Products / 02 — Reasoning
Fractal recursive decomposition. A structural constant that breaks any goal into 3 × 3 × 7 = 63 tractable elements — and keeps the tree it produced as the reasoning path, rather than discarding it.
The problem
When a model "thinks step by step," the steps are prose. They are not addressable, not typed, not comparable between runs, and not guaranteed to correspond to the computation that produced the answer. You cannot diff two chains of thought. You cannot ask which branch was pruned and why.
F.R.A.C.C. imposes a shape on decomposition. Every goal descends through the same constant, so every reasoning path has the same skeleton — which makes paths comparable, auditable, and storable in the lattice as structure rather than text.
The constant
The three top-level axes are Risk, Reward, Relation — the minimum basis for evaluating any decision that has consequences, a payoff, and other agents in it. Each axis resolves into three postures, and each posture into seven tactics.
| Level 1 — Axis | Risk · Reward · Relation. What could go wrong, what is gained, who else is involved. |
|---|---|
| Level 2 — Posture | Three stances per axis. The orientation taken toward that axis. |
| Level 3 — Tactic | Seven concrete moves per posture. The actionable layer. |
| Terminal count | 3 × 3 × 7 = 63 per frame, at every scale of descent. |
Seven at the tactic layer is not arbitrary: it is the same width as the explanatory basis used by the Arc Lab and the same width as the lattice's per-axis address space. The systems share a constant so that a decomposition can be written directly into memory without translation loss.
Recursion
A terminal that is still too large to act on becomes the root of its own 63-element frame. Descent stops at the cognitive ceiling — the point at which an element is small enough to be executed or answered directly.
Every level has exactly 63 terminals. Search never explodes combinatorially, and cost per level is known in advance — which is what makes the descent schedulable.
A strategic frame and a tactical frame have identical structure. The same evaluation machinery works at any depth, so nothing needs re-implementing per level.
The descent tree is the answer's provenance. Ask "why this?" and the system returns the branch — every node it passed through and every sibling it declined.
Coupling
This is the part that makes the portfolio a system rather than a collection. The lattice is a 7-per-axis address space. F.R.A.C.C. terminates in sevens. The Arc Lab projects onto seven axes by default. A completed decomposition maps onto lattice coordinates directly — the reasoning path and the memory address are expressions of the same constant.
Practically: when the system solves something, the shape of how it solved it is storable, and the next encounter with a similar goal can retrieve not just the answer but the descent that produced it.
F.R.A.C.C. is not a whitepaper abstraction. Cubex³ is the constant made executable — three commanders, three axes, seven tactics, 63 doctrines per side, arbitrating a single move under stress on an observable board. If the decomposition is unsound, the testbed loses. That is the point of building it.