Mind · Reasoning

SolverDecomposition

Breaking a concept into solver-contract-bound sub-concepts — the move that enables fractal recursion

Definition

Mechanism

The cognitive act of taking a concept, typically the capability that frames a problem, once its claim frame is stated and it has been located among broader kinds, and breaking it into sub-concepts where each sub-concept is bound by the Solver contract (it exposes at least the Manifest and Execute surfaces of the five-surface contract, so it is independently delegatable). Generic Decompose requires independent parts that combine into the whole; this method adds the claim frame, the location and the tests of the general method it extends, and binds every part to the solver contract, so the same five-surface contract governs every level and the structure can recurse. It asks which differentiated dimensions the capability needs across the instances it claims, not which steps would accomplish it, which would produce a procedural carve. Candidate dimensions are generated and each is put to the DecompositionGate tests; a failed or uncertain candidate may be reframed, narrowed or kept as a labelled alternative in the frontier of the ArchiveServingFrontier. A bounded search then looks for any dimension the accepted set still misses, and a RoutingSanityCheck routes a few concrete tasks through the carve before it is kept. Accepted dimensions are bound to the parent by CompositionEdge links, the split declares the Synthesis that recomposes them, and recursion continues into a dimension only while the MarginalValueRule says further depth pays. A few agents can take these solver roles for one problem, and the resulting structure may persist as a reusable pattern or be torn down at completion.

Invariants

  1. The claim frame is stated before any candidate is tested.
  2. The concept is located among broader kinds before it is carved.
  3. Every sub-concept exposes at least the Manifest and Execute surfaces of the Solver interface as a condition of the split being accepted, not as later repair.
  4. Only candidate dimensions that pass the DecompositionGate tests are spawned as children.
  5. The split declares the Synthesis that will recompose it; a concept with no available synthesis is not decomposed.

Risks

Failure modes

  1. Premature decomposition

    the parent concept is broken apart before it is clearly framed, producing sub-concepts that don't cover the actual problem.

  2. Coupled split

    two dimensions cannot vary or fail separately; the DecompositionGate Independence test should catch this but can miss overlap that is semantic rather than structural.

  3. Contract violation

    sub-concepts that do not cleanly expose Manifest + Execute cannot be dispatched — the decomposition produced descriptions, not delegatable units.

  4. Leaky abstraction

    sub-concepts that require global context the Solver contract doesn't carry, forcing each child to reach back for the parent's context.

  5. Procedural carve

    the concept is split into the steps of one way of doing it rather than the dimensions it needs, so the carve fits one workflow and not the capability.

Relationships

Builds on

Composes with

DecompositionGate

Four tests of a decomposition against a stated claim frame: each candidate dimension must pass Necessity, Independence and Universality, and the accepted set must pass Completeness

References

ArchiveServingFrontier

Keep evaluated structures in three layers: an inclusive archive, a selective serving layer and an experimental frontier

Infrastructure

CompositionEdge

A link stating that a child supplies a differentiated contribution its parent's outward capability requires

Decompose

Dividing complexity into manageable units

MarginalValueRule

Deepen only while expected improvement plus an exploration credit, divided by incremental cost, exceeds a domain threshold

RoutingSanityCheck

Test a candidate carve by routing a few concrete tasks through it before it is kept

Solver

Abstract five-surface contract: Manifest, Execute, Consult, Verify, Feedback

Extends

ConceptualDecomposition

Finding what a concept is made of: locate it, carve it into the dimensions every case it claims needs, test each, search for what is missing, route real cases through it, say how the parts make the whole, and carve again below

Used by

Composes with

FractalIntelligence

Expansion of cognitive capability through recursive decomposition of concepts into contract-bounded sub-concepts

References

MandatoryAbstraction

Before decomposing a concrete problem, locate it by climbing specialization links to the root, then retrace the route

Reference

Identity

Ref
SolverDecomposition#ff4b
Sema ID
sema:SolverDecomposition#mh:SHA-256:ff4b4921d148c7672540eb0ec6201e5eed9b7c06b6442c6525399a856f121bfa
Ring
1
Tier
1
Updated
2026-11-11