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Predicate Binding B(p)=(p,eₚ)

A predicate binding relates a directional actuator to the discrepancy it regulates. The cornerstone emotions are these operative bindings: B(p) = (p, eₚ).

Actuator, discrepancy, and regulation

The primitive p supplies a direction of selection or routing. The discrepancy eₚ gives that direction a regulated concern. The binding is the controller organization through which changes in the discrepancy can alter the operation.

The notation records a relation, not a complete implementation. A particular controller can also specify gains, thresholds, retained state, and available actions. These determine how effectively it regulates the discrepancy under its constraints.

The cornerstone bindings

Binding	Actuator	Regulated discrepancy
Love	Toward	relational gap
Fear	Away	boundary violation
Apology	Loop-back	self-model error
Gratitude	Propagation	undischarged received value

The primitive/binding distinction explains the construction. A direction by itself does not identify the concern it regulates. This is the distinction protected by the Cardinal Error.

Reduction of error and continuity of function

Regulation acts on a discrepancy toward a setpoint or admissible range. The discrepancy is reduced or controlled; it is not a conserved stock of emotion. Successful regulation can nevertheless preserve a boundary, relation, or other function. Preserving a function and preserving its error are different claims.

A controller can operate successfully while disturbance continues. The relevant question is whether its causal response maintains or improves the regulated relation under the actual conditions, rather than whether every signal reaches an exact numerical zero.

Expression and composition

A spoken apology, an act of generosity, or a bodily response can express a binding. An expression's form alone does not establish which regulation occurred; evidence concerns the operative discrepancy and what changed.

Already-bound emotions can compose a Force. Binding and composition are separate operations: B(p) constructs the binding; b₁ ⊕ b₂ relates bound regulators over a transition. The operator notation should preserve those types.

Higher-order regulation can exhibit related control structure without becoming another cornerstone emotion. Closure and marking regulate formulations and corrective operations at their own level.

Formal status

E: Derived, AC for the named bindings and their actuator/discrepancy relations; particular implementations state their own constraints. A: maps operative emotional regulation through differentiated causal relations. Provenance: the framework's binding architecture.