fields changedSep 4, 2026
- removedInput schema / properties / q / description
```
Removed value: -"claimed Eisenstein q, decimal"
```
- removedInput schema / properties / r / description
```
Removed value: -"claimed Eisenstein r, decimal"
```
- removedInput schema / properties / word / description
```
Removed value: -"the cited word"
```
- removedInput schema / properties / word / enum
```
Removed value: -[
-  "Z2_a2b",
-  "Z2_abAB"
-]
```
Changed4 schema fields changedSep 4, 2026
- addedInput schema / properties / q / description
```
Added value: +"claimed Eisenstein q, decimal"
```
- addedInput schema / properties / r / description
```
Added value: +"claimed Eisenstein r, decimal"
```
- addedInput schema / properties / word / description
```
Added value: +"the cited word"
```
- addedInput schema / properties / word / enum
```
Added value: +[
+  "Z2_a2b",
+  "Z2_abAB"
+]
```
Changed4 schema fields changedSep 4, 2026
- removedInput schema / properties / q / description
```
Removed value: -"claimed Eisenstein q, decimal"
```
- removedInput schema / properties / r / description
```
Removed value: -"claimed Eisenstein r, decimal"
```
- removedInput schema / properties / word / description
```
Removed value: -"the cited word"
```
- removedInput schema / properties / word / enum
```
Removed value: -[
-  "Z2_a2b",
-  "Z2_abAB"
-]
```
Changed4 schema fields changedSep 4, 2026
- addedInput schema / properties / q / description
```
Added value: +"claimed Eisenstein q, decimal"
```
- addedInput schema / properties / r / description
```
Added value: +"claimed Eisenstein r, decimal"
```
- addedInput schema / properties / word / description
```
Added value: +"the cited word"
```
- addedInput schema / properties / word / enum
```
Added value: +[
+  "Z2_a2b",
+  "Z2_abAB"
+]
```
Changed4 schema fields changedSep 4, 2026
- removedInput schema / properties / q / description
```
Removed value: -"claimed Eisenstein q, decimal"
```
- removedInput schema / properties / r / description
```
Removed value: -"claimed Eisenstein r, decimal"
```
- removedInput schema / properties / word / description
```
Removed value: -"the cited word"
```
- removedInput schema / properties / word / enum
```
Removed value: -[
-  "Z2_a2b",
-  "Z2_abAB"
-]
```
Changed4 schema fields changedSep 4, 2026
- addedInput schema / properties / q / description
```
Added value: +"claimed Eisenstein q, decimal"
```
- addedInput schema / properties / r / description
```
Added value: +"claimed Eisenstein r, decimal"
```
- addedInput schema / properties / word / description
```
Added value: +"the cited word"
```
- addedInput schema / properties / word / enum
```
Added value: +[
+  "Z2_a2b",
+  "Z2_abAB"
+]
```
Changed4 schema fields changedSep 4, 2026
- removedInput schema / properties / q / description
```
Removed value: -"claimed Eisenstein q, decimal"
```
- removedInput schema / properties / r / description
```
Removed value: -"claimed Eisenstein r, decimal"
```
- removedInput schema / properties / word / description
```
Removed value: -"the cited word"
```
- removedInput schema / properties / word / enum
```
Removed value: -[
-  "Z2_a2b",
-  "Z2_abAB"
-]
```
Changed4 schema fields changedSep 4, 2026
- addedInput schema / properties / q / description
```
Added value: +"claimed Eisenstein q, decimal"
```
- addedInput schema / properties / r / description
```
Added value: +"claimed Eisenstein r, decimal"
```
- addedInput schema / properties / word / description
```
Added value: +"the cited word"
```
- addedInput schema / properties / word / enum
```
Added value: +[
+  "Z2_a2b",
+  "Z2_abAB"
+]
```
Changed4 schema fields changedSep 3, 2026
- removedInput schema / properties / q / description
```
Removed value: -"claimed Eisenstein q, decimal"
```
- removedInput schema / properties / r / description
```
Removed value: -"claimed Eisenstein r, decimal"
```
- removedInput schema / properties / word / description
```
Removed value: -"the cited word"
```
- removedInput schema / properties / word / enum
```
Removed value: -[
-  "Z2_a2b",
-  "Z2_abAB"
-]
```
Changed4 schema fields changedSep 3, 2026
- addedInput schema / properties / q / description
```
Added value: +"claimed Eisenstein q, decimal"
```
- addedInput schema / properties / r / description
```
Added value: +"claimed Eisenstein r, decimal"
```
- addedInput schema / properties / word / description
```
Added value: +"the cited word"
```
- addedInput schema / properties / word / enum
```
Added value: +[
+  "Z2_a2b",
+  "Z2_abAB"
+]
```
Changed4 schema fields changedSep 3, 2026
- removedInput schema / properties / q / description
```
Removed value: -"claimed Eisenstein q, decimal"
```
- removedInput schema / properties / r / description
```
Removed value: -"claimed Eisenstein r, decimal"
```
- removedInput schema / properties / word / description
```
Removed value: -"the cited word"
```
- removedInput schema / properties / word / enum
```
Removed value: -[
-  "Z2_a2b",
-  "Z2_abAB"
-]
```
Changed4 schema fields changedSep 3, 2026
- addedInput schema / properties / q / description
```
Added value: +"claimed Eisenstein q, decimal"
```
- addedInput schema / properties / r / description
```
Added value: +"claimed Eisenstein r, decimal"
```
- addedInput schema / properties / word / description
```
Added value: +"the cited word"
```
- addedInput schema / properties / word / enum
```
Added value: +[
+  "Z2_a2b",
+  "Z2_abAB"
+]
```
Changed4 schema fields changedSep 3, 2026
- removedInput schema / properties / q / description
```
Removed value: -"claimed Eisenstein q, decimal"
```
- removedInput schema / properties / r / description
```
Removed value: -"claimed Eisenstein r, decimal"
```
- removedInput schema / properties / word / description
```
Removed value: -"the cited word"
```
- removedInput schema / properties / word / enum
```
Removed value: -[
-  "Z2_a2b",
-  "Z2_abAB"
-]
```
Changed4 schema fields changedSep 3, 2026
- addedInput schema / properties / q / description
```
Added value: +"claimed Eisenstein q, decimal"
```
- addedInput schema / properties / r / description
```
Added value: +"claimed Eisenstein r, decimal"
```
- addedInput schema / properties / word / description
```
Added value: +"the cited word"
```
- addedInput schema / properties / word / enum
```
Added value: +[
+  "Z2_a2b",
+  "Z2_abAB"
+]
```
Changed4 schema fields changedSep 3, 2026
- removedInput schema / properties / q / description
```
Removed value: -"claimed Eisenstein q, decimal"
```
- removedInput schema / properties / r / description
```
Removed value: -"claimed Eisenstein r, decimal"
```
- removedInput schema / properties / word / description
```
Removed value: -"the cited word"
```
- removedInput schema / properties / word / enum
```
Removed value: -[
-  "Z2_a2b",
-  "Z2_abAB"
-]
```
Changed4 schema fields changedSep 3, 2026
- addedInput schema / properties / q / description
```
Added value: +"claimed Eisenstein q, decimal"
```
- addedInput schema / properties / r / description
```
Added value: +"claimed Eisenstein r, decimal"
```
- addedInput schema / properties / word / description
```
Added value: +"the cited word"
```
- addedInput schema / properties / word / enum
```
Added value: +[
+  "Z2_a2b",
+  "Z2_abAB"
+]
```
Changed4 schema fields changedSep 3, 2026
- removedInput schema / properties / q / description
```
Removed value: -"claimed Eisenstein q, decimal"
```
- removedInput schema / properties / r / description
```
Removed value: -"claimed Eisenstein r, decimal"
```
- removedInput schema / properties / word / description
```
Removed value: -"the cited word"
```
- removedInput schema / properties / word / enum
```
Removed value: -[
-  "Z2_a2b",
-  "Z2_abAB"
-]
```
Changed4 schema fields changedSep 3, 2026
- addedInput schema / properties / q / description
```
Added value: +"claimed Eisenstein q, decimal"
```
- addedInput schema / properties / r / description
```
Added value: +"claimed Eisenstein r, decimal"
```
- addedInput schema / properties / word / description
```
Added value: +"the cited word"
```
- addedInput schema / properties / word / enum
```
Added value: +[
+  "Z2_a2b",
+  "Z2_abAB"
+]
```
Changed4 schema fields changedSep 3, 2026
- removedInput schema / properties / q / description
```
Removed value: -"claimed Eisenstein q, decimal"
```
- removedInput schema / properties / r / description
```
Removed value: -"claimed Eisenstein r, decimal"
```
- removedInput schema / properties / word / description
```
Removed value: -"the cited word"
```
- removedInput schema / properties / word / enum
```
Removed value: -[
-  "Z2_a2b",
-  "Z2_abAB"
-]
```
Changed4 schema fields changedSep 3, 2026
- addedInput schema / properties / q / description
```
Added value: +"claimed Eisenstein q, decimal"
```
- addedInput schema / properties / r / description
```
Added value: +"claimed Eisenstein r, decimal"
```
- addedInput schema / properties / word / description
```
Added value: +"the cited word"
```
- addedInput schema / properties / word / enum
```
Added value: +[
+  "Z2_a2b",
+  "Z2_abAB"
+]
```
Changed4 schema fields changedSep 3, 2026
- removedInput schema / properties / q / description
```
Removed value: -"claimed Eisenstein q, decimal"
```
- removedInput schema / properties / r / description
```
Removed value: -"claimed Eisenstein r, decimal"
```
- removedInput schema / properties / word / description
```
Removed value: -"the cited word"
```
- removedInput schema / properties / word / enum
```
Removed value: -[
-  "Z2_a2b",
-  "Z2_abAB"
-]
```
Changed4 schema fields changedSep 3, 2026
- addedInput schema / properties / q / description
```
Added value: +"claimed Eisenstein q, decimal"
```
- addedInput schema / properties / r / description
```
Added value: +"claimed Eisenstein r, decimal"
```
- addedInput schema / properties / word / description
```
Added value: +"the cited word"
```
- addedInput schema / properties / word / enum
```
Added value: +[
+  "Z2_a2b",
+  "Z2_abAB"
+]
```
Changed4 schema fields changedSep 3, 2026
- removedInput schema / properties / q / description
```
Removed value: -"claimed Eisenstein q, decimal"
```
- removedInput schema / properties / r / description
```
Removed value: -"claimed Eisenstein r, decimal"
```
- removedInput schema / properties / word / description
```
Removed value: -"the cited word"
```
- removedInput schema / properties / word / enum
```
Removed value: -[
-  "Z2_a2b",
-  "Z2_abAB"
-]
```
Changed4 schema fields changedSep 3, 2026
- addedInput schema / properties / q / description
```
Added value: +"claimed Eisenstein q, decimal"
```
- addedInput schema / properties / r / description
```
Added value: +"claimed Eisenstein r, decimal"
```
- addedInput schema / properties / word / description
```
Added value: +"the cited word"
```
- addedInput schema / properties / word / enum
```
Added value: +[
+  "Z2_a2b",
+  "Z2_abAB"
+]
```
Changed4 schema fields changedSep 3, 2026
- removedInput schema / properties / q / description
```
Removed value: -"claimed Eisenstein q, decimal"
```
- removedInput schema / properties / r / description
```
Removed value: -"claimed Eisenstein r, decimal"
```
- removedInput schema / properties / word / description
```
Removed value: -"the cited word"
```
- removedInput schema / properties / word / enum
```
Removed value: -[
-  "Z2_a2b",
-  "Z2_abAB"
-]
```
Changed4 schema fields changedSep 3, 2026
- addedInput schema / properties / q / description
```
Added value: +"claimed Eisenstein q, decimal"
```
- addedInput schema / properties / r / description
```
Added value: +"claimed Eisenstein r, decimal"
```
- addedInput schema / properties / word / description
```
Added value: +"the cited word"
```
- addedInput schema / properties / word / enum
```
Added value: +[
+  "Z2_a2b",
+  "Z2_abAB"
+]
```
Changed4 schema fields changedSep 3, 2026
- removedInput schema / properties / q / description
```
Removed value: -"claimed Eisenstein q, decimal"
```
- removedInput schema / properties / r / description
```
Removed value: -"claimed Eisenstein r, decimal"
```
- removedInput schema / properties / word / description
```
Removed value: -"the cited word"
```
- removedInput schema / properties / word / enum
```
Removed value: -[
-  "Z2_a2b",
-  "Z2_abAB"
-]
```
Changed4 schema fields changedSep 3, 2026
- addedInput schema / properties / q / description
```
Added value: +"claimed Eisenstein q, decimal"
```
- addedInput schema / properties / r / description
```
Added value: +"claimed Eisenstein r, decimal"
```
- addedInput schema / properties / word / description
```
Added value: +"the cited word"
```
- addedInput schema / properties / word / enum
```
Added value: +[
+  "Z2_a2b",
+  "Z2_abAB"
+]
```
Changed4 schema fields changedSep 3, 2026
- removedInput schema / properties / q / description
```
Removed value: -"claimed Eisenstein q, decimal"
```
- removedInput schema / properties / r / description
```
Removed value: -"claimed Eisenstein r, decimal"
```
- removedInput schema / properties / word / description
```
Removed value: -"the cited word"
```
- removedInput schema / properties / word / enum
```
Removed value: -[
-  "Z2_a2b",
-  "Z2_abAB"
-]
```
Changed4 schema fields changedSep 3, 2026
- addedInput schema / properties / q / description
```
Added value: +"claimed Eisenstein q, decimal"
```
- addedInput schema / properties / r / description
```
Added value: +"claimed Eisenstein r, decimal"
```
- addedInput schema / properties / word / description
```
Added value: +"the cited word"
```
- addedInput schema / properties / word / enum
```
Added value: +[
+  "Z2_a2b",
+  "Z2_abAB"
+]
```
Changed4 schema fields changedSep 2, 2026
- removedInput schema / properties / q / description
```
Removed value: -"claimed Eisenstein q, decimal"
```
- removedInput schema / properties / r / description
```
Removed value: -"claimed Eisenstein r, decimal"
```
- removedInput schema / properties / word / description
```
Removed value: -"the cited word"
```
- removedInput schema / properties / word / enum
```
Removed value: -[
-  "Z2_a2b",
-  "Z2_abAB"
-]
```
Changed4 schema fields changedSep 2, 2026
- addedInput schema / properties / q / description
```
Added value: +"claimed Eisenstein q, decimal"
```
- addedInput schema / properties / r / description
```
Added value: +"claimed Eisenstein r, decimal"
```
- addedInput schema / properties / word / description
```
Added value: +"the cited word"
```
- addedInput schema / properties / word / enum
```
Added value: +[
+  "Z2_a2b",
+  "Z2_abAB"
+]
```
First observedSep 1, 2026

TDQS

A3.7/5.0

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 it does disclose the key behaviors: the outcome semantics (WIN when the pair matches, MISS otherwise) and an input-validation rule ('Floats refused'). It does not describe permissions or side effects, but for a pure verifier the result and rejection behavior are the traits that matter.

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?

The purpose is front-loaded in the first clause and the four short sentences each carry a distinct fact (scope, constraint, outcome, input rule). It is dense with jargon but not padded.

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

Completeness3/5

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

There is no output schema, and the description partially compensates by describing WIN/MISS results. But 'MISS naming it' is ambiguous and key terms like 'sealed pair' are left undefined, so an agent has an incomplete picture of what the response actually reports without domain knowledge.

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

Parameters4/5

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

Schema coverage is 100%, so the baseline is 3. The description adds a meaningful constraint not fully captured by the schema: q and r are 'claimed integers' and floats are refused, clarifying that the decimal-typed string params must be integral. The word parameter's sealed-corpus context is reinforced.

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?

The description names a specific verb (certify/verify) and resource (the Eisenstein pair (q, r) for a cited word), and explicitly scopes it against alternatives with 'the sealed corpus; not a group scan'. An agent can distinguish it from sibling verifiers, though the heavy domain jargon ('sealed pair', 'Eisenstein') adds cognitive load.

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?

It constrains usage by limiting word to the two cited words Z2_a2b or Z2_abAB and warns it is not a group scan, which is useful negative scoping. However, it never names which sibling tool (e.g. verify_presented_pair) to use instead when the input falls outside this narrow case, leaving the when-to-use routing implicit.

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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