Completion Tower Morphism

Abstract

Natural wormholes transport fixed threads between completion towers.

Theorem 1.1 (Map Thread Coherent).

$\forall so u rce : T o w er, t a r g e t : T o w er, m or p hi s m : T o w er M or p hi s m so u rce t a r g e t, t h re a d : T h re a d so u rce, (I s C o h ere n tT h re a d so u rce t h re a d) \Rightarrow (I s C o h ere n tT h re a d t a r g e t (m or p hi s m . ma pT h re a d t h re a d)) .$

Proof. Machine-checked in Lean as D5/S3/Observer/WorldModel/CompletionTowerMorphism.map_thread_coherent (✓ std3). ∎

Source. Repository-derived.

Commentary.

Naturality transports coherent threads.

The declaration keeps its parameters and hypotheses explicit; the result makes no converse or broader existence claim beyond that scope.

Theorem 1.2 (Map Thread Fixed).

$\forall so u rce : T o w er, t a r g e t : T o w er, m or p hi s m : T o w er M or p hi s m so u rce t a r g e t, t h re a d : T h re a d so u rce, (I s F i x e d T h re a d so u rce t h re a d) \Rightarrow (I s F i x e d T h re a d t a r g e t (m or p hi s m . ma pT h re a d t h re a d)) .$

Proof. Machine-checked in Lean as D5/S3/Observer/WorldModel/CompletionTowerMorphism.map_thread_fixed (✓ std3). ∎

Source. Repository-derived.

Commentary.

Levelwise semiconjugacy transports fixed threads.

The declaration keeps its parameters and hypotheses explicit; the result makes no converse or broader existence claim beyond that scope.

Theorem 1.3 (Map Truth Thread).

$\forall so u rce : T o w er, t a r g e t : T o w er, m or p hi s m : T o w er M or p hi s m so u rce t a r g e t, t h re a d : T h re a d so u rce, (I s T r u t h T h re a d so u rce t h re a d) \Rightarrow (I s T r u t h T h re a d t a r g e t (m or p hi s m . ma pT h re a d t h re a d)) .$

Proof. Machine-checked in Lean as D5/S3/Observer/WorldModel/CompletionTowerMorphism.map_truth_thread (✓ std3). ∎

Source. Repository-derived.

Commentary.

Every tower morphism transports truth threads.

The declaration keeps its parameters and hypotheses explicit; the result makes no converse or broader existence claim beyond that scope.

Theorem 1.4 (Map Thread Compose).

$\forall so u rce : T o w er, mi dd l e : T o w er, t a r g e t : T o w er, seco n d : T o w er M or p hi s mmi dd l e t a r g e t, f i rs t : T o w er M or p hi s m so u rce mi dd l e, t h re a d : T h re a d so u rce, ((co m p oseseco n df i rs t) . ma pT h re a d t h re a d = seco n d . ma pT h re a d (f i rs t . ma pT h re a d t h re a d)) .$

Proof. Machine-checked in Lean as D5/S3/Observer/WorldModel/CompletionTowerMorphism.mapThread_compose (✓ std3). ∎

Source. Repository-derived.

Commentary.

Coordinatewise transport respects composition.

The declaration keeps its parameters and hypotheses explicit; the result makes no converse or broader existence claim beyond that scope.

References

Truth anchor: D5/S3/Observer/WorldModel/CompletionTowerMorphism.mapThread_compose
Truth anchor: D5/S3/Observer/WorldModel/CompletionTowerMorphism.map_thread_coherent
Truth anchor: D5/S3/Observer/WorldModel/CompletionTowerMorphism.map_thread_fixed
Truth anchor: D5/S3/Observer/WorldModel/CompletionTowerMorphism.map_truth_thread
Dependency: D5/S3/Observer/WorldModel/CompletionTower

Keyboard shortcuts

trureturing Blueprint

Completion Tower Morphism

Abstract

References