Affine Earth Math Court Remote

verify_phase_kickback

QC-011 Phase kickback: certify that the presented phase equals k / 2^m exactly, as a rational. m is the register width (decimal), k the integer eigenphase index, phase the claimed rational written num/den (e.g. 1/2 for m=1, k=1). WIN or MISS with the exact rational the court computed. No estimation is performed; floats refused.

Input Schema

TableJSON Schema

Name	Required	Description
`k`	No	eigenphase index, decimal, 0 <= k < 2^m
`m`	No	register width, decimal, >= 1
`phase`	No	claimed phase as an exact rational num/den, e.g. 1/2

Schema Changelog

Changes observed during successful MCP inspections.

Changed3 schema fields changedSep 7, 2026
- addedInput schema / properties / k / description
```
Added value: +"eigenphase index, decimal, 0 <= k < 2^m"
```
- addedInput schema / properties / m / description
```
Added value: +"register width, decimal, >= 1"
```
- addedInput schema / properties / phase / description
```
Added value: +"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 7, 2026
- removedInput schema / properties / k / description
```
Removed value: -"eigenphase index, decimal, 0 <= k < 2^m"
```
- removedInput schema / properties / m / description
```
Removed value: -"register width, decimal, >= 1"
```
- removedInput schema / properties / phase / description
```
Removed value: -"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 7, 2026
- addedInput schema / properties / k / description
```
Added value: +"eigenphase index, decimal, 0 <= k < 2^m"
```
- addedInput schema / properties / m / description
```
Added value: +"register width, decimal, >= 1"
```
- addedInput schema / properties / phase / description
```
Added value: +"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 7, 2026
- removedInput schema / properties / k / description
```
Removed value: -"eigenphase index, decimal, 0 <= k < 2^m"
```
- removedInput schema / properties / m / description
```
Removed value: -"register width, decimal, >= 1"
```
- removedInput schema / properties / phase / description
```
Removed value: -"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 6, 2026
- addedInput schema / properties / k / description
```
Added value: +"eigenphase index, decimal, 0 <= k < 2^m"
```
- addedInput schema / properties / m / description
```
Added value: +"register width, decimal, >= 1"
```
- addedInput schema / properties / phase / description
```
Added value: +"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 6, 2026
- removedInput schema / properties / k / description
```
Removed value: -"eigenphase index, decimal, 0 <= k < 2^m"
```
- removedInput schema / properties / m / description
```
Removed value: -"register width, decimal, >= 1"
```
- removedInput schema / properties / phase / description
```
Removed value: -"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 6, 2026
- addedInput schema / properties / k / description
```
Added value: +"eigenphase index, decimal, 0 <= k < 2^m"
```
- addedInput schema / properties / m / description
```
Added value: +"register width, decimal, >= 1"
```
- addedInput schema / properties / phase / description
```
Added value: +"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 6, 2026
- removedInput schema / properties / k / description
```
Removed value: -"eigenphase index, decimal, 0 <= k < 2^m"
```
- removedInput schema / properties / m / description
```
Removed value: -"register width, decimal, >= 1"
```
- removedInput schema / properties / phase / description
```
Removed value: -"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 6, 2026
- addedInput schema / properties / k / description
```
Added value: +"eigenphase index, decimal, 0 <= k < 2^m"
```
- addedInput schema / properties / m / description
```
Added value: +"register width, decimal, >= 1"
```
- addedInput schema / properties / phase / description
```
Added value: +"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 6, 2026
- removedInput schema / properties / k / description
```
Removed value: -"eigenphase index, decimal, 0 <= k < 2^m"
```
- removedInput schema / properties / m / description
```
Removed value: -"register width, decimal, >= 1"
```
- removedInput schema / properties / phase / description
```
Removed value: -"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 6, 2026
- addedInput schema / properties / k / description
```
Added value: +"eigenphase index, decimal, 0 <= k < 2^m"
```
- addedInput schema / properties / m / description
```
Added value: +"register width, decimal, >= 1"
```
- addedInput schema / properties / phase / description
```
Added value: +"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 6, 2026
- removedInput schema / properties / k / description
```
Removed value: -"eigenphase index, decimal, 0 <= k < 2^m"
```
- removedInput schema / properties / m / description
```
Removed value: -"register width, decimal, >= 1"
```
- removedInput schema / properties / phase / description
```
Removed value: -"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 6, 2026
- addedInput schema / properties / k / description
```
Added value: +"eigenphase index, decimal, 0 <= k < 2^m"
```
- addedInput schema / properties / m / description
```
Added value: +"register width, decimal, >= 1"
```
- addedInput schema / properties / phase / description
```
Added value: +"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 6, 2026
- removedInput schema / properties / k / description
```
Removed value: -"eigenphase index, decimal, 0 <= k < 2^m"
```
- removedInput schema / properties / m / description
```
Removed value: -"register width, decimal, >= 1"
```
- removedInput schema / properties / phase / description
```
Removed value: -"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 6, 2026
- addedInput schema / properties / k / description
```
Added value: +"eigenphase index, decimal, 0 <= k < 2^m"
```
- addedInput schema / properties / m / description
```
Added value: +"register width, decimal, >= 1"
```
- addedInput schema / properties / phase / description
```
Added value: +"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 6, 2026
- removedInput schema / properties / k / description
```
Removed value: -"eigenphase index, decimal, 0 <= k < 2^m"
```
- removedInput schema / properties / m / description
```
Removed value: -"register width, decimal, >= 1"
```
- removedInput schema / properties / phase / description
```
Removed value: -"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 6, 2026
- addedInput schema / properties / k / description
```
Added value: +"eigenphase index, decimal, 0 <= k < 2^m"
```
- addedInput schema / properties / m / description
```
Added value: +"register width, decimal, >= 1"
```
- addedInput schema / properties / phase / description
```
Added value: +"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 6, 2026
- removedInput schema / properties / k / description
```
Removed value: -"eigenphase index, decimal, 0 <= k < 2^m"
```
- removedInput schema / properties / m / description
```
Removed value: -"register width, decimal, >= 1"
```
- removedInput schema / properties / phase / description
```
Removed value: -"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 6, 2026
- addedInput schema / properties / k / description
```
Added value: +"eigenphase index, decimal, 0 <= k < 2^m"
```
- addedInput schema / properties / m / description
```
Added value: +"register width, decimal, >= 1"
```
- addedInput schema / properties / phase / description
```
Added value: +"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 6, 2026
- removedInput schema / properties / k / description
```
Removed value: -"eigenphase index, decimal, 0 <= k < 2^m"
```
- removedInput schema / properties / m / description
```
Removed value: -"register width, decimal, >= 1"
```
- removedInput schema / properties / phase / description
```
Removed value: -"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 6, 2026
- addedInput schema / properties / k / description
```
Added value: +"eigenphase index, decimal, 0 <= k < 2^m"
```
- addedInput schema / properties / m / description
```
Added value: +"register width, decimal, >= 1"
```
- addedInput schema / properties / phase / description
```
Added value: +"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 6, 2026
- removedInput schema / properties / k / description
```
Removed value: -"eigenphase index, decimal, 0 <= k < 2^m"
```
- removedInput schema / properties / m / description
```
Removed value: -"register width, decimal, >= 1"
```
- removedInput schema / properties / phase / description
```
Removed value: -"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 6, 2026
- addedInput schema / properties / k / description
```
Added value: +"eigenphase index, decimal, 0 <= k < 2^m"
```
- addedInput schema / properties / m / description
```
Added value: +"register width, decimal, >= 1"
```
- addedInput schema / properties / phase / description
```
Added value: +"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 6, 2026
- removedInput schema / properties / k / description
```
Removed value: -"eigenphase index, decimal, 0 <= k < 2^m"
```
- removedInput schema / properties / m / description
```
Removed value: -"register width, decimal, >= 1"
```
- removedInput schema / properties / phase / description
```
Removed value: -"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 6, 2026
- addedInput schema / properties / k / description
```
Added value: +"eigenphase index, decimal, 0 <= k < 2^m"
```
- addedInput schema / properties / m / description
```
Added value: +"register width, decimal, >= 1"
```
- addedInput schema / properties / phase / description
```
Added value: +"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 6, 2026
- removedInput schema / properties / k / description
```
Removed value: -"eigenphase index, decimal, 0 <= k < 2^m"
```
- removedInput schema / properties / m / description
```
Removed value: -"register width, decimal, >= 1"
```
- removedInput schema / properties / phase / description
```
Removed value: -"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 6, 2026
- addedInput schema / properties / k / description
```
Added value: +"eigenphase index, decimal, 0 <= k < 2^m"
```
- addedInput schema / properties / m / description
```
Added value: +"register width, decimal, >= 1"
```
- addedInput schema / properties / phase / description
```
Added value: +"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 6, 2026
- removedInput schema / properties / k / description
```
Removed value: -"eigenphase index, decimal, 0 <= k < 2^m"
```
- removedInput schema / properties / m / description
```
Removed value: -"register width, decimal, >= 1"
```
- removedInput schema / properties / phase / description
```
Removed value: -"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 6, 2026
- addedInput schema / properties / k / description
```
Added value: +"eigenphase index, decimal, 0 <= k < 2^m"
```
- addedInput schema / properties / m / description
```
Added value: +"register width, decimal, >= 1"
```
- addedInput schema / properties / phase / description
```
Added value: +"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 6, 2026
- removedInput schema / properties / k / description
```
Removed value: -"eigenphase index, decimal, 0 <= k < 2^m"
```
- removedInput schema / properties / m / description
```
Removed value: -"register width, decimal, >= 1"
```
- removedInput schema / properties / phase / description
```
Removed value: -"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 6, 2026
- addedInput schema / properties / k / description
```
Added value: +"eigenphase index, decimal, 0 <= k < 2^m"
```
- addedInput schema / properties / m / description
```
Added value: +"register width, decimal, >= 1"
```
- addedInput schema / properties / phase / description
```
Added value: +"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 6, 2026
- removedInput schema / properties / k / description
```
Removed value: -"eigenphase index, decimal, 0 <= k < 2^m"
```
- removedInput schema / properties / m / description
```
Removed value: -"register width, decimal, >= 1"
```
- removedInput schema / properties / phase / description
```
Removed value: -"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 6, 2026
- addedInput schema / properties / k / description
```
Added value: +"eigenphase index, decimal, 0 <= k < 2^m"
```
- addedInput schema / properties / m / description
```
Added value: +"register width, decimal, >= 1"
```
- addedInput schema / properties / phase / description
```
Added value: +"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 6, 2026
- removedInput schema / properties / k / description
```
Removed value: -"eigenphase index, decimal, 0 <= k < 2^m"
```
- removedInput schema / properties / m / description
```
Removed value: -"register width, decimal, >= 1"
```
- removedInput schema / properties / phase / description
```
Removed value: -"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 6, 2026
- addedInput schema / properties / k / description
```
Added value: +"eigenphase index, decimal, 0 <= k < 2^m"
```
- addedInput schema / properties / m / description
```
Added value: +"register width, decimal, >= 1"
```
- addedInput schema / properties / phase / description
```
Added value: +"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 5, 2026
- removedInput schema / properties / k / description
```
Removed value: -"eigenphase index, decimal, 0 <= k < 2^m"
```
- removedInput schema / properties / m / description
```
Removed value: -"register width, decimal, >= 1"
```
- removedInput schema / properties / phase / description
```
Removed value: -"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 5, 2026
- addedInput schema / properties / k / description
```
Added value: +"eigenphase index, decimal, 0 <= k < 2^m"
```
- addedInput schema / properties / m / description
```
Added value: +"register width, decimal, >= 1"
```
- addedInput schema / properties / phase / description
```
Added value: +"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 5, 2026
- removedInput schema / properties / k / description
```
Removed value: -"eigenphase index, decimal, 0 <= k < 2^m"
```
- removedInput schema / properties / m / description
```
Removed value: -"register width, decimal, >= 1"
```
- removedInput schema / properties / phase / description
```
Removed value: -"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 5, 2026
- addedInput schema / properties / k / description
```
Added value: +"eigenphase index, decimal, 0 <= k < 2^m"
```
- addedInput schema / properties / m / description
```
Added value: +"register width, decimal, >= 1"
```
- addedInput schema / properties / phase / description
```
Added value: +"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 5, 2026
- removedInput schema / properties / k / description
```
Removed value: -"eigenphase index, decimal, 0 <= k < 2^m"
```
- removedInput schema / properties / m / description
```
Removed value: -"register width, decimal, >= 1"
```
- removedInput schema / properties / phase / description
```
Removed value: -"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 5, 2026
- addedInput schema / properties / k / description
```
Added value: +"eigenphase index, decimal, 0 <= k < 2^m"
```
- addedInput schema / properties / m / description
```
Added value: +"register width, decimal, >= 1"
```
- addedInput schema / properties / phase / description
```
Added value: +"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 5, 2026
- removedInput schema / properties / k / description
```
Removed value: -"eigenphase index, decimal, 0 <= k < 2^m"
```
- removedInput schema / properties / m / description
```
Removed value: -"register width, decimal, >= 1"
```
- removedInput schema / properties / phase / description
```
Removed value: -"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 5, 2026
- addedInput schema / properties / k / description
```
Added value: +"eigenphase index, decimal, 0 <= k < 2^m"
```
- addedInput schema / properties / m / description
```
Added value: +"register width, decimal, >= 1"
```
- addedInput schema / properties / phase / description
```
Added value: +"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 5, 2026
- removedInput schema / properties / k / description
```
Removed value: -"eigenphase index, decimal, 0 <= k < 2^m"
```
- removedInput schema / properties / m / description
```
Removed value: -"register width, decimal, >= 1"
```
- removedInput schema / properties / phase / description
```
Removed value: -"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 5, 2026
- addedInput schema / properties / k / description
```
Added value: +"eigenphase index, decimal, 0 <= k < 2^m"
```
- addedInput schema / properties / m / description
```
Added value: +"register width, decimal, >= 1"
```
- addedInput schema / properties / phase / description
```
Added value: +"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 5, 2026
- removedInput schema / properties / k / description
```
Removed value: -"eigenphase index, decimal, 0 <= k < 2^m"
```
- removedInput schema / properties / m / description
```
Removed value: -"register width, decimal, >= 1"
```
- removedInput schema / properties / phase / description
```
Removed value: -"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 5, 2026
- addedInput schema / properties / k / description
```
Added value: +"eigenphase index, decimal, 0 <= k < 2^m"
```
- addedInput schema / properties / m / description
```
Added value: +"register width, decimal, >= 1"
```
- addedInput schema / properties / phase / description
```
Added value: +"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 5, 2026
- removedInput schema / properties / k / description
```
Removed value: -"eigenphase index, decimal, 0 <= k < 2^m"
```
- removedInput schema / properties / m / description
```
Removed value: -"register width, decimal, >= 1"
```
- removedInput schema / properties / phase / description
```
Removed value: -"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 5, 2026
- addedInput schema / properties / k / description
```
Added value: +"eigenphase index, decimal, 0 <= k < 2^m"
```
- addedInput schema / properties / m / description
```
Added value: +"register width, decimal, >= 1"
```
- addedInput schema / properties / phase / description
```
Added value: +"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 5, 2026
- removedInput schema / properties / k / description
```
Removed value: -"eigenphase index, decimal, 0 <= k < 2^m"
```
- removedInput schema / properties / m / description
```
Removed value: -"register width, decimal, >= 1"
```
- removedInput schema / properties / phase / description
```
Removed value: -"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 5, 2026
- addedInput schema / properties / k / description
```
Added value: +"eigenphase index, decimal, 0 <= k < 2^m"
```
- addedInput schema / properties / m / description
```
Added value: +"register width, decimal, >= 1"
```
- addedInput schema / properties / phase / description
```
Added value: +"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 5, 2026
- removedInput schema / properties / k / description
```
Removed value: -"eigenphase index, decimal, 0 <= k < 2^m"
```
- removedInput schema / properties / m / description
```
Removed value: -"register width, decimal, >= 1"
```
- removedInput schema / properties / phase / description
```
Removed value: -"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 5, 2026
- addedInput schema / properties / k / description
```
Added value: +"eigenphase index, decimal, 0 <= k < 2^m"
```
- addedInput schema / properties / m / description
```
Added value: +"register width, decimal, >= 1"
```
- addedInput schema / properties / phase / description
```
Added value: +"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 5, 2026
- removedInput schema / properties / k / description
```
Removed value: -"eigenphase index, decimal, 0 <= k < 2^m"
```
- removedInput schema / properties / m / description
```
Removed value: -"register width, decimal, >= 1"
```
- removedInput schema / properties / phase / description
```
Removed value: -"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 5, 2026
- addedInput schema / properties / k / description
```
Added value: +"eigenphase index, decimal, 0 <= k < 2^m"
```
- addedInput schema / properties / m / description
```
Added value: +"register width, decimal, >= 1"
```
- addedInput schema / properties / phase / description
```
Added value: +"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 5, 2026
- removedInput schema / properties / k / description
```
Removed value: -"eigenphase index, decimal, 0 <= k < 2^m"
```
- removedInput schema / properties / m / description
```
Removed value: -"register width, decimal, >= 1"
```
- removedInput schema / properties / phase / description
```
Removed value: -"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 5, 2026
- addedInput schema / properties / k / description
```
Added value: +"eigenphase index, decimal, 0 <= k < 2^m"
```
- addedInput schema / properties / m / description
```
Added value: +"register width, decimal, >= 1"
```
- addedInput schema / properties / phase / description
```
Added value: +"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 5, 2026
- removedInput schema / properties / k / description
```
Removed value: -"eigenphase index, decimal, 0 <= k < 2^m"
```
- removedInput schema / properties / m / description
```
Removed value: -"register width, decimal, >= 1"
```
- removedInput schema / properties / phase / description
```
Removed value: -"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 5, 2026
- addedInput schema / properties / k / description
```
Added value: +"eigenphase index, decimal, 0 <= k < 2^m"
```
- addedInput schema / properties / m / description
```
Added value: +"register width, decimal, >= 1"
```
- addedInput schema / properties / phase / description
```
Added value: +"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 5, 2026
- removedInput schema / properties / k / description
```
Removed value: -"eigenphase index, decimal, 0 <= k < 2^m"
```
- removedInput schema / properties / m / description
```
Removed value: -"register width, decimal, >= 1"
```
- removedInput schema / properties / phase / description
```
Removed value: -"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 5, 2026
- addedInput schema / properties / k / description
```
Added value: +"eigenphase index, decimal, 0 <= k < 2^m"
```
- addedInput schema / properties / m / description
```
Added value: +"register width, decimal, >= 1"
```
- addedInput schema / properties / phase / description
```
Added value: +"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 5, 2026
- removedInput schema / properties / k / description
```
Removed value: -"eigenphase index, decimal, 0 <= k < 2^m"
```
- removedInput schema / properties / m / description
```
Removed value: -"register width, decimal, >= 1"
```
- removedInput schema / properties / phase / description
```
Removed value: -"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 5, 2026
- addedInput schema / properties / k / description
```
Added value: +"eigenphase index, decimal, 0 <= k < 2^m"
```
- addedInput schema / properties / m / description
```
Added value: +"register width, decimal, >= 1"
```
- addedInput schema / properties / phase / description
```
Added value: +"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 5, 2026
- removedInput schema / properties / k / description
```
Removed value: -"eigenphase index, decimal, 0 <= k < 2^m"
```
- removedInput schema / properties / m / description
```
Removed value: -"register width, decimal, >= 1"
```
- removedInput schema / properties / phase / description
```
Removed value: -"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 4, 2026
- addedInput schema / properties / k / description
```
Added value: +"eigenphase index, decimal, 0 <= k < 2^m"
```
- addedInput schema / properties / m / description
```
Added value: +"register width, decimal, >= 1"
```
- addedInput schema / properties / phase / description
```
Added value: +"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 4, 2026
- removedInput schema / properties / k / description
```
Removed value: -"eigenphase index, decimal, 0 <= k < 2^m"
```
- removedInput schema / properties / m / description
```
Removed value: -"register width, decimal, >= 1"
```
- removedInput schema / properties / phase / description
```
Removed value: -"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 4, 2026
- addedInput schema / properties / k / description
```
Added value: +"eigenphase index, decimal, 0 <= k < 2^m"
```
- addedInput schema / properties / m / description
```
Added value: +"register width, decimal, >= 1"
```
- addedInput schema / properties / phase / description
```
Added value: +"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 4, 2026
- removedInput schema / properties / k / description
```
Removed value: -"eigenphase index, decimal, 0 <= k < 2^m"
```
- removedInput schema / properties / m / description
```
Removed value: -"register width, decimal, >= 1"
```
- removedInput schema / properties / phase / description
```
Removed value: -"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 4, 2026
- addedInput schema / properties / k / description
```
Added value: +"eigenphase index, decimal, 0 <= k < 2^m"
```
- addedInput schema / properties / m / description
```
Added value: +"register width, decimal, >= 1"
```
- addedInput schema / properties / phase / description
```
Added value: +"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 4, 2026
- removedInput schema / properties / k / description
```
Removed value: -"eigenphase index, decimal, 0 <= k < 2^m"
```
- removedInput schema / properties / m / description
```
Removed value: -"register width, decimal, >= 1"
```
- removedInput schema / properties / phase / description
```
Removed value: -"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 4, 2026
- addedInput schema / properties / k / description
```
Added value: +"eigenphase index, decimal, 0 <= k < 2^m"
```
- addedInput schema / properties / m / description
```
Added value: +"register width, decimal, >= 1"
```
- addedInput schema / properties / phase / description
```
Added value: +"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 4, 2026
- removedInput schema / properties / k / description
```
Removed value: -"eigenphase index, decimal, 0 <= k < 2^m"
```
- removedInput schema / properties / m / description
```
Removed value: -"register width, decimal, >= 1"
```
- removedInput schema / properties / phase / description
```
Removed value: -"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 4, 2026
- addedInput schema / properties / k / description
```
Added value: +"eigenphase index, decimal, 0 <= k < 2^m"
```
- addedInput schema / properties / m / description
```
Added value: +"register width, decimal, >= 1"
```
- addedInput schema / properties / phase / description
```
Added value: +"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 4, 2026
- removedInput schema / properties / k / description
```
Removed value: -"eigenphase index, decimal, 0 <= k < 2^m"
```
- removedInput schema / properties / m / description
```
Removed value: -"register width, decimal, >= 1"
```
- removedInput schema / properties / phase / description
```
Removed value: -"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 4, 2026
- addedInput schema / properties / k / description
```
Added value: +"eigenphase index, decimal, 0 <= k < 2^m"
```
- addedInput schema / properties / m / description
```
Added value: +"register width, decimal, >= 1"
```
- addedInput schema / properties / phase / description
```
Added value: +"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 4, 2026
- removedInput schema / properties / k / description
```
Removed value: -"eigenphase index, decimal, 0 <= k < 2^m"
```
- removedInput schema / properties / m / description
```
Removed value: -"register width, decimal, >= 1"
```
- removedInput schema / properties / phase / description
```
Removed value: -"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 4, 2026
- addedInput schema / properties / k / description
```
Added value: +"eigenphase index, decimal, 0 <= k < 2^m"
```
- addedInput schema / properties / m / description
```
Added value: +"register width, decimal, >= 1"
```
- addedInput schema / properties / phase / description
```
Added value: +"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 4, 2026
- removedInput schema / properties / k / description
```
Removed value: -"eigenphase index, decimal, 0 <= k < 2^m"
```
- removedInput schema / properties / m / description
```
Removed value: -"register width, decimal, >= 1"
```
- removedInput schema / properties / phase / description
```
Removed value: -"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 4, 2026
- addedInput schema / properties / k / description
```
Added value: +"eigenphase index, decimal, 0 <= k < 2^m"
```
- addedInput schema / properties / m / description
```
Added value: +"register width, decimal, >= 1"
```
- addedInput schema / properties / phase / description
```
Added value: +"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 4, 2026
- removedInput schema / properties / k / description
```
Removed value: -"eigenphase index, decimal, 0 <= k < 2^m"
```
- removedInput schema / properties / m / description
```
Removed value: -"register width, decimal, >= 1"
```
- removedInput schema / properties / phase / description
```
Removed value: -"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 4, 2026
- addedInput schema / properties / k / description
```
Added value: +"eigenphase index, decimal, 0 <= k < 2^m"
```
- addedInput schema / properties / m / description
```
Added value: +"register width, decimal, >= 1"
```
- addedInput schema / properties / phase / description
```
Added value: +"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 4, 2026
- removedInput schema / properties / k / description
```
Removed value: -"eigenphase index, decimal, 0 <= k < 2^m"
```
- removedInput schema / properties / m / description
```
Removed value: -"register width, decimal, >= 1"
```
- removedInput schema / properties / phase / description
```
Removed value: -"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 4, 2026
- addedInput schema / properties / k / description
```
Added value: +"eigenphase index, decimal, 0 <= k < 2^m"
```
- addedInput schema / properties / m / description
```
Added value: +"register width, decimal, >= 1"
```
- addedInput schema / properties / phase / description
```
Added value: +"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 4, 2026
- removedInput schema / properties / k / description
```
Removed value: -"eigenphase index, decimal, 0 <= k < 2^m"
```
- removedInput schema / properties / m / description
```
Removed value: -"register width, decimal, >= 1"
```
- removedInput schema / properties / phase / description
```
Removed value: -"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 4, 2026
- addedInput schema / properties / k / description
```
Added value: +"eigenphase index, decimal, 0 <= k < 2^m"
```
- addedInput schema / properties / m / description
```
Added value: +"register width, decimal, >= 1"
```
- addedInput schema / properties / phase / description
```
Added value: +"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 3, 2026
- removedInput schema / properties / k / description
```
Removed value: -"eigenphase index, decimal, 0 <= k < 2^m"
```
- removedInput schema / properties / m / description
```
Removed value: -"register width, decimal, >= 1"
```
- removedInput schema / properties / phase / description
```
Removed value: -"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 3, 2026
- addedInput schema / properties / k / description
```
Added value: +"eigenphase index, decimal, 0 <= k < 2^m"
```
- addedInput schema / properties / m / description
```
Added value: +"register width, decimal, >= 1"
```
- addedInput schema / properties / phase / description
```
Added value: +"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 3, 2026
- removedInput schema / properties / k / description
```
Removed value: -"eigenphase index, decimal, 0 <= k < 2^m"
```
- removedInput schema / properties / m / description
```
Removed value: -"register width, decimal, >= 1"
```
- removedInput schema / properties / phase / description
```
Removed value: -"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 3, 2026
- addedInput schema / properties / k / description
```
Added value: +"eigenphase index, decimal, 0 <= k < 2^m"
```
- addedInput schema / properties / m / description
```
Added value: +"register width, decimal, >= 1"
```
- addedInput schema / properties / phase / description
```
Added value: +"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 3, 2026
- removedInput schema / properties / k / description
```
Removed value: -"eigenphase index, decimal, 0 <= k < 2^m"
```
- removedInput schema / properties / m / description
```
Removed value: -"register width, decimal, >= 1"
```
- removedInput schema / properties / phase / description
```
Removed value: -"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 3, 2026
- addedInput schema / properties / k / description
```
Added value: +"eigenphase index, decimal, 0 <= k < 2^m"
```
- addedInput schema / properties / m / description
```
Added value: +"register width, decimal, >= 1"
```
- addedInput schema / properties / phase / description
```
Added value: +"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 3, 2026
- removedInput schema / properties / k / description
```
Removed value: -"eigenphase index, decimal, 0 <= k < 2^m"
```
- removedInput schema / properties / m / description
```
Removed value: -"register width, decimal, >= 1"
```
- removedInput schema / properties / phase / description
```
Removed value: -"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 3, 2026
- addedInput schema / properties / k / description
```
Added value: +"eigenphase index, decimal, 0 <= k < 2^m"
```
- addedInput schema / properties / m / description
```
Added value: +"register width, decimal, >= 1"
```
- addedInput schema / properties / phase / description
```
Added value: +"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 3, 2026
- removedInput schema / properties / k / description
```
Removed value: -"eigenphase index, decimal, 0 <= k < 2^m"
```
- removedInput schema / properties / m / description
```
Removed value: -"register width, decimal, >= 1"
```
- removedInput schema / properties / phase / description
```
Removed value: -"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 3, 2026
- addedInput schema / properties / k / description
```
Added value: +"eigenphase index, decimal, 0 <= k < 2^m"
```
- addedInput schema / properties / m / description
```
Added value: +"register width, decimal, >= 1"
```
- addedInput schema / properties / phase / description
```
Added value: +"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 3, 2026
- removedInput schema / properties / k / description
```
Removed value: -"eigenphase index, decimal, 0 <= k < 2^m"
```
- removedInput schema / properties / m / description
```
Removed value: -"register width, decimal, >= 1"
```
- removedInput schema / properties / phase / description
```
Removed value: -"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 3, 2026
- addedInput schema / properties / k / description
```
Added value: +"eigenphase index, decimal, 0 <= k < 2^m"
```
- addedInput schema / properties / m / description
```
Added value: +"register width, decimal, >= 1"
```
- addedInput schema / properties / phase / description
```
Added value: +"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 3, 2026
- removedInput schema / properties / k / description
```
Removed value: -"eigenphase index, decimal, 0 <= k < 2^m"
```
- removedInput schema / properties / m / description
```
Removed value: -"register width, decimal, >= 1"
```
- removedInput schema / properties / phase / description
```
Removed value: -"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 3, 2026
- addedInput schema / properties / k / description
```
Added value: +"eigenphase index, decimal, 0 <= k < 2^m"
```
- addedInput schema / properties / m / description
```
Added value: +"register width, decimal, >= 1"
```
- addedInput schema / properties / phase / description
```
Added value: +"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 3, 2026
- removedInput schema / properties / k / description
```
Removed value: -"eigenphase index, decimal, 0 <= k < 2^m"
```
- removedInput schema / properties / m / description
```
Removed value: -"register width, decimal, >= 1"
```
- removedInput schema / properties / phase / description
```
Removed value: -"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 3, 2026
- addedInput schema / properties / k / description
```
Added value: +"eigenphase index, decimal, 0 <= k < 2^m"
```
- addedInput schema / properties / m / description
```
Added value: +"register width, decimal, >= 1"
```
- addedInput schema / properties / phase / description
```
Added value: +"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 3, 2026
- removedInput schema / properties / k / description
```
Removed value: -"eigenphase index, decimal, 0 <= k < 2^m"
```
- removedInput schema / properties / m / description
```
Removed value: -"register width, decimal, >= 1"
```
- removedInput schema / properties / phase / description
```
Removed value: -"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 3, 2026
- addedInput schema / properties / k / description
```
Added value: +"eigenphase index, decimal, 0 <= k < 2^m"
```
- addedInput schema / properties / m / description
```
Added value: +"register width, decimal, >= 1"
```
- addedInput schema / properties / phase / description
```
Added value: +"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 3, 2026
- removedInput schema / properties / k / description
```
Removed value: -"eigenphase index, decimal, 0 <= k < 2^m"
```
- removedInput schema / properties / m / description
```
Removed value: -"register width, decimal, >= 1"
```
- removedInput schema / properties / phase / description
```
Removed value: -"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 3, 2026
- addedInput schema / properties / k / description
```
Added value: +"eigenphase index, decimal, 0 <= k < 2^m"
```
- addedInput schema / properties / m / description
```
Added value: +"register width, decimal, >= 1"
```
- addedInput schema / properties / phase / description
```
Added value: +"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 3, 2026
- removedInput schema / properties / k / description
```
Removed value: -"eigenphase index, decimal, 0 <= k < 2^m"
```
- removedInput schema / properties / m / description
```
Removed value: -"register width, decimal, >= 1"
```
- removedInput schema / properties / phase / description
```
Removed value: -"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 3, 2026
- addedInput schema / properties / k / description
```
Added value: +"eigenphase index, decimal, 0 <= k < 2^m"
```
- addedInput schema / properties / m / description
```
Added value: +"register width, decimal, >= 1"
```
- addedInput schema / properties / phase / description
```
Added value: +"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 2, 2026
- removedInput schema / properties / k / description
```
Removed value: -"eigenphase index, decimal, 0 <= k < 2^m"
```
- removedInput schema / properties / m / description
```
Removed value: -"register width, decimal, >= 1"
```
- removedInput schema / properties / phase / description
```
Removed value: -"claimed phase as an exact rational num/den, e.g. 1/2"
```
Changed3 schema fields changedSep 2, 2026
- addedInput schema / properties / k / description
```
Added value: +"eigenphase index, decimal, 0 <= k < 2^m"
```
- addedInput schema / properties / m / description
```
Added value: +"register width, decimal, >= 1"
```
- addedInput schema / properties / phase / description
```
Added value: +"claimed phase as an exact rational num/den, e.g. 1/2"
```
First observedSep 1, 2026

TDQS

A4.6/5.0

Behavior4/5

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

With no annotations provided, the description carries the full burden of behavioral disclosure. It states the tool's exact output (WIN or MISS with the exact rational computed), the input constraints (phase as num/den, m as register width, k as index), and the refusal of floats. It does not mention error handling or side effects, but for a pure verification tool this is sufficient and transparent.

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

Conciseness5/5

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

The description is four sentences, each dense with information: purpose, parameter definitions, example, output format, and behavioral constraints. The core purpose is front-loaded ('certify that the presented phase equals k / 2^m exactly'), followed by parameter explanations and a clear final note on float refusal. No wasted words.

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

Completeness5/5

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

The tool is moderately complex (mathematical verification), and the description fully covers the required inputs, their relationship, the expected format, the output (WIN or MISS with exact rational), and constraints (floats refused). There is no output schema, so the description appropriately explains the return value. Everything an agent needs to invoke it correctly is present.

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

Parameters5/5

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

The schema already describes each parameter (k, m, phase) individually, but the description adds substantial meaning by connecting them: it explains the mathematical relationship (k / 2^m), the required format for phase (num/den), and provides a concrete example. This goes well beyond the schema's field-level descriptions, making the parameters' purpose and interplay fully clear.

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

Purpose5/5

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

The description uses a specific verb ('certify') and a precise resource ('Phase kickback'), then defines the exact mathematical condition (phase equals k / 2^m exactly as a rational). It includes an example (1/2 for m=1, k=1), which removes any ambiguity. The phrase 'No estimation is performed; floats refused' further distinguishes it from approximate verification tools among the siblings.

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

Usage Guidelines4/5

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

The description clearly states what the tool does and what it does not do ('No estimation is performed; floats refused'), giving implicit guidance on when to use it (exact rational verification) and when not (estimation or float-based checks). However, it does not explicitly name alternative tools or provide a direct 'use this when...' statement, so the guidance is implied rather than explicit.

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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