induce

# Periagoge Protocol Crystallize in-process abstraction by aligning concrete cases first and naming last, with the live alternative readings held visible throughout. Type: `(AbstractionInProcess, AI, INDUCE, A) → CrystallizedAbstraction`. ## Definition **Periagoge** (περιαγωγή): A dialogical act of turning an in-process abstraction toward its crystallized form, where AI detects when an instance set has converged toward an unnamed essence, puts the two most alignable cases side by side for the user to correspond, extracts the invariant relation that correspondence carries together with the readings it leaves open, probes those open readings apart against further cases and near-misses the user judges, and only then proposes a name and rule for what survived — so the abstraction is located by the correspondences the user built rather than steered from a candidate offered ahead of them (the Greek dialectical vocabulary supplies the source terms). ``` ── FLOW ── Periagoge(A) → Detect(A) → InProcess(Iᵢ, E, L?): Pair(Iᵢ, E) → (i₁, i₂) → Align(i₁, i₂, ctx) → Stop → A�� → (AsShown: M committed | Correct(slot, value): re-present Align | Repartner(ref): re-enter Align with ref as partner | Abandon: declare(alignment_trace, open_trace) → AlignmentSuspended) → Extract(M, Iᵢ, H?) → (R, H) → Probe(H, Iᵢ, ctx, gap?) → p → Qp(p, H) → Stop → W → narrow(H, W) → H' → loop until (settled(H) ∧ probed(Λ)) ∨ budget_spen...