10.1 The missing algorithmic layer

A purely formal DIAL object says that two involution-algebroid directions and an interchange comparison coexist. A computational system needs more. The four-phase reading scaffold of Chapter 0 becomes an implementation contract:

Declare.

What object is being learned or constructed? Which changes count as motion inside the current declaration?

Diagnose.

Which observer distinguishes compatible interaction from a persistent obstruction? Which registered controls rule out less-disruptive explanations?

Construct.

Which finite-realization test distinguishes a coherent repair from a one-step improvement? Which typed proposals may be constructed, relative to which frozen reference space, and in which creative mode?

Admit.

Which independent test can retain a repair or package change? Which declarations, failures, transports, and provenance persist after admission, rejection, or abstention?

Without these answers, a bracket, commutator, or interchange residual is only a number. It does not say whether to continue optimization, collect a new experiment, change a factorization, restore a prior state, or abstain.

. Never introduce DIAL-X by naming two operators alone. Declare its target, side semantics, mixed witness, finite-realization gate, creative mandate, proposal language, less-disruptive controls, package comparison, admission contract, and persistence semantics.