Symbolic Algebra Engine
Ki · Single Ability
The Problem
The equation x + y = 10 is solved by reasoning exclusively in natural language without attempting algebraic manipulation.
The Operation
This ability makes the model convert all entities into manipulable symbols, do not leave graph nodes as opaque labels. Apply symbolic simplification: factor common structures, cancel redundancies, reduce to minimal form. Search for invariants, properties preserved across transformations. Derive conclusions through symbolic computation, not natural language paraphrase. If simplification reveals a missed reduction, trace back and re-factor. If it detects reason exclusively in natural language when formal notation, it halts and corrects.
The Structure
The reasoning structure is a disassemble-transform-reassemble pattern that breaks the problem apart, modifies each piece, and reconstructs.
If a conclusion relies on informal reasoning when formal symbolic derivation would have caught a logical error, formal verification 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.