TotalVariation

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Contents

• Asymptotics
• Bhattacharyya Affinity and the Bretagnolle–Huber Bound
• Bhattacharyya Affinity on Finite Products
• Joint Convexity of Total Variation and Squared Hellinger Distance
• Sharp coupling budgets on a permutation cycle
• Data Processing for Finite Total Variation
• Equality
• Squared Hellinger Distance and Total Variation
• Hellinger Data Processing Through Affinity
• Squared Hellinger Distance, Divergence, and Metric Laws
• Independent finite convolution: the exact L1 minimum
• Exponential Bound for Repeated Failure Factors
• Metric Laws and Variational Characterization for Finite Total Variation
• The Finite Negentropy Budget
• Composition parity and biased Bernoulli parity
• Parity kernel masses
• The bilateral Parry source and its signed path law
• Mixing and measurable selection for the bilateral Parry source
• Boundary selection from actual run cylinders
• Three-step common mass
• The stationary signed Parry law
• Unique parsing of complete Parry runs
• Uniform stationary defect of the shared rule
• Complete zero runs and the shared window rule
• Actual mixing and complete-prefix comparison
• Finite Parry window upper bounds
• Conditional Parry words and collisions
• Finite Total Variation and Pinsker’s Inequality
• Primitive bridge cancellation
• Product Subadditivity of Total Variation
• A shared-rule defect requires a boundary event
• The Spectral Sharpness Negentropy Budget
• Actual Finite-Tree Markov Stability
• Tree Parity Kernels
• Complete Twisted Prefix Comparison
• Twisted Reset Paths
• Twisted Rotation and Parry Window Defects
• Same-rule Defects on Twisted Cycles