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 CONSEQUENCES4
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
RELATED KNOWLEDGE
Structural connections
- 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
- Entropy and Capacity under Carrier Forgettingstructural-affinity · Closed
- Entropy Telescoping along Deterministic Trajectoriesstructural-affinity · Closed
- Equality at the Lower Endpoint of Conditional Entropystructural-affinity · Closed
- Equality in the Upper Mixture-Entropy Boundstructural-affinity · Closed
- Fusion State Entropystructural-affinity · Closed
- Information Cost of Concept Completionstructural-affinity · Closed
- Multi-Target Information Chainstructural-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
Documents & exposition
Other authored & advisory relationships
None recorded in this release.
LIBRARY / RELEASE VERSIONS
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