Parent: recursive-harness
The middle nodes of the recursion are agents that split a task into sub-tasks and recombine their results. Two failure-prone moves, two requirements.
Split along near-decomposable seams (Simon–Ando)
Decompose where coupling is weak, so the interface between sub-tasks is small and sufficient (the parent answer is reconstructible from the parts + a clean summary — simon-ando). Split along strong-coupling seams → the interface is huge/lossy → you can't recompose → divergence. So the core skill of a middle agent is finding the weak seam, not just cutting.
Reassembly is where the gate lives
The "recombine" step is the per-level gate: it must verify the parts compose correctly (the interface contract / Hoare postcondition / LCF-kernel re-check), not just glue. Reassembly is also where the residual P×C concentrates (pc-well-founded-recursion); if a join's P×C is still high, the reassembly itself recurses + gets gated.
What a middle agent passes up
Only the verified summary/interface, not its internal mess (Simon–Ando's stabilized sub-assembly). The parent builds on the interface; the child's internals are sealed behind the passed gate. Tokens/mints nest — the child gate mints evidence the parent gate consumes (recursive-stages).
The determinism question
"How do I decompose this task?" can be made unique by the recursive instruction supplied at the top: instruction + local state → a unique split (see tacit-spec-as-spec-compression for why a recursive instruction is finite yet covers every situation, and where tacit judgment still leaks in).
Revisited — under the theory layer
- "Find the weak seam" is now measurable: the split certificate's length is the seam-quality proxy (split-granularity-equilibrium) — a short ⋀Sᵢ ⟹ S argument means a real Simon seam; a tortured one means you're cutting load-bearing structure. And how fine to cut is the U-curve equilibrium, weighed in P×C.
- The reassembly gate's obligations are now stated: it checks against the parent's spec (not the children's — the wrong-split failure mode of safe-recursion-theorem) and must be a contraction on the error metric (inexact-contraction) so children's errors damp instead of amplify.
- This note only had the downward direction — the upward channel is upward-reequilibration: a child that can't meet its spec at any grain sends up a feasibility cut (reshape the split) and a price (rebalance sibling budgets).