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MechanicalAtomicMeasureRegistration

Abstract

The atomic measure is compared with its mass, distribution, hit, and support targets on complete admissible parameter families.

Definition 1.1 (Mass parameters).

Lean statement: D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.MassInput

Formalization. D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.MassInput (✓ std3).

Source. Repository-derived.

Commentary.

The input stores a real ratio and phase; the target law checks the admissible range.

Definition 1.2 (Mass readout).

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

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

Source. Repository-derived.

Commentary.

The first coordinate is total mass and the second is mass on the positive unit interval.

Definition 1.3 (Mass target).

Lean statement: D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.massTarget

Formalization. D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.massTarget (✓ std3).

Source. Repository-derived.

Commentary.

Both coordinates equal one on admissible parameters; elsewhere the target equals the measured readout.

Definition 1.4 (Mass family).

Lean statement: D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.MassOutput

Formalization. D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.MassOutput (✓ std3).

Source. Repository-derived.

Commentary.

Each readout retains its value on every admissible mass input.

Definition 1.5 (Distribution parameters).

Lean statement: D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.DistributionInput

Formalization. D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.DistributionInput (✓ std3).

Source. Repository-derived.

Commentary.

The input stores a real ratio, threshold, and phase; the target law checks their admissible ranges.

Definition 1.6 (Distribution readout).

Lean statement: D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.distributionReadout

Formalization. D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.distributionReadout (✓ std3).

Source. Repository-derived.

Commentary.

The geometric atomic measure is evaluated on the interval below the threshold.

Definition 1.7 (Distribution target).

Lean statement: D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.distributionTarget

Formalization. D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.distributionTarget (✓ std3).

Source. Repository-derived.

Commentary.

On admissible parameters the target is the completed mechanical readout; elsewhere it equals the measured distribution.

Definition 1.8 (Distribution family).

Lean statement: D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.DistributionOutput

Formalization. D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.DistributionOutput (✓ std3).

Source. Repository-derived.

Commentary.

The readout is a function on all admissible distribution parameters.

Definition 1.9 (Singleton parameters).

Lean statement: D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.HitInput

Formalization. D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.HitInput (✓ std3).

Source. Repository-derived.

Commentary.

The input stores a real ratio, phase, and threshold; the target law checks the phase and interior threshold conditions.

Definition 1.10 (Singleton mass).

Lean statement: D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.hitReadout

Formalization. D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.hitReadout (✓ std3).

Source. Repository-derived.

Commentary.

The atomic measure is evaluated at the singleton threshold.

Definition 1.11 (Integer-hit series).

Lean statement: D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.hitTarget

Formalization. D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.hitTarget (✓ std3).

Source. Repository-derived.

Commentary.

On admissible parameters each integer-hit time contributes its coefficient; elsewhere the target equals singleton mass.

Definition 1.12 (Singleton family).

Lean statement: D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.HitOutput

Formalization. D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.HitOutput (✓ std3).

Source. Repository-derived.

Commentary.

The singleton law retains all admissible ratios, phases, and thresholds.

Definition 1.13 (Support parameters).

Lean statement: D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.SupportInput

Formalization. D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.SupportInput (✓ std3).

Source. Repository-derived.

Commentary.

The input stores a real ratio and phase; the target law checks their admissible ranges.

Definition 1.14 (Measured support).

Lean statement: D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.supportReadout

Formalization. D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.supportReadout (✓ std3).

Source. Repository-derived.

Commentary.

The readout is the topological support of the geometric atomic measure.

Definition 1.15 (Support target).

Lean statement: D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.supportTarget

Formalization. D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.supportTarget (✓ std3).

Source. Repository-derived.

Commentary.

The target is the closed unit interval on admissible parameters and the measured support elsewhere.

Definition 1.16 (Support family).

Lean statement: D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.SupportOutput

Formalization. D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.SupportOutput (✓ std3).

Source. Repository-derived.

Commentary.

The support comparison retains every admissible ratio and phase.

Definition 1.17 (Mass comparison).

Lean statement: D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.massArena

Formalization. D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.massArena (✓ std3).

Source. Repository-derived.

Commentary.

One CUT role reads the complete mass function; the law equates it with the target on every parameter.

Definition 1.18 (Distribution comparison).

Lean statement: D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.distributionArena

Formalization. D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.distributionArena (✓ std3).

Source. Repository-derived.

Commentary.

One CUT role reads the atomic distribution function; the law equates it with the completed mechanical readout.

Definition 1.19 (Singleton comparison).

Lean statement: D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.hitArena

Formalization. D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.hitArena (✓ std3).

Source. Repository-derived.

Commentary.

One CUT role reads singleton mass; the law equates it with the integer-hit series.

Definition 1.20 (Support comparison).

Lean statement: D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.supportArena

Formalization. D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.supportArena (✓ std3).

Source. Repository-derived.

Commentary.

One CUT role reads the support function; the law equates it with the closed-interval target.

Definition 1.21 (Mass realization).

Lean statement: D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.massRealization

Formalization. D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.massRealization (✓ std3).

Source. Repository-derived.

Commentary.

The selected readout is the measured mass pair at each ratio and phase.

Definition 1.22 (Distribution realization).

Lean statement: D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.distributionRealization

Formalization. D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.distributionRealization (✓ std3).

Source. Repository-derived.

Commentary.

The selected readout is the atomic distribution at each ratio, threshold, and phase.

Definition 1.23 (Singleton realization).

Lean statement: D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.hitRealization

Formalization. D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.hitRealization (✓ std3).

Source. Repository-derived.

Commentary.

The selected readout is singleton mass at each ratio, phase, and threshold.

Definition 1.24 (Support realization).

Lean statement: D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.supportRealization

Formalization. D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.supportRealization (✓ std3).

Source. Repository-derived.

Commentary.

The selected readout is measured support at each ratio and phase.

Definition 1.25 (Complete readout).

Lean statement: D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.JumpOutput

Formalization. D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.JumpOutput (✓ std3).

Source. Repository-derived.

Commentary.

The output records the completed mechanical readout at every ratio, slope, and phase.

Definition 1.26 (Selected readout).

Lean statement: D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.jumpReadout

Formalization. D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.jumpReadout (✓ std3).

Source. Repository-derived.

Commentary.

The selected function is the completed mechanical readout.

Definition 1.27 (Rational jump law).

Lean statement: D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.rationalJumpArena

Formalization. D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.rationalJumpArena (✓ std3).

Source. Repository-derived.

Commentary.

At reduced rational slopes and zero phase, the CUT function has the stated geometric jump.

Definition 1.28 (Readout realization).

Lean statement: D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.jumpRealization

Formalization. D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.jumpRealization (✓ std3).

Source. Repository-derived.

Commentary.

The realization uses the completed mechanical readout in the rational jump law.

References

  • Truth anchor: D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.DistributionInput
  • Truth anchor: D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.DistributionOutput
  • Truth anchor: D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.HitInput
  • Truth anchor: D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.HitOutput
  • Truth anchor: D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.JumpOutput
  • Truth anchor: D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.MassInput
  • Truth anchor: D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.MassOutput
  • Truth anchor: D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.SupportInput
  • Truth anchor: D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.SupportOutput
  • Truth anchor: D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.distributionArena
  • Truth anchor: D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.distributionReadout
  • Truth anchor: D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.distributionRealization
  • Truth anchor: D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.distributionTarget
  • Truth anchor: D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.hitArena
  • Truth anchor: D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.hitReadout
  • Truth anchor: D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.hitRealization
  • Truth anchor: D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.hitTarget
  • Truth anchor: D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.jumpReadout
  • Truth anchor: D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.jumpRealization
  • Truth anchor: D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.massArena
  • Truth anchor: D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.massReadout
  • Truth anchor: D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.massRealization
  • Truth anchor: D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.massTarget
  • Truth anchor: D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.rationalJumpArena
  • Truth anchor: D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.supportArena
  • Truth anchor: D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.supportReadout
  • Truth anchor: D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.supportRealization
  • Truth anchor: D5/S3/ConceptDynamics/InformationEscape/MechanicalAtomicMeasureRegistration.supportTarget
  • Dependency: D5/S1/Words/Mechanical/MechanicalReadoutAtomicMeasure
  • Dependency: D5/S3/ConceptDynamics/InformationEscape/MechanicalDyadicRegistration
  • Dependency: D5/S3/ConceptDynamics/InformationEscape/MechanicalReadoutSources
  • Dependency: D5/S3/ConceptDynamics/InformationEscape/ObjectDomainArena
  • Dependency: D5/S3/ConceptDynamics/InformationEscape/PointwiseRegistrationTemplates