Adjunction Detector
Ki · Single Ability
The Problem
The algorithm claims to convert Celsius to Fahrenheit without considering the inverse transformation back to Celsius.
The Operation
The model is directed to identify two abstract domains connected by a pair of mappings (functors) going in opposite directions. Check the adjunction condition: verify whether a natural bijection exists between hom-sets of the two domains. If adjunction holds, label the left adjoint (free construction) and right adjoint (forgetful projection). Extract the universal property that the adjunction guarantees for every object in both domains. Replace any brute-force cross-domain search with the universal property lookup.
The Structure
This ability runs on a bidirectional verification that checks conclusions from both directions.
If a forward transformation is defined without checking whether a meaningful reverse operation exists, reversibility verification was omitted.
Haki · Multi Ability
Synergy Topology
In Haki mode, the API retrieves the primary ability first, then fans out to three synergy roles that compound its reasoning.
When retrieved in Haki mode, these four abilities don't run in sequence. They merge into a single injection where the dependency grounds the reasoning context, the amplifier sharpens the primary's output, and the alternative provides a fallback path if the primary's topology cannot converge. The result is a multi-angle reasoning scaffold that covers failure modes no single ability can reach alone.