Engine Census Self-Application

Abstract

The escape engine characterizes its own census on a two-stage arena.

Definition 1.1 (Stage type).

Lean statement: D5/S3/ConceptDynamics/InformationEscape/SystemUnit.Stage

Formalization. D5/S3/ConceptDynamics/InformationEscape/SystemUnit.Stage (✓ std3).

Source. Repository-derived.

Commentary.

The finite meta-arena has a before and an after stage.

Definition 1.2 (Census arena).

Lean statement: D5/S3/ConceptDynamics/InformationEscape/SystemUnit.censusArena

Formalization. D5/S3/ConceptDynamics/InformationEscape/SystemUnit.censusArena (✓ std3).

Source. Repository-derived.

Commentary.

The engine census ranges over the two Boolean states.

Definition 1.3 (Stage-indexed catalog).

Lean statement: D5/S3/ConceptDynamics/InformationEscape/SystemUnit.censusCatalog

Formalization. D5/S3/ConceptDynamics/InformationEscape/SystemUnit.censusCatalog (✓ std3).

Source. Repository-derived.

Commentary.

Its lone CUT is constant before separation and identity afterward.

Definition 1.4 (SYSTEM readout).

Lean statement: D5/S3/ConceptDynamics/InformationEscape/SystemUnit.systemReadout

Formalization. D5/S3/ConceptDynamics/InformationEscape/SystemUnit.systemReadout (✓ std3).

Source. Repository-derived.

Commentary.

The readout is the canonical leave-one-out unique-capture count.

Definition 1.5 (Engine characterization).

Lean statement: D5/S3/ConceptDynamics/InformationEscape/SystemUnit.SystemCharacterization

Formalization. D5/S3/ConceptDynamics/InformationEscape/SystemUnit.SystemCharacterization (✓ std3).

Source. Repository-derived.

Commentary.

Every stage specializes the canonical exact-rate criterion.

Definition 1.6 (Primitive-law Stage arena).

Lean statement: D5/S3/ConceptDynamics/InformationEscape/SystemUnit.arena

Formalization. D5/S3/ConceptDynamics/InformationEscape/SystemUnit.arena (✓ std3).

Source. Repository-derived.

Commentary.

One CUT slot reads a natural-valued engine census at each stage.

Definition 1.7 (Census realization).

Lean statement: D5/S3/ConceptDynamics/InformationEscape/SystemUnit.systemRealization

Formalization. D5/S3/ConceptDynamics/InformationEscape/SystemUnit.systemRealization (✓ std3).

Source. Repository-derived.

Commentary.

The realization calls the catalog’s unique-capture census directly.

Definition 1.8 (SYSTEM statement).

Lean statement: D5/S3/ConceptDynamics/InformationEscape/SystemUnit.SystemStatement

Formalization. D5/S3/ConceptDynamics/InformationEscape/SystemUnit.SystemStatement (✓ std3).

Source. Repository-derived.

Commentary.

The law joins readout identity, exact-rate characterization, and true-stage irredundancy.

Theorem 1.9 (The engine census self-applies).

$$\begin{gathered} (\forall stage:Stage, \\ readout\left(systemRealization,0,stage\right)=uniqueCaptureCount\left(censusCatalog\left(stage\right),0\right))\wedge \\ (\forall stage:Stage, \\ LowersEscape\left(censusCatalog\left(stage\right),0\right)⟺0<uniqueCaptureCount\left(censusCatalog\left(stage\right),0\right))\wedge \\ CatalogIrredundant\left(censusCatalog\left(true\right)\right). \end{gathered}$$

Proof. Machine-checked in Lean as D5/S3/ConceptDynamics/InformationEscape/SystemUnit.engine_census_self_application (✓ std3). ∎

Source. Repository-derived.

Commentary.

The canonical exact-rate theorem proves the characterization; the stage census changes from zero to two.

Theorem 1.10 (Self-application realization certificate).

$$LegacyPrimitiveRealization\left(arena,SystemStatement,systemRealization\right).$$

Proof. Machine-checked in Lean as D5/S3/ConceptDynamics/InformationEscape/SystemUnit.system_self_application_realization (✓ std3). ∎

Source. Repository-derived.

Commentary.

The SYSTEM theorem uses the same legacy registration interface as the ten frozen applications.

References

• Truth anchor: D5/S3/ConceptDynamics/InformationEscape/SystemUnit.Stage
• Truth anchor: D5/S3/ConceptDynamics/InformationEscape/SystemUnit.SystemCharacterization
• Truth anchor: D5/S3/ConceptDynamics/InformationEscape/SystemUnit.SystemStatement
• Truth anchor: D5/S3/ConceptDynamics/InformationEscape/SystemUnit.arena
• Truth anchor: D5/S3/ConceptDynamics/InformationEscape/SystemUnit.censusArena
• Truth anchor: D5/S3/ConceptDynamics/InformationEscape/SystemUnit.censusCatalog
• Truth anchor: D5/S3/ConceptDynamics/InformationEscape/SystemUnit.engine_census_self_application
• Truth anchor: D5/S3/ConceptDynamics/InformationEscape/SystemUnit.systemReadout
• Truth anchor: D5/S3/ConceptDynamics/InformationEscape/SystemUnit.systemRealization
• Truth anchor: D5/S3/ConceptDynamics/InformationEscape/SystemUnit.system_self_application_realization
• Dependency: D5/S3/ConceptDynamics/InformationEscape/Laws