MechanicalPhaseAverageRegistration

Abstract

The atomic phase average and volume are functions on the same admissible inputs.

Definition 1.1 (Admissible input).

Lean statement: D5/S3/ConceptDynamics/InformationEscape/MechanicalPhaseAverageRegistration.PhaseAverageInput

Formalization. D5/S3/ConceptDynamics/InformationEscape/MechanicalPhaseAverageRegistration.PhaseAverageInput (✓ std3).

Source. Repository-derived.

Commentary.

An input contains a ratio strictly between zero and one and a measurable real set contained in the unit interval.

Definition 1.2 (Phase average).

Lean statement: D5/S3/ConceptDynamics/InformationEscape/MechanicalPhaseAverageRegistration.phaseAverageIntegral

Formalization. D5/S3/ConceptDynamics/InformationEscape/MechanicalPhaseAverageRegistration.phaseAverageIntegral (✓ std3).

Source. Repository-derived.

Commentary.

The first function integrates the geometric atomic measure over half-open phases.

Definition 1.3 (Volume).

Lean statement: D5/S3/ConceptDynamics/InformationEscape/MechanicalPhaseAverageRegistration.phaseAverageVolume

Formalization. D5/S3/ConceptDynamics/InformationEscape/MechanicalPhaseAverageRegistration.phaseAverageVolume (✓ std3).

Source. Repository-derived.

Commentary.

The second function assigns the volume of the same target set.

Definition 1.4 (Readout comparison).

Lean statement: D5/S3/ConceptDynamics/InformationEscape/MechanicalPhaseAverageRegistration.phaseAverageArena

Formalization. D5/S3/ConceptDynamics/InformationEscape/MechanicalPhaseAverageRegistration.phaseAverageArena (✓ std3).

Source. Repository-derived.

Commentary.

Two CUT roles compare the full functions on admissible inputs. The source object domain is the type of real sets; finite readout states only select the roles.

Definition 1.5 (Selected readouts).

Lean statement: D5/S3/ConceptDynamics/InformationEscape/MechanicalPhaseAverageRegistration.phaseAverageRealization

Formalization. D5/S3/ConceptDynamics/InformationEscape/MechanicalPhaseAverageRegistration.phaseAverageRealization (✓ std3).

Source. Repository-derived.

Commentary.

The selected realization reads the phase-average and volume functions.

References

• Truth anchor: D5/S3/ConceptDynamics/InformationEscape/MechanicalPhaseAverageRegistration.PhaseAverageInput
• Truth anchor: D5/S3/ConceptDynamics/InformationEscape/MechanicalPhaseAverageRegistration.phaseAverageArena
• Truth anchor: D5/S3/ConceptDynamics/InformationEscape/MechanicalPhaseAverageRegistration.phaseAverageIntegral
• Truth anchor: D5/S3/ConceptDynamics/InformationEscape/MechanicalPhaseAverageRegistration.phaseAverageRealization
• Truth anchor: D5/S3/ConceptDynamics/InformationEscape/MechanicalPhaseAverageRegistration.phaseAverageVolume
• Dependency: D5/S1/Words/Mechanical/MechanicalReadoutAtomicMeasure
• Dependency: D5/S3/ConceptDynamics/InformationEscape/MechanicalReadoutSources
• Dependency: D5/S3/ConceptDynamics/InformationEscape/ObjectDomainArena
• Dependency: D5/S3/ConceptDynamics/InformationEscape/PointwiseRegistrationTemplates