Fourth and Fifth Legacy Primitive Realizations

Abstract

Two frozen statements are equivalent to contextual and causal realization laws.

Definition 1.1 (Context realization).

Lean statement: D5/S3/ConceptDynamics/InformationEscapeRealizations/FourthFifthRealizations.contextRealization

Formalization. D5/S3/ConceptDynamics/InformationEscapeRealizations/FourthFifthRealizations.contextRealization (✓ std3).

Source. Repository-derived.

Commentary.

The typed realization reads every context field, decides both fixed-meaning predicates, and anchors the baseline and alternate contexts.

Theorem 1.2 (Context-selected fixed meanings certificate).

$((ba se l in e C o n t e x t . t e x t = a lt er na t e C o n t e x t . t e x t) \land (ba se l in e C o n t e x t . in t er p re t a t i o n R u l e = a lt er na t e C o n t e x t . in t er p re t a t i o n R u l e) \land (ba se l in e C o n t e x t . re a d er A d mi ss i o n \neq = a lt er na t e C o n t e x t . re a d er A d mi ss i o n) \land (ba se l in e C o n t e x t . ba c k g ro u n d \neq = a lt er na t e C o n t e x t . ba c k g ro u n d) \land (ba se l in e C o n t e x t . e v a l u a t i o n G o a l \neq = a lt er na t e C o n t e x t . e v a l u a t i o n G o a l) \land (IsBinaryFixedMeaning (ba se l in e C o n t e x t, (f a l se, f a l se, f a l se))) \land (IsBinaryFixedMeaning (a lt er na t e C o n t e x t, (t r u e, t r u e, t r u e))) \land ((f a l se, f a l se, f a l se) \neq = (t r u e, t r u e, t r u e))) ⟺ co n t e x t A re na . L a w co n t e x tR e a l i z a t i o n .$

Proof. Machine-checked in Lean as D5/S3/ConceptDynamics/InformationEscapeRealizations/FourthFifthRealizations.context_parameters_can_select_distinct_fixed_points_realization (✓ std3). ∎

Source. Repository-derived.

Commentary.

The certificate identifies every clause of the frozen context proposition with contextArena.Law contextRealization.

Definition 1.3 (Intervention realization).

Lean statement: D5/S3/ConceptDynamics/InformationEscapeRealizations/FourthFifthRealizations.interventionRealization

Formalization. D5/S3/ConceptDynamics/InformationEscapeRealizations/FourthFifthRealizations.interventionRealization (✓ std3).

Source. Repository-derived.

Commentary.

The typed realization uses Int and CF as its intervention and counterfactual readouts and has no point anchors.

Theorem 1.4 (Intervention is weaker than counterfactual certificate).

$(\exists MN : De t er mini s t i c B oo lSCM, (Int (M) = Int (N)) \land (CF (M) \neq = CF (N))) ⟺ in t er v e n t i o n A re na . L a w in t er v e n t i o n R e a l i z a t i o n .$

Proof. Machine-checked in Lean as D5/S3/ConceptDynamics/InformationEscapeRealizations/FourthFifthRealizations.intervention_strictly_weaker_than_counterfactual_realization (✓ std3). ∎

Source. Repository-derived.

Commentary.

The certificate identifies the frozen existential Int-versus-CF separation with interventionArena.Law interventionRealization.

References

Truth anchor: D5/S3/ConceptDynamics/InformationEscapeRealizations/FourthFifthRealizations.contextRealization
Truth anchor: D5/S3/ConceptDynamics/InformationEscapeRealizations/FourthFifthRealizations.context_parameters_can_select_distinct_fixed_points_realization
Truth anchor: D5/S3/ConceptDynamics/InformationEscapeRealizations/FourthFifthRealizations.interventionRealization
Truth anchor: D5/S3/ConceptDynamics/InformationEscapeRealizations/FourthFifthRealizations.intervention_strictly_weaker_than_counterfactual_realization
Dependency: D5/S3/ConceptDynamics/InformationEscapeArenas/FourthFifthArenas

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Fourth and Fifth Legacy Primitive Realizations

Abstract

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