Sheaf-Theoretic Gluer
Ki · Single Ability
The Problem
The local analysis shows that each department's budget is balanced, but the overall financial report is inconsistent across sections without a global check.
The Operation
The model is directed to enumerate all local conclusions produced across sub-analyses of the problem. Compare each pair for mutual consistency -- verify that both can hold simultaneously. Classify each conflict as a reasoning error or genuine regional complexity requiring different local rules. If reasoning error, trace back and identify the faulty premise. Never concatenate local results without cross-checking global consistency. Concatenate local results without crosschecking global is rejected.
The Structure
This ability runs on a constraint net that tests the conclusion against all known constraints simultaneously. The procedure repeats until diminishing returns trigger an exit.
If locally valid conclusions are combined without checking whether they remain consistent at the global level, local-global consistency checking was skipped.
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.