Mechanical Readout Sources

Abstract

Mechanical observations retain their real parameters, finite words, countable atoms, and phase averages.

Definition 1.1 (slopeReadout).

Lean statement: D5/S3/ConceptDynamics/InformationEscape/MechanicalReadoutSources.slopeReadout

Formalization. D5/S3/ConceptDynamics/InformationEscape/MechanicalReadoutSources.slopeReadout (✓ std3).

Source. Repository-derived.

Commentary.

The set contains precisely the unit phases where two finite lower mechanical words differ.

Definition 1.2 (phaseReadout).

Lean statement: D5/S3/ConceptDynamics/InformationEscape/MechanicalReadoutSources.phaseReadout

Formalization. D5/S3/ConceptDynamics/InformationEscape/MechanicalReadoutSources.phaseReadout (✓ std3).

Source. Repository-derived.

Commentary.

The volume measures word disagreement under simultaneous slope and phase changes.

Definition 1.3 (actualPrefix).

Lean statement: D5/S3/ConceptDynamics/InformationEscape/MechanicalReadoutSources.actualPrefix

Formalization. D5/S3/ConceptDynamics/InformationEscape/MechanicalReadoutSources.actualPrefix (✓ std3).

Source. Repository-derived.

Commentary.

An arbitrary real weight sequence sums the observed mechanical letters to a finite horizon.

Definition 1.4 (actualCompletion).

Lean statement: D5/S3/ConceptDynamics/InformationEscape/MechanicalReadoutSources.actualCompletion

Formalization. D5/S3/ConceptDynamics/InformationEscape/MechanicalReadoutSources.actualCompletion (✓ std3).

Source. Repository-derived.

Commentary.

The geometric infinite readout is paired with all its finite weighted prefixes.

Definition 1.5 (seriesReadout).

Lean statement: D5/S3/ConceptDynamics/InformationEscape/MechanicalReadoutSources.seriesReadout

Formalization. D5/S3/ConceptDynamics/InformationEscape/MechanicalReadoutSources.seriesReadout (✓ std3).

Source. Repository-derived.

Commentary.

The floor series, its coefficient mass, and the threshold-counting series share the same parameters.

Definition 1.6 (geometricAtomicMeasure).

Lean statement: D5/S3/ConceptDynamics/InformationEscape/MechanicalReadoutSources.geometricAtomicMeasure

Formalization. D5/S3/ConceptDynamics/InformationEscape/MechanicalReadoutSources.geometricAtomicMeasure (✓ std3).

Source. Repository-derived.

Commentary.

Each numbered threshold contributes its geometric weight as a Dirac mass.

Definition 1.7 (massReadout).

Lean statement: D5/S3/ConceptDynamics/InformationEscape/MechanicalReadoutSources.massReadout

Formalization. D5/S3/ConceptDynamics/InformationEscape/MechanicalReadoutSources.massReadout (✓ std3).

Source. Repository-derived.

Commentary.

For admissible ratio and phase, the readout records total mass and mass on the positive unit interval.

Definition 1.8 (phaseAverageIntegral).

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

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

Source. Repository-derived.

Commentary.

The phase average integrates the atomic measure of a measurable target over the unit phase interval.

References

• Truth anchor: D5/S3/ConceptDynamics/InformationEscape/MechanicalReadoutSources.actualCompletion
• Truth anchor: D5/S3/ConceptDynamics/InformationEscape/MechanicalReadoutSources.actualPrefix
• Truth anchor: D5/S3/ConceptDynamics/InformationEscape/MechanicalReadoutSources.geometricAtomicMeasure
• Truth anchor: D5/S3/ConceptDynamics/InformationEscape/MechanicalReadoutSources.massReadout
• Truth anchor: D5/S3/ConceptDynamics/InformationEscape/MechanicalReadoutSources.phaseAverageIntegral
• Truth anchor: D5/S3/ConceptDynamics/InformationEscape/MechanicalReadoutSources.phaseReadout
• Truth anchor: D5/S3/ConceptDynamics/InformationEscape/MechanicalReadoutSources.seriesReadout
• Truth anchor: D5/S3/ConceptDynamics/InformationEscape/MechanicalReadoutSources.slopeReadout
• Dependency: D5/S1/Words/Mechanical/MechanicalBalance