Completion Tower

Abstract

Coherent fixed threads define truth in a typed completion tower.

Theorem 1.1 (Transport From Base Zero).

$\forall t o w er : T o w er, ba se : t o w er . St a t e 0, (t r an s p or tF ro m B a se t o w er ba se 0 = ba se) .$

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

Source. Repository-derived.

Commentary.

This theorem establishes transport from base zero in the module’s typed setting.

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

Theorem 1.2 (Transport From Base Succ).

$\forall t o w er : T o w er, ba se : t o w er . St a t e 0, l e v e l : N, (t r an s p or tF ro m B a se t o w er ba se (l e v e l + 1) = t o w er . b o n d l e v e l (t r an s p or tF ro m B a se t o w er ba se l e v e l)) .$

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

Source. Repository-derived.

Commentary.

This theorem establishes transport from base succ in the module’s typed setting.

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

Theorem 1.3 (Transport From Base Coherent).

$\forall t o w er : T o w er, ba se : t o w er . St a t e 0, (I s C o h ere n tT h re a d t o w er (t r an s p or tF ro m B a se t o w er ba se)) .$

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

Source. Repository-derived.

Commentary.

The recursively transported thread is coherent by construction.

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

Theorem 1.4 (Transport From Fixed Base Is Fixed).

$\forall t o w er : T o w er, ba se : t o w er . St a t e 0, (F u n c t i o n . I s F i x e d Pt (t o w er . d y nami cs 0) ba se) \Rightarrow (I s F i x e d T h re a d t o w er (t r an s p or tF ro m B a se t o w er ba se)) .$

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

Source. Repository-derived.

Commentary.

Fixedness of one base state propagates to every completion level.

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

Theorem 1.5 (Transport From Fixed Base Is Truth).

$\forall t o w er : T o w er, ba se : t o w er . St a t e 0, (F u n c t i o n . I s F i x e d Pt (t o w er . d y nami cs 0) ba se) \Rightarrow (I s T r u t h T h re a d t o w er (t r an s p or tF ro m B a se t o w er ba se)) .$

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

Source. Repository-derived.

Commentary.

A fixed base state canonically generates a truth thread.

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

Theorem 1.6 (Coherent Thread eq Transport From Base).

$\forall t o w er : T o w er, t h re a d : T h re a d t o w er, (I s C o h ere n tT h re a d t o w er t h re a d) \Rightarrow (t h re a d = t r an s p or tF ro m B a se t o w er (t h re a d 0)) .$

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

Source. Repository-derived.

Commentary.

Every coherent thread is determined by its base coordinate.

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

Theorem 1.7 (Coherent Threads Ext).

$\forall t o w er : T o w er, f i rs t : T h re a d t o w er, seco n d : T h re a d t o w er, (I s C o h ere n tT h re a d t o w er f i rs t) \land (I s C o h ere n tT h re a d t o w erseco n d) \land (f i rs t 0 = seco n d 0) \Rightarrow (f i rs t = seco n d) .$

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

Source. Repository-derived.

Commentary.

Two coherent threads with the same base state are equal.

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/CompletionTower.coherent_thread_eq_transport_from_base
Truth anchor: D5/S3/Observer/WorldModel/CompletionTower.coherent_threads_ext
Truth anchor: D5/S3/Observer/WorldModel/CompletionTower.transportFromBase_succ
Truth anchor: D5/S3/Observer/WorldModel/CompletionTower.transportFromBase_zero
Truth anchor: D5/S3/Observer/WorldModel/CompletionTower.transport_from_base_coherent
Truth anchor: D5/S3/Observer/WorldModel/CompletionTower.transport_from_fixed_base_is_fixed
Truth anchor: D5/S3/Observer/WorldModel/CompletionTower.transport_from_fixed_base_is_truth
Dependency: D5/S3/Observer/Bridges/WormholeCategory

Keyboard shortcuts

trureturing Blueprint

Completion Tower

Abstract

References