Affine Earth Math Court Remote

verify_quantum_walk

QC-012 Quantum walk on the two-vertex cycle C2: from start (0 or 1), an even number of steps returns to start and an odd number lands on the other vertex; certify that the presented end matches. steps, start and end are decimal strings (start and end are 0 or 1). WIN or MISS naming the vertex the walk reaches. Floats refused.

Input Schema

TableJSON Schema

Name	Required	Description
`end`	No	claimed ending vertex, 0 or 1
`start`	No	starting vertex, 0 or 1
`steps`	No	number of steps, decimal, >= 0

Schema Changelog

Changes observed during successful MCP inspections.

Changed3 schema fields changedSep 7, 2026
- addedInput schema / properties / end / description
```
Added value: +"claimed ending vertex, 0 or 1"
```
- addedInput schema / properties / start / description
```
Added value: +"starting vertex, 0 or 1"
```
- addedInput schema / properties / steps / description
```
Added value: +"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 7, 2026
- removedInput schema / properties / end / description
```
Removed value: -"claimed ending vertex, 0 or 1"
```
- removedInput schema / properties / start / description
```
Removed value: -"starting vertex, 0 or 1"
```
- removedInput schema / properties / steps / description
```
Removed value: -"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 7, 2026
- addedInput schema / properties / end / description
```
Added value: +"claimed ending vertex, 0 or 1"
```
- addedInput schema / properties / start / description
```
Added value: +"starting vertex, 0 or 1"
```
- addedInput schema / properties / steps / description
```
Added value: +"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 7, 2026
- removedInput schema / properties / end / description
```
Removed value: -"claimed ending vertex, 0 or 1"
```
- removedInput schema / properties / start / description
```
Removed value: -"starting vertex, 0 or 1"
```
- removedInput schema / properties / steps / description
```
Removed value: -"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 6, 2026
- addedInput schema / properties / end / description
```
Added value: +"claimed ending vertex, 0 or 1"
```
- addedInput schema / properties / start / description
```
Added value: +"starting vertex, 0 or 1"
```
- addedInput schema / properties / steps / description
```
Added value: +"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 6, 2026
- removedInput schema / properties / end / description
```
Removed value: -"claimed ending vertex, 0 or 1"
```
- removedInput schema / properties / start / description
```
Removed value: -"starting vertex, 0 or 1"
```
- removedInput schema / properties / steps / description
```
Removed value: -"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 6, 2026
- addedInput schema / properties / end / description
```
Added value: +"claimed ending vertex, 0 or 1"
```
- addedInput schema / properties / start / description
```
Added value: +"starting vertex, 0 or 1"
```
- addedInput schema / properties / steps / description
```
Added value: +"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 6, 2026
- removedInput schema / properties / end / description
```
Removed value: -"claimed ending vertex, 0 or 1"
```
- removedInput schema / properties / start / description
```
Removed value: -"starting vertex, 0 or 1"
```
- removedInput schema / properties / steps / description
```
Removed value: -"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 6, 2026
- addedInput schema / properties / end / description
```
Added value: +"claimed ending vertex, 0 or 1"
```
- addedInput schema / properties / start / description
```
Added value: +"starting vertex, 0 or 1"
```
- addedInput schema / properties / steps / description
```
Added value: +"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 6, 2026
- removedInput schema / properties / end / description
```
Removed value: -"claimed ending vertex, 0 or 1"
```
- removedInput schema / properties / start / description
```
Removed value: -"starting vertex, 0 or 1"
```
- removedInput schema / properties / steps / description
```
Removed value: -"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 6, 2026
- addedInput schema / properties / end / description
```
Added value: +"claimed ending vertex, 0 or 1"
```
- addedInput schema / properties / start / description
```
Added value: +"starting vertex, 0 or 1"
```
- addedInput schema / properties / steps / description
```
Added value: +"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 6, 2026
- removedInput schema / properties / end / description
```
Removed value: -"claimed ending vertex, 0 or 1"
```
- removedInput schema / properties / start / description
```
Removed value: -"starting vertex, 0 or 1"
```
- removedInput schema / properties / steps / description
```
Removed value: -"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 6, 2026
- addedInput schema / properties / end / description
```
Added value: +"claimed ending vertex, 0 or 1"
```
- addedInput schema / properties / start / description
```
Added value: +"starting vertex, 0 or 1"
```
- addedInput schema / properties / steps / description
```
Added value: +"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 6, 2026
- removedInput schema / properties / end / description
```
Removed value: -"claimed ending vertex, 0 or 1"
```
- removedInput schema / properties / start / description
```
Removed value: -"starting vertex, 0 or 1"
```
- removedInput schema / properties / steps / description
```
Removed value: -"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 6, 2026
- addedInput schema / properties / end / description
```
Added value: +"claimed ending vertex, 0 or 1"
```
- addedInput schema / properties / start / description
```
Added value: +"starting vertex, 0 or 1"
```
- addedInput schema / properties / steps / description
```
Added value: +"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 6, 2026
- removedInput schema / properties / end / description
```
Removed value: -"claimed ending vertex, 0 or 1"
```
- removedInput schema / properties / start / description
```
Removed value: -"starting vertex, 0 or 1"
```
- removedInput schema / properties / steps / description
```
Removed value: -"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 6, 2026
- addedInput schema / properties / end / description
```
Added value: +"claimed ending vertex, 0 or 1"
```
- addedInput schema / properties / start / description
```
Added value: +"starting vertex, 0 or 1"
```
- addedInput schema / properties / steps / description
```
Added value: +"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 6, 2026
- removedInput schema / properties / end / description
```
Removed value: -"claimed ending vertex, 0 or 1"
```
- removedInput schema / properties / start / description
```
Removed value: -"starting vertex, 0 or 1"
```
- removedInput schema / properties / steps / description
```
Removed value: -"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 6, 2026
- addedInput schema / properties / end / description
```
Added value: +"claimed ending vertex, 0 or 1"
```
- addedInput schema / properties / start / description
```
Added value: +"starting vertex, 0 or 1"
```
- addedInput schema / properties / steps / description
```
Added value: +"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 6, 2026
- removedInput schema / properties / end / description
```
Removed value: -"claimed ending vertex, 0 or 1"
```
- removedInput schema / properties / start / description
```
Removed value: -"starting vertex, 0 or 1"
```
- removedInput schema / properties / steps / description
```
Removed value: -"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 6, 2026
- addedInput schema / properties / end / description
```
Added value: +"claimed ending vertex, 0 or 1"
```
- addedInput schema / properties / start / description
```
Added value: +"starting vertex, 0 or 1"
```
- addedInput schema / properties / steps / description
```
Added value: +"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 6, 2026
- removedInput schema / properties / end / description
```
Removed value: -"claimed ending vertex, 0 or 1"
```
- removedInput schema / properties / start / description
```
Removed value: -"starting vertex, 0 or 1"
```
- removedInput schema / properties / steps / description
```
Removed value: -"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 6, 2026
- addedInput schema / properties / end / description
```
Added value: +"claimed ending vertex, 0 or 1"
```
- addedInput schema / properties / start / description
```
Added value: +"starting vertex, 0 or 1"
```
- addedInput schema / properties / steps / description
```
Added value: +"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 6, 2026
- removedInput schema / properties / end / description
```
Removed value: -"claimed ending vertex, 0 or 1"
```
- removedInput schema / properties / start / description
```
Removed value: -"starting vertex, 0 or 1"
```
- removedInput schema / properties / steps / description
```
Removed value: -"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 6, 2026
- addedInput schema / properties / end / description
```
Added value: +"claimed ending vertex, 0 or 1"
```
- addedInput schema / properties / start / description
```
Added value: +"starting vertex, 0 or 1"
```
- addedInput schema / properties / steps / description
```
Added value: +"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 6, 2026
- removedInput schema / properties / end / description
```
Removed value: -"claimed ending vertex, 0 or 1"
```
- removedInput schema / properties / start / description
```
Removed value: -"starting vertex, 0 or 1"
```
- removedInput schema / properties / steps / description
```
Removed value: -"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 6, 2026
- addedInput schema / properties / end / description
```
Added value: +"claimed ending vertex, 0 or 1"
```
- addedInput schema / properties / start / description
```
Added value: +"starting vertex, 0 or 1"
```
- addedInput schema / properties / steps / description
```
Added value: +"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 6, 2026
- removedInput schema / properties / end / description
```
Removed value: -"claimed ending vertex, 0 or 1"
```
- removedInput schema / properties / start / description
```
Removed value: -"starting vertex, 0 or 1"
```
- removedInput schema / properties / steps / description
```
Removed value: -"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 6, 2026
- addedInput schema / properties / end / description
```
Added value: +"claimed ending vertex, 0 or 1"
```
- addedInput schema / properties / start / description
```
Added value: +"starting vertex, 0 or 1"
```
- addedInput schema / properties / steps / description
```
Added value: +"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 6, 2026
- removedInput schema / properties / end / description
```
Removed value: -"claimed ending vertex, 0 or 1"
```
- removedInput schema / properties / start / description
```
Removed value: -"starting vertex, 0 or 1"
```
- removedInput schema / properties / steps / description
```
Removed value: -"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 6, 2026
- addedInput schema / properties / end / description
```
Added value: +"claimed ending vertex, 0 or 1"
```
- addedInput schema / properties / start / description
```
Added value: +"starting vertex, 0 or 1"
```
- addedInput schema / properties / steps / description
```
Added value: +"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 6, 2026
- removedInput schema / properties / end / description
```
Removed value: -"claimed ending vertex, 0 or 1"
```
- removedInput schema / properties / start / description
```
Removed value: -"starting vertex, 0 or 1"
```
- removedInput schema / properties / steps / description
```
Removed value: -"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 6, 2026
- addedInput schema / properties / end / description
```
Added value: +"claimed ending vertex, 0 or 1"
```
- addedInput schema / properties / start / description
```
Added value: +"starting vertex, 0 or 1"
```
- addedInput schema / properties / steps / description
```
Added value: +"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 6, 2026
- removedInput schema / properties / end / description
```
Removed value: -"claimed ending vertex, 0 or 1"
```
- removedInput schema / properties / start / description
```
Removed value: -"starting vertex, 0 or 1"
```
- removedInput schema / properties / steps / description
```
Removed value: -"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 6, 2026
- addedInput schema / properties / end / description
```
Added value: +"claimed ending vertex, 0 or 1"
```
- addedInput schema / properties / start / description
```
Added value: +"starting vertex, 0 or 1"
```
- addedInput schema / properties / steps / description
```
Added value: +"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 5, 2026
- removedInput schema / properties / end / description
```
Removed value: -"claimed ending vertex, 0 or 1"
```
- removedInput schema / properties / start / description
```
Removed value: -"starting vertex, 0 or 1"
```
- removedInput schema / properties / steps / description
```
Removed value: -"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 5, 2026
- addedInput schema / properties / end / description
```
Added value: +"claimed ending vertex, 0 or 1"
```
- addedInput schema / properties / start / description
```
Added value: +"starting vertex, 0 or 1"
```
- addedInput schema / properties / steps / description
```
Added value: +"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 5, 2026
- removedInput schema / properties / end / description
```
Removed value: -"claimed ending vertex, 0 or 1"
```
- removedInput schema / properties / start / description
```
Removed value: -"starting vertex, 0 or 1"
```
- removedInput schema / properties / steps / description
```
Removed value: -"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 5, 2026
- addedInput schema / properties / end / description
```
Added value: +"claimed ending vertex, 0 or 1"
```
- addedInput schema / properties / start / description
```
Added value: +"starting vertex, 0 or 1"
```
- addedInput schema / properties / steps / description
```
Added value: +"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 5, 2026
- removedInput schema / properties / end / description
```
Removed value: -"claimed ending vertex, 0 or 1"
```
- removedInput schema / properties / start / description
```
Removed value: -"starting vertex, 0 or 1"
```
- removedInput schema / properties / steps / description
```
Removed value: -"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 5, 2026
- addedInput schema / properties / end / description
```
Added value: +"claimed ending vertex, 0 or 1"
```
- addedInput schema / properties / start / description
```
Added value: +"starting vertex, 0 or 1"
```
- addedInput schema / properties / steps / description
```
Added value: +"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 5, 2026
- removedInput schema / properties / end / description
```
Removed value: -"claimed ending vertex, 0 or 1"
```
- removedInput schema / properties / start / description
```
Removed value: -"starting vertex, 0 or 1"
```
- removedInput schema / properties / steps / description
```
Removed value: -"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 5, 2026
- addedInput schema / properties / end / description
```
Added value: +"claimed ending vertex, 0 or 1"
```
- addedInput schema / properties / start / description
```
Added value: +"starting vertex, 0 or 1"
```
- addedInput schema / properties / steps / description
```
Added value: +"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 5, 2026
- removedInput schema / properties / end / description
```
Removed value: -"claimed ending vertex, 0 or 1"
```
- removedInput schema / properties / start / description
```
Removed value: -"starting vertex, 0 or 1"
```
- removedInput schema / properties / steps / description
```
Removed value: -"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 5, 2026
- addedInput schema / properties / end / description
```
Added value: +"claimed ending vertex, 0 or 1"
```
- addedInput schema / properties / start / description
```
Added value: +"starting vertex, 0 or 1"
```
- addedInput schema / properties / steps / description
```
Added value: +"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 5, 2026
- removedInput schema / properties / end / description
```
Removed value: -"claimed ending vertex, 0 or 1"
```
- removedInput schema / properties / start / description
```
Removed value: -"starting vertex, 0 or 1"
```
- removedInput schema / properties / steps / description
```
Removed value: -"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 5, 2026
- addedInput schema / properties / end / description
```
Added value: +"claimed ending vertex, 0 or 1"
```
- addedInput schema / properties / start / description
```
Added value: +"starting vertex, 0 or 1"
```
- addedInput schema / properties / steps / description
```
Added value: +"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 5, 2026
- removedInput schema / properties / end / description
```
Removed value: -"claimed ending vertex, 0 or 1"
```
- removedInput schema / properties / start / description
```
Removed value: -"starting vertex, 0 or 1"
```
- removedInput schema / properties / steps / description
```
Removed value: -"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 5, 2026
- addedInput schema / properties / end / description
```
Added value: +"claimed ending vertex, 0 or 1"
```
- addedInput schema / properties / start / description
```
Added value: +"starting vertex, 0 or 1"
```
- addedInput schema / properties / steps / description
```
Added value: +"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 5, 2026
- removedInput schema / properties / end / description
```
Removed value: -"claimed ending vertex, 0 or 1"
```
- removedInput schema / properties / start / description
```
Removed value: -"starting vertex, 0 or 1"
```
- removedInput schema / properties / steps / description
```
Removed value: -"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 5, 2026
- addedInput schema / properties / end / description
```
Added value: +"claimed ending vertex, 0 or 1"
```
- addedInput schema / properties / start / description
```
Added value: +"starting vertex, 0 or 1"
```
- addedInput schema / properties / steps / description
```
Added value: +"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 5, 2026
- removedInput schema / properties / end / description
```
Removed value: -"claimed ending vertex, 0 or 1"
```
- removedInput schema / properties / start / description
```
Removed value: -"starting vertex, 0 or 1"
```
- removedInput schema / properties / steps / description
```
Removed value: -"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 5, 2026
- addedInput schema / properties / end / description
```
Added value: +"claimed ending vertex, 0 or 1"
```
- addedInput schema / properties / start / description
```
Added value: +"starting vertex, 0 or 1"
```
- addedInput schema / properties / steps / description
```
Added value: +"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 5, 2026
- removedInput schema / properties / end / description
```
Removed value: -"claimed ending vertex, 0 or 1"
```
- removedInput schema / properties / start / description
```
Removed value: -"starting vertex, 0 or 1"
```
- removedInput schema / properties / steps / description
```
Removed value: -"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 5, 2026
- addedInput schema / properties / end / description
```
Added value: +"claimed ending vertex, 0 or 1"
```
- addedInput schema / properties / start / description
```
Added value: +"starting vertex, 0 or 1"
```
- addedInput schema / properties / steps / description
```
Added value: +"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 5, 2026
- removedInput schema / properties / end / description
```
Removed value: -"claimed ending vertex, 0 or 1"
```
- removedInput schema / properties / start / description
```
Removed value: -"starting vertex, 0 or 1"
```
- removedInput schema / properties / steps / description
```
Removed value: -"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 5, 2026
- addedInput schema / properties / end / description
```
Added value: +"claimed ending vertex, 0 or 1"
```
- addedInput schema / properties / start / description
```
Added value: +"starting vertex, 0 or 1"
```
- addedInput schema / properties / steps / description
```
Added value: +"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 5, 2026
- removedInput schema / properties / end / description
```
Removed value: -"claimed ending vertex, 0 or 1"
```
- removedInput schema / properties / start / description
```
Removed value: -"starting vertex, 0 or 1"
```
- removedInput schema / properties / steps / description
```
Removed value: -"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 5, 2026
- addedInput schema / properties / end / description
```
Added value: +"claimed ending vertex, 0 or 1"
```
- addedInput schema / properties / start / description
```
Added value: +"starting vertex, 0 or 1"
```
- addedInput schema / properties / steps / description
```
Added value: +"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 5, 2026
- removedInput schema / properties / end / description
```
Removed value: -"claimed ending vertex, 0 or 1"
```
- removedInput schema / properties / start / description
```
Removed value: -"starting vertex, 0 or 1"
```
- removedInput schema / properties / steps / description
```
Removed value: -"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 5, 2026
- addedInput schema / properties / end / description
```
Added value: +"claimed ending vertex, 0 or 1"
```
- addedInput schema / properties / start / description
```
Added value: +"starting vertex, 0 or 1"
```
- addedInput schema / properties / steps / description
```
Added value: +"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 5, 2026
- removedInput schema / properties / end / description
```
Removed value: -"claimed ending vertex, 0 or 1"
```
- removedInput schema / properties / start / description
```
Removed value: -"starting vertex, 0 or 1"
```
- removedInput schema / properties / steps / description
```
Removed value: -"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 5, 2026
- addedInput schema / properties / end / description
```
Added value: +"claimed ending vertex, 0 or 1"
```
- addedInput schema / properties / start / description
```
Added value: +"starting vertex, 0 or 1"
```
- addedInput schema / properties / steps / description
```
Added value: +"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 5, 2026
- removedInput schema / properties / end / description
```
Removed value: -"claimed ending vertex, 0 or 1"
```
- removedInput schema / properties / start / description
```
Removed value: -"starting vertex, 0 or 1"
```
- removedInput schema / properties / steps / description
```
Removed value: -"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 4, 2026
- addedInput schema / properties / end / description
```
Added value: +"claimed ending vertex, 0 or 1"
```
- addedInput schema / properties / start / description
```
Added value: +"starting vertex, 0 or 1"
```
- addedInput schema / properties / steps / description
```
Added value: +"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 4, 2026
- removedInput schema / properties / end / description
```
Removed value: -"claimed ending vertex, 0 or 1"
```
- removedInput schema / properties / start / description
```
Removed value: -"starting vertex, 0 or 1"
```
- removedInput schema / properties / steps / description
```
Removed value: -"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 4, 2026
- addedInput schema / properties / end / description
```
Added value: +"claimed ending vertex, 0 or 1"
```
- addedInput schema / properties / start / description
```
Added value: +"starting vertex, 0 or 1"
```
- addedInput schema / properties / steps / description
```
Added value: +"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 4, 2026
- removedInput schema / properties / end / description
```
Removed value: -"claimed ending vertex, 0 or 1"
```
- removedInput schema / properties / start / description
```
Removed value: -"starting vertex, 0 or 1"
```
- removedInput schema / properties / steps / description
```
Removed value: -"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 4, 2026
- addedInput schema / properties / end / description
```
Added value: +"claimed ending vertex, 0 or 1"
```
- addedInput schema / properties / start / description
```
Added value: +"starting vertex, 0 or 1"
```
- addedInput schema / properties / steps / description
```
Added value: +"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 4, 2026
- removedInput schema / properties / end / description
```
Removed value: -"claimed ending vertex, 0 or 1"
```
- removedInput schema / properties / start / description
```
Removed value: -"starting vertex, 0 or 1"
```
- removedInput schema / properties / steps / description
```
Removed value: -"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 4, 2026
- addedInput schema / properties / end / description
```
Added value: +"claimed ending vertex, 0 or 1"
```
- addedInput schema / properties / start / description
```
Added value: +"starting vertex, 0 or 1"
```
- addedInput schema / properties / steps / description
```
Added value: +"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 4, 2026
- removedInput schema / properties / end / description
```
Removed value: -"claimed ending vertex, 0 or 1"
```
- removedInput schema / properties / start / description
```
Removed value: -"starting vertex, 0 or 1"
```
- removedInput schema / properties / steps / description
```
Removed value: -"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 4, 2026
- addedInput schema / properties / end / description
```
Added value: +"claimed ending vertex, 0 or 1"
```
- addedInput schema / properties / start / description
```
Added value: +"starting vertex, 0 or 1"
```
- addedInput schema / properties / steps / description
```
Added value: +"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 4, 2026
- removedInput schema / properties / end / description
```
Removed value: -"claimed ending vertex, 0 or 1"
```
- removedInput schema / properties / start / description
```
Removed value: -"starting vertex, 0 or 1"
```
- removedInput schema / properties / steps / description
```
Removed value: -"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 4, 2026
- addedInput schema / properties / end / description
```
Added value: +"claimed ending vertex, 0 or 1"
```
- addedInput schema / properties / start / description
```
Added value: +"starting vertex, 0 or 1"
```
- addedInput schema / properties / steps / description
```
Added value: +"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 4, 2026
- removedInput schema / properties / end / description
```
Removed value: -"claimed ending vertex, 0 or 1"
```
- removedInput schema / properties / start / description
```
Removed value: -"starting vertex, 0 or 1"
```
- removedInput schema / properties / steps / description
```
Removed value: -"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 4, 2026
- addedInput schema / properties / end / description
```
Added value: +"claimed ending vertex, 0 or 1"
```
- addedInput schema / properties / start / description
```
Added value: +"starting vertex, 0 or 1"
```
- addedInput schema / properties / steps / description
```
Added value: +"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 4, 2026
- removedInput schema / properties / end / description
```
Removed value: -"claimed ending vertex, 0 or 1"
```
- removedInput schema / properties / start / description
```
Removed value: -"starting vertex, 0 or 1"
```
- removedInput schema / properties / steps / description
```
Removed value: -"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 4, 2026
- addedInput schema / properties / end / description
```
Added value: +"claimed ending vertex, 0 or 1"
```
- addedInput schema / properties / start / description
```
Added value: +"starting vertex, 0 or 1"
```
- addedInput schema / properties / steps / description
```
Added value: +"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 4, 2026
- removedInput schema / properties / end / description
```
Removed value: -"claimed ending vertex, 0 or 1"
```
- removedInput schema / properties / start / description
```
Removed value: -"starting vertex, 0 or 1"
```
- removedInput schema / properties / steps / description
```
Removed value: -"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 4, 2026
- addedInput schema / properties / end / description
```
Added value: +"claimed ending vertex, 0 or 1"
```
- addedInput schema / properties / start / description
```
Added value: +"starting vertex, 0 or 1"
```
- addedInput schema / properties / steps / description
```
Added value: +"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 4, 2026
- removedInput schema / properties / end / description
```
Removed value: -"claimed ending vertex, 0 or 1"
```
- removedInput schema / properties / start / description
```
Removed value: -"starting vertex, 0 or 1"
```
- removedInput schema / properties / steps / description
```
Removed value: -"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 4, 2026
- addedInput schema / properties / end / description
```
Added value: +"claimed ending vertex, 0 or 1"
```
- addedInput schema / properties / start / description
```
Added value: +"starting vertex, 0 or 1"
```
- addedInput schema / properties / steps / description
```
Added value: +"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 4, 2026
- removedInput schema / properties / end / description
```
Removed value: -"claimed ending vertex, 0 or 1"
```
- removedInput schema / properties / start / description
```
Removed value: -"starting vertex, 0 or 1"
```
- removedInput schema / properties / steps / description
```
Removed value: -"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 4, 2026
- addedInput schema / properties / end / description
```
Added value: +"claimed ending vertex, 0 or 1"
```
- addedInput schema / properties / start / description
```
Added value: +"starting vertex, 0 or 1"
```
- addedInput schema / properties / steps / description
```
Added value: +"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 3, 2026
- removedInput schema / properties / end / description
```
Removed value: -"claimed ending vertex, 0 or 1"
```
- removedInput schema / properties / start / description
```
Removed value: -"starting vertex, 0 or 1"
```
- removedInput schema / properties / steps / description
```
Removed value: -"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 3, 2026
- addedInput schema / properties / end / description
```
Added value: +"claimed ending vertex, 0 or 1"
```
- addedInput schema / properties / start / description
```
Added value: +"starting vertex, 0 or 1"
```
- addedInput schema / properties / steps / description
```
Added value: +"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 3, 2026
- removedInput schema / properties / end / description
```
Removed value: -"claimed ending vertex, 0 or 1"
```
- removedInput schema / properties / start / description
```
Removed value: -"starting vertex, 0 or 1"
```
- removedInput schema / properties / steps / description
```
Removed value: -"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 3, 2026
- addedInput schema / properties / end / description
```
Added value: +"claimed ending vertex, 0 or 1"
```
- addedInput schema / properties / start / description
```
Added value: +"starting vertex, 0 or 1"
```
- addedInput schema / properties / steps / description
```
Added value: +"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 3, 2026
- removedInput schema / properties / end / description
```
Removed value: -"claimed ending vertex, 0 or 1"
```
- removedInput schema / properties / start / description
```
Removed value: -"starting vertex, 0 or 1"
```
- removedInput schema / properties / steps / description
```
Removed value: -"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 3, 2026
- addedInput schema / properties / end / description
```
Added value: +"claimed ending vertex, 0 or 1"
```
- addedInput schema / properties / start / description
```
Added value: +"starting vertex, 0 or 1"
```
- addedInput schema / properties / steps / description
```
Added value: +"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 3, 2026
- removedInput schema / properties / end / description
```
Removed value: -"claimed ending vertex, 0 or 1"
```
- removedInput schema / properties / start / description
```
Removed value: -"starting vertex, 0 or 1"
```
- removedInput schema / properties / steps / description
```
Removed value: -"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 3, 2026
- addedInput schema / properties / end / description
```
Added value: +"claimed ending vertex, 0 or 1"
```
- addedInput schema / properties / start / description
```
Added value: +"starting vertex, 0 or 1"
```
- addedInput schema / properties / steps / description
```
Added value: +"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 3, 2026
- removedInput schema / properties / end / description
```
Removed value: -"claimed ending vertex, 0 or 1"
```
- removedInput schema / properties / start / description
```
Removed value: -"starting vertex, 0 or 1"
```
- removedInput schema / properties / steps / description
```
Removed value: -"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 3, 2026
- addedInput schema / properties / end / description
```
Added value: +"claimed ending vertex, 0 or 1"
```
- addedInput schema / properties / start / description
```
Added value: +"starting vertex, 0 or 1"
```
- addedInput schema / properties / steps / description
```
Added value: +"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 3, 2026
- removedInput schema / properties / end / description
```
Removed value: -"claimed ending vertex, 0 or 1"
```
- removedInput schema / properties / start / description
```
Removed value: -"starting vertex, 0 or 1"
```
- removedInput schema / properties / steps / description
```
Removed value: -"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 3, 2026
- addedInput schema / properties / end / description
```
Added value: +"claimed ending vertex, 0 or 1"
```
- addedInput schema / properties / start / description
```
Added value: +"starting vertex, 0 or 1"
```
- addedInput schema / properties / steps / description
```
Added value: +"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 3, 2026
- removedInput schema / properties / end / description
```
Removed value: -"claimed ending vertex, 0 or 1"
```
- removedInput schema / properties / start / description
```
Removed value: -"starting vertex, 0 or 1"
```
- removedInput schema / properties / steps / description
```
Removed value: -"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 3, 2026
- addedInput schema / properties / end / description
```
Added value: +"claimed ending vertex, 0 or 1"
```
- addedInput schema / properties / start / description
```
Added value: +"starting vertex, 0 or 1"
```
- addedInput schema / properties / steps / description
```
Added value: +"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 3, 2026
- removedInput schema / properties / end / description
```
Removed value: -"claimed ending vertex, 0 or 1"
```
- removedInput schema / properties / start / description
```
Removed value: -"starting vertex, 0 or 1"
```
- removedInput schema / properties / steps / description
```
Removed value: -"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 3, 2026
- addedInput schema / properties / end / description
```
Added value: +"claimed ending vertex, 0 or 1"
```
- addedInput schema / properties / start / description
```
Added value: +"starting vertex, 0 or 1"
```
- addedInput schema / properties / steps / description
```
Added value: +"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 3, 2026
- removedInput schema / properties / end / description
```
Removed value: -"claimed ending vertex, 0 or 1"
```
- removedInput schema / properties / start / description
```
Removed value: -"starting vertex, 0 or 1"
```
- removedInput schema / properties / steps / description
```
Removed value: -"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 3, 2026
- addedInput schema / properties / end / description
```
Added value: +"claimed ending vertex, 0 or 1"
```
- addedInput schema / properties / start / description
```
Added value: +"starting vertex, 0 or 1"
```
- addedInput schema / properties / steps / description
```
Added value: +"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 3, 2026
- removedInput schema / properties / end / description
```
Removed value: -"claimed ending vertex, 0 or 1"
```
- removedInput schema / properties / start / description
```
Removed value: -"starting vertex, 0 or 1"
```
- removedInput schema / properties / steps / description
```
Removed value: -"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 3, 2026
- addedInput schema / properties / end / description
```
Added value: +"claimed ending vertex, 0 or 1"
```
- addedInput schema / properties / start / description
```
Added value: +"starting vertex, 0 or 1"
```
- addedInput schema / properties / steps / description
```
Added value: +"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 3, 2026
- removedInput schema / properties / end / description
```
Removed value: -"claimed ending vertex, 0 or 1"
```
- removedInput schema / properties / start / description
```
Removed value: -"starting vertex, 0 or 1"
```
- removedInput schema / properties / steps / description
```
Removed value: -"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 3, 2026
- addedInput schema / properties / end / description
```
Added value: +"claimed ending vertex, 0 or 1"
```
- addedInput schema / properties / start / description
```
Added value: +"starting vertex, 0 or 1"
```
- addedInput schema / properties / steps / description
```
Added value: +"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 2, 2026
- removedInput schema / properties / end / description
```
Removed value: -"claimed ending vertex, 0 or 1"
```
- removedInput schema / properties / start / description
```
Removed value: -"starting vertex, 0 or 1"
```
- removedInput schema / properties / steps / description
```
Removed value: -"number of steps, decimal, >= 0"
```
Changed3 schema fields changedSep 2, 2026
- addedInput schema / properties / end / description
```
Added value: +"claimed ending vertex, 0 or 1"
```
- addedInput schema / properties / start / description
```
Added value: +"starting vertex, 0 or 1"
```
- addedInput schema / properties / steps / description
```
Added value: +"number of steps, decimal, >= 0"
```
First observedSep 1, 2026

TDQS

A4.3/5.0

Behavior4/5

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

With no annotations, the description carries the full burden. It discloses the mathematical logic, input format (decimal strings, 0/1), output (WIN/MISS naming vertex), and a rejection condition ('Floats refused'). It does not cover error handling for invalid inputs, but the core behavior is well explained.

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 description is a single dense sentence that front-loads the purpose. It packs in the rule, input constraints, and output format without fluff, though the 'QC-012' prefix is unexplained but not harmful.

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

Completeness4/5

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

The tool is simple, and the description covers the verification logic, parameter types, and output. A minor gap is that the schema lists all parameters as optional while the tool likely requires them for verification, and this is not clarified. Still, an agent can infer the necessary inputs.

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 relational meaning by explaining how steps, start, and end interact via the even/odd rule, going beyond the individual field descriptions.

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 states a specific verb ('certify') and resource ('quantum walk on the two-vertex cycle C2'), with an explicit rule for even/odd steps. It clearly distinguishes from sibling verify_* tools by naming the exact algorithm and cycle type.

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?

Provides clear context: this verifies a quantum walk on C2. It does not explicitly mention alternatives or when not to use it, but the algorithm-specific nature makes the intended use obvious among sibling tools.

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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