Entropy / CONCEPT
Equality and Strict Loss under Deterministic Forgetting
Deterministic finite pushforwards preserve entropy exactly on support-injective maps and lose entropy strictly otherwise.
Closed
DIRECT PREREQUISITES3
DIRECT CONSEQUENCES6
PROOF DEPTH6
DOCUMENT LINKS1
Pushforward entropy equality is injectivity on support
RELATIONSHIP ATLAS
Every connection, in context.
Direct recorded relationships
Proof dependencyStructural affinityDocument link
Certified topology / UPSTREAM
Prerequisites
Certified topology / DOWNSTREAM
Consequences
- Concept Entropy under Refinementtruth-dependency · Closed
- Deterministic Entropy Steptruth-dependency · Closed
- Deterministic Output Entropy Ratetruth-dependency · Closed
- Information Loss under a Finite Free Group Quotienttruth-dependency · Closed
- Labelled Responses and Completion Geometrytruth-dependency · Closed
- Quotient-Fiber Entropy Decompositiontruth-dependency · Closed
RELATED KNOWLEDGE
Structural connections
- Actual Same-Task Cut Boundsstructural-affinity · Closed
- Binary Character Uniform Information Exactnessstructural-affinity · Closed
- Concept Entropy under Refinementstructural-affinity · Closed
- Deterministic Entropy Stepstructural-affinity · Closed
- Deterministic Output Entropy Ratestructural-affinity · Closed
- Deterministic Readout Entropy Decompositionstructural-affinity · Closed
- Dual Repair Entropy Decompositionstructural-affinity · Closed
- Equality at the Lower Endpoint of Conditional Entropystructural-affinity · Closed
- Equality in the Upper Mixture-Entropy Boundstructural-affinity · Closed
- Hidden Arithmetic Weightstructural-affinity · Closed
- Information Cost of Concept Completionstructural-affinity · Closed
- Information Loss under a Finite Free Group Quotientstructural-affinity · Closed
- Labelled Responses and Completion Geometrystructural-affinity · Closed
- Perfect Observational Correlation from a Shared Sourcestructural-affinity · Closed
- Quotient-Fiber Entropy Decompositionstructural-affinity · Closed
- Shannon Entropy Is Invariant Under Injective Relabelingstructural-affinity · Closed
- Shared Source Observation Dependencestructural-affinity · Closed
- Shared-Source Local Interventionstructural-affinity · Closed
- The Actual Boolean Obstruction and Original Upper Contractstructural-affinity · Closed
Documents & exposition
Other authored & advisory relationships
None recorded in this release.
LIBRARY / RELEASE VERSIONS
Content history
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