Shared-Arena Analysis Laws

Abstract

Shared-arena capture sets support certified overlap, refinement, multiplicity-spectrum, and role-histogram analysis.

Definition 1.1 (Occurrence capture pairs).

Lean statement: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.capturePairs

Formalization. D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.capturePairs (✓ std3).

Source. Repository-derived.

Commentary.

The capture set removes the singleton-kernel escape set from all ordered off-diagonal state pairs.

Definition 1.2 (Exclusive capture vector).

Lean statement: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.exclusiveCaptureVector

Formalization. D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.exclusiveCaptureVector (✓ std3).

Source. Repository-derived.

Commentary.

Each catalog coordinate is its peer-relative unique-capture cardinality.

Definition 1.3 (Pairwise capture overlap).

Lean statement: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.pairwiseCaptureOverlapPairs

Formalization. D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.pairwiseCaptureOverlapPairs (✓ std3).

Source. Repository-derived.

Commentary.

An overlap cell is the intersection of two occurrence capture sets.

Definition 1.4 (Pairwise overlap count).

Lean statement: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.pairwiseCaptureOverlapCount

Formalization. D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.pairwiseCaptureOverlapCount (✓ std3).

Source. Repository-derived.

Commentary.

The count is the exact cardinality of one overlap cell.

Definition 1.5 (Pairwise overlap rate).

Lean statement: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.pairwiseCaptureOverlapRate

Formalization. D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.pairwiseCaptureOverlapRate (✓ std3).

Source. Repository-derived.

Commentary.

The exact rational rate uses the common arena denominator.

Definition 1.6 (Role-signature rate).

Lean statement: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.roleSignatureRate

Formalization. D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.roleSignatureRate (✓ std3).

Source. Repository-derived.

Commentary.

The exact rational rate divides one role-signature count by the common arena denominator.

Definition 1.7 (Occurrence kernel refinement).

Lean statement: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.KernelRefines

Formalization. D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.KernelRefines (✓ std3).

Source. Repository-derived.

Commentary.

The finer occurrence agreement relation is pointwise contained in the coarser relation.

Definition 1.8 (Occurrence kernel equivalence).

Lean statement: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.KernelEquivalent

Formalization. D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.KernelEquivalent (✓ std3).

Source. Repository-derived.

Commentary.

Two occurrence kernels are equivalent when they refine one another.

Definition 1.9 (Capture multiplicity).

Lean statement: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.captureMultiplicity

Formalization. D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.captureMultiplicity (✓ std3).

Source. Repository-derived.

Commentary.

Multiplicity counts how many catalog occurrences capture one ordered state pair.

Definition 1.10 (Capture-multiplicity spectrum).

Lean statement: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.captureSpectrum

Formalization. D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.captureSpectrum (✓ std3).

Source. Repository-derived.

Commentary.

Each bucket counts off-diagonal pairs having exactly its indexed multiplicity.

Definition 1.11 (Multiplicity-one index).

Lean statement: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.captureMultiplicityOne

Formalization. D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.captureMultiplicityOne (✓ std3).

Source. Repository-derived.

Commentary.

A nonempty catalog has a genuine spectrum coordinate for multiplicity one.

Definition 1.12 (Ordered distinct overlap total).

Lean statement: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.orderedDistinctOverlapTotal

Formalization. D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.orderedDistinctOverlapTotal (✓ std3).

Source. Repository-derived.

Commentary.

The total sums all overlap counts over ordered distinct occurrence pairs.

Definition 1.13 (Second factorial spectrum moment).

Lean statement: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.captureSpectrumSecondFactorialMoment

Formalization. D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.captureSpectrumSecondFactorialMoment (✓ std3).

Source. Repository-derived.

Commentary.

The second factorial moment weights each bucket by k times k minus one.

Definition 1.14 (Role column total).

Lean statement: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.roleHistogramTotal

Formalization. D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.roleHistogramTotal (✓ std3).

Source. Repository-derived.

Commentary.

A role-signature column is summed across the entire catalog.

Definition 1.15 (Role profile equality).

Lean statement: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.roleProfileEq

Formalization. D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.roleProfileEq (✓ std3).

Source. Repository-derived.

Commentary.

Two occurrences have equal role profiles when every role-signature count agrees.

Definition 1.16 (Role histogram difference).

Lean statement: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.roleHistogramDifference

Formalization. D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.roleHistogramDifference (✓ std3).

Source. Repository-derived.

Commentary.

A signed column difference compares two catalog occurrences.

Theorem 1.17 (Zero role difference exactly means equal counts).

$$\mathrm{roleHistogramDifference}(C,i,j,s)=0\iff \mathrm{roleHistogram}(C,i,s)=\mathrm{roleHistogram}(C,j,s).$$

Proof. Machine-checked in Lean as D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.roleHistogramDifference_eq_zero_iff (✓ std3). ∎

Source. Repository-derived.

Commentary.

The certificate follows from finite capture-set algebra and the landed escape and role-histogram laws.

Theorem 1.18 (Role profiles agree exactly when every difference vanishes).

$$\mathrm{roleProfileEq}(C,i,j)\iff \forall s,\mathrm{roleHistogramDifference}(C,i,j,s)=0.$$

Proof. Machine-checked in Lean as D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.roleProfileEq_iff_difference_zero (✓ std3). ∎

Source. Repository-derived.

Commentary.

The certificate follows from finite capture-set algebra and the landed escape and role-histogram laws.

Definition 1.19 (Redundant occurrence indices).

Lean statement: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.redundantIndices

Formalization. D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.redundantIndices (✓ std3).

Source. Repository-derived.

Commentary.

The redundant-index set contains exactly occurrences with zero unique capture.

Definition 1.20 (Catalog redundancy).

Lean statement: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.CatalogRedundant

Formalization. D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.CatalogRedundant (✓ std3).

Source. Repository-derived.

Commentary.

A catalog is redundant when at least one occurrence has zero unique capture.

Theorem 1.21 (Unique capture is capture minus peer capture).

$$\mathrm{uniqueCapturePairs}(C,i)=\mathrm{sdiff}(\mathrm{capturePairs}(C,i),\mathrm{biUnion}(\mathrm{erase}(\mathrm{univ}(),i),\lambda j,\mathrm{capturePairs}(C,j))).$$

Proof. Machine-checked in Lean as D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.uniqueCapturePairs_eq_capture_sdiff_iUnion (✓ std3). ∎

Source. Repository-derived.

Commentary.

The certificate follows from finite capture-set algebra and the landed escape and role-histogram laws.

Theorem 1.22 (Unique-capture sets are pairwise disjoint).

$$i\ne j\Rightarrow \mathrm{Disjoint}(\mathrm{uniqueCapturePairs}(C,i),\mathrm{uniqueCapturePairs}(C,j)).$$

Proof. Machine-checked in Lean as D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.uniqueCapturePairs_pairwise_disjoint (✓ std3). ∎

Source. Repository-derived.

Commentary.

The certificate follows from finite capture-set algebra and the landed escape and role-histogram laws.

Theorem 1.23 (Exclusive capture is bounded by full capture).

$$\sum _i\mathrm{uniqueCaptureCount}(C,i)\le \mathrm{card}(\mathrm{sdiff}(\mathrm{offDiagonalPairs}(\mathrm{State}(A)),\mathrm{escapePairs}(C,\mathrm{fullIndexSet}(C)))).$$

Proof. Machine-checked in Lean as D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.sum_uniqueCaptureCount_le_capturedCount (✓ std3). ∎

Source. Repository-derived.

Commentary.

The certificate follows from finite capture-set algebra and the landed escape and role-histogram laws.

Theorem 1.24 (Pairwise overlap is symmetric).

$$\mathrm{pairwiseCaptureOverlapPairs}(C,i,j)=\mathrm{pairwiseCaptureOverlapPairs}(C,j,i).$$

Proof. Machine-checked in Lean as D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.pairwiseCaptureOverlap_comm (✓ std3). ∎

Source. Repository-derived.

Commentary.

The certificate follows from finite capture-set algebra and the landed escape and role-histogram laws.

Theorem 1.25 (Diagonal overlap is capture).

$$\mathrm{pairwiseCaptureOverlapPairs}(C,i,i)=\mathrm{capturePairs}(C,i).$$

Proof. Machine-checked in Lean as D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.pairwiseCaptureOverlap_diag (✓ std3). ∎

Source. Repository-derived.

Commentary.

The certificate follows from finite capture-set algebra and the landed escape and role-histogram laws.

Theorem 1.26 (Overlap lies in both capture cells).

$$\mathrm{pairwiseCaptureOverlapPairs}(C,i,j)\subseteq \mathrm{capturePairs}(C,i)\wedge \mathrm{pairwiseCaptureOverlapPairs}(C,i,j)\subseteq \mathrm{capturePairs}(C,j).$$

Proof. Machine-checked in Lean as D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.pairwiseCaptureOverlap_subset (✓ std3). ∎

Source. Repository-derived.

Commentary.

The certificate follows from finite capture-set algebra and the landed escape and role-histogram laws.

Theorem 1.27 (Overlap count is bounded by both capture counts).

$$\mathrm{pairwiseCaptureOverlapCount}(C,i,j)\le \mathrm{card}(\mathrm{capturePairs}(C,i))\wedge \mathrm{pairwiseCaptureOverlapCount}(C,i,j)\le \mathrm{card}(\mathrm{capturePairs}(C,j)).$$

Proof. Machine-checked in Lean as D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.pairwiseCaptureOverlapCount_le (✓ std3). ∎

Source. Repository-derived.

Commentary.

The certificate follows from finite capture-set algebra and the landed escape and role-histogram laws.

Theorem 1.28 (Kernel refinement is a preorder).

$$(\forall i,\mathrm{KernelRefines}(C,i,i))\wedge (\forall i,j,k,\mathrm{KernelRefines}(C,i,j)\Rightarrow \left(\mathrm{KernelRefines}(C,j,k)\Rightarrow \mathrm{KernelRefines}(C,i,k)\right)).$$

Proof. Machine-checked in Lean as D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.kernelRefines_preorder (✓ std3). ∎

Source. Repository-derived.

Commentary.

The certificate follows from finite capture-set algebra and the landed escape and role-histogram laws.

Theorem 1.29 (Refinement reverses capture inclusion).

$$\mathrm{KernelRefines}(C,i,j)\iff \mathrm{capturePairs}(C,j)\subseteq \mathrm{capturePairs}(C,i).$$

Proof. Machine-checked in Lean as D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.kernelRefines_iff_capturePairs_subset (✓ std3). ∎

Source. Repository-derived.

Commentary.

The certificate follows from finite capture-set algebra and the landed escape and role-histogram laws.

Theorem 1.30 (A distinct finer peer zeros coarser unique capture).

$$\left(i\ne j\wedge \mathrm{KernelRefines}(C,i,j)\right)\Rightarrow \mathrm{uniqueCapturePairs}(C,j)=\varnothing .$$

Proof. Machine-checked in Lean as D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.kernelRefines_implies_zero_uniqueCapture (✓ std3). ∎

Source. Repository-derived.

Commentary.

The certificate follows from finite capture-set algebra and the landed escape and role-histogram laws.

Theorem 1.31 (A distinct finer peer zeros coarser unique count).

$$\left(i\ne j\wedge \mathrm{KernelRefines}(C,i,j)\right)\Rightarrow \mathrm{uniqueCaptureCount}(C,j)=0.$$

Proof. Machine-checked in Lean as D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.kernelRefines_implies_zero_uniqueCaptureCount (✓ std3). ∎

Source. Repository-derived.

Commentary.

The certificate follows from finite capture-set algebra and the landed escape and role-histogram laws.

Theorem 1.32 (Redundancy is existence of a zero coordinate).

$$\mathrm{CatalogRedundant}(C)\iff \exists i,\mathrm{uniqueCaptureCount}(C,i)=0.$$

Proof. Machine-checked in Lean as D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.catalogRedundant_iff_exists_zero (✓ std3). ∎

Source. Repository-derived.

Commentary.

The certificate follows from finite capture-set algebra and the landed escape and role-histogram laws.

Theorem 1.33 (Redundancy negates catalog irredundancy).

$$\mathrm{CatalogRedundant}(C)\iff \neg \mathrm{CatalogIrredundant}(C).$$

Proof. Machine-checked in Lean as D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.catalogRedundant_iff_not_catalogIrredundant (✓ std3). ∎

Source. Repository-derived.

Commentary.

The certificate follows from finite capture-set algebra and the landed escape and role-histogram laws.

Theorem 1.34 (Irredundancy empties the redundant-index set).

$$\mathrm{CatalogIrredundant}(C)\iff \mathrm{redundantIndices}(C)=\varnothing .$$

Proof. Machine-checked in Lean as D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.catalogIrredundant_iff_redundantIndices_eq_empty (✓ std3). ∎

Source. Repository-derived.

Commentary.

The certificate follows from finite capture-set algebra and the landed escape and role-histogram laws.

Theorem 1.35 (Spec-name redundancy equivalence).

$$\mathrm{CatalogRedundant}(C)\iff \neg \mathrm{CatalogIrredundant}(C).$$

Proof. Machine-checked in Lean as D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.catalogRedundant_iff_not_irredundant (✓ std3). ∎

Source. Repository-derived.

Commentary.

The certificate follows from finite capture-set algebra and the landed escape and role-histogram laws.

Theorem 1.36 (Spectrum buckets partition the arena denominator).

$$\sum _k\mathrm{captureSpectrum}(C,k)=\mathrm{card}(\mathrm{offDiagonalPairs}(\mathrm{State}(A))).$$

Proof. Machine-checked in Lean as D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.captureSpectrum_sum_eq_denominator (✓ std3). ∎

Source. Repository-derived.

Commentary.

The certificate follows from finite capture-set algebra and the landed escape and role-histogram laws.

Theorem 1.37 (Zero multiplicity is full escape).

$$\mathrm{captureSpectrum}(C,0)=\mathrm{card}(\mathrm{escapePairs}(C,\mathrm{fullIndexSet}(C))).$$

Proof. Machine-checked in Lean as D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.captureSpectrum_zero_eq_fullEscape (✓ std3). ∎

Source. Repository-derived.

Commentary.

The certificate follows from finite capture-set algebra and the landed escape and role-histogram laws.

Theorem 1.38 (Multiplicity one is total exclusive capture).

$$\mathrm{captureSpectrum}(C,\mathrm{captureMultiplicityOne}(C))=\sum _i\mathrm{uniqueCaptureCount}(C,i).$$

Proof. Machine-checked in Lean as D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.captureSpectrum_one_eq_sum_unique (✓ std3). ∎

Source. Repository-derived.

Commentary.

The certificate follows from finite capture-set algebra and the landed escape and role-histogram laws.

Theorem 1.39 (The first moment double-counts capture incidence).

$$\sum _{k}k\times \mathrm{captureSpectrum}(C,k)=\sum _i\mathrm{card}(\mathrm{capturePairs}(C,i)).$$

Proof. Machine-checked in Lean as D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.captureSpectrum_incidence_double_count (✓ std3). ∎

Source. Repository-derived.

Commentary.

The certificate follows from finite capture-set algebra and the landed escape and role-histogram laws.

Theorem 1.40 (Overlap is the second factorial moment).

$$\mathrm{orderedDistinctOverlapTotal}(C)=\mathrm{captureSpectrumSecondFactorialMoment}(C).$$

Proof. Machine-checked in Lean as D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.pairwiseOverlap_spectrum_doubleCount (✓ std3). ∎

Source. Repository-derived.

Commentary.

The certificate follows from finite capture-set algebra and the landed escape and role-histogram laws.

Theorem 1.41 (Role columns sum to exclusive capture).

$$\sum _{swiths\ne (\lambda b,false)}\mathrm{roleHistogramTotal}(C,s)=\sum _i\mathrm{uniqueCaptureCount}(C,i)\wedge \sum _i\mathrm{uniqueCaptureCount}(C,i)=\mathrm{captureSpectrum}(C,\mathrm{captureMultiplicityOne}(C)).$$

Proof. Machine-checked in Lean as D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.catalogRoleHistogram_sum (✓ std3). ∎

Source. Repository-derived.

Commentary.

The certificate follows from finite capture-set algebra and the landed escape and role-histogram laws.

Theorem 1.42 (Hierarchy spectrum total).

$$\sum _k\mathrm{captureSpectrum}(C,k)=\mathrm{card}(\mathrm{offDiagonalPairs}(\mathrm{State}(A))).$$

Proof. Machine-checked in Lean as D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.spectrum_total (✓ std3). ∎

Source. Repository-derived.

Commentary.

The certificate follows from finite capture-set algebra and the landed escape and role-histogram laws.

Theorem 1.43 (Hierarchy zero-multiplicity bucket).

$$\mathrm{captureSpectrum}(C,0)=\mathrm{card}(\mathrm{escapePairs}(C,\mathrm{fullIndexSet}(C))).$$

Proof. Machine-checked in Lean as D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.spectrum_zero (✓ std3). ∎

Source. Repository-derived.

Commentary.

The certificate follows from finite capture-set algebra and the landed escape and role-histogram laws.

Theorem 1.44 (Hierarchy multiplicity-one bucket).

$$\mathrm{captureSpectrum}(C,\mathrm{captureMultiplicityOne}(C))=\sum _i\mathrm{uniqueCaptureCount}(C,i).$$

Proof. Machine-checked in Lean as D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.spectrum_unique (✓ std3). ∎

Source. Repository-derived.

Commentary.

The certificate follows from finite capture-set algebra and the landed escape and role-histogram laws.

Theorem 1.45 (Hierarchy first spectrum moment).

$$\sum _{k}k\times \mathrm{captureSpectrum}(C,k)=\sum _i\mathrm{card}(\mathrm{capturePairs}(C,i)).$$

Proof. Machine-checked in Lean as D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.spectrum_first_moment (✓ std3). ∎

Source. Repository-derived.

Commentary.

The certificate follows from finite capture-set algebra and the landed escape and role-histogram laws.

Theorem 1.46 (Hierarchy second spectrum moment).

$$\mathrm{captureSpectrumSecondFactorialMoment}(C)=\mathrm{orderedDistinctOverlapTotal}(C).$$

Proof. Machine-checked in Lean as D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.spectrum_second_moment (✓ std3). ∎

Source. Repository-derived.

Commentary.

The certificate follows from finite capture-set algebra and the landed escape and role-histogram laws.

Theorem 1.47 (Overlap symmetry and diagonal law).

$$\mathrm{pairwiseCaptureOverlapPairs}(C,i,j)=\mathrm{pairwiseCaptureOverlapPairs}(C,j,i)\wedge \mathrm{pairwiseCaptureOverlapPairs}(C,i,i)=\mathrm{capturePairs}(C,i).$$

Proof. Machine-checked in Lean as D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.overlap_symmetric_diagonal (✓ std3). ∎

Source. Repository-derived.

Commentary.

The certificate follows from finite capture-set algebra and the landed escape and role-histogram laws.

Theorem 1.48 (Refinement determines overlap).

$$\mathrm{KernelRefines}(C,i,j)\Rightarrow \left(\mathrm{capturePairs}(C,j)\subseteq \mathrm{capturePairs}(C,i)\wedge \mathrm{pairwiseCaptureOverlapPairs}(C,i,j)=\mathrm{capturePairs}(C,j)\right).$$

Proof. Machine-checked in Lean as D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.refinement_overlap (✓ std3). ∎

Source. Repository-derived.

Commentary.

The certificate follows from finite capture-set algebra and the landed escape and role-histogram laws.

References

• Truth anchor: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.CatalogRedundant
• Truth anchor: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.KernelEquivalent
• Truth anchor: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.KernelRefines
• Truth anchor: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.captureMultiplicity
• Truth anchor: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.captureMultiplicityOne
• Truth anchor: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.capturePairs
• Truth anchor: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.captureSpectrum
• Truth anchor: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.captureSpectrumSecondFactorialMoment
• Truth anchor: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.captureSpectrum_incidence_double_count
• Truth anchor: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.captureSpectrum_one_eq_sum_unique
• Truth anchor: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.captureSpectrum_sum_eq_denominator
• Truth anchor: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.captureSpectrum_zero_eq_fullEscape
• Truth anchor: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.catalogIrredundant_iff_redundantIndices_eq_empty
• Truth anchor: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.catalogRedundant_iff_exists_zero
• Truth anchor: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.catalogRedundant_iff_not_catalogIrredundant
• Truth anchor: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.catalogRedundant_iff_not_irredundant
• Truth anchor: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.catalogRoleHistogram_sum
• Truth anchor: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.exclusiveCaptureVector
• Truth anchor: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.kernelRefines_iff_capturePairs_subset
• Truth anchor: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.kernelRefines_implies_zero_uniqueCapture
• Truth anchor: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.kernelRefines_implies_zero_uniqueCaptureCount
• Truth anchor: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.kernelRefines_preorder
• Truth anchor: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.orderedDistinctOverlapTotal
• Truth anchor: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.overlap_symmetric_diagonal
• Truth anchor: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.pairwiseCaptureOverlapCount
• Truth anchor: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.pairwiseCaptureOverlapCount_le
• Truth anchor: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.pairwiseCaptureOverlapPairs
• Truth anchor: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.pairwiseCaptureOverlapRate
• Truth anchor: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.pairwiseCaptureOverlap_comm
• Truth anchor: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.pairwiseCaptureOverlap_diag
• Truth anchor: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.pairwiseCaptureOverlap_subset
• Truth anchor: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.pairwiseOverlap_spectrum_doubleCount
• Truth anchor: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.redundantIndices
• Truth anchor: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.refinement_overlap
• Truth anchor: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.roleHistogramDifference
• Truth anchor: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.roleHistogramDifference_eq_zero_iff
• Truth anchor: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.roleHistogramTotal
• Truth anchor: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.roleProfileEq
• Truth anchor: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.roleProfileEq_iff_difference_zero
• Truth anchor: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.roleSignatureRate
• Truth anchor: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.spectrum_first_moment
• Truth anchor: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.spectrum_second_moment
• Truth anchor: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.spectrum_total
• Truth anchor: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.spectrum_unique
• Truth anchor: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.spectrum_zero
• Truth anchor: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.sum_uniqueCaptureCount_le_capturedCount
• Truth anchor: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.uniqueCapturePairs_eq_capture_sdiff_iUnion
• Truth anchor: D5/S3/ConceptDynamics/InformationEscapeHierarchy/AnalysisLaws.uniqueCapturePairs_pairwise_disjoint
• Dependency: D5/S3/ConceptDynamics/InformationEscape/RoleHistogram