trureturingGitHub MATHEMATICAL ATLAS

Entropy / CONCEPT

Entropy and Capacity under Carrier Forgetting

A genuine finite carrier merge lowers accessible capacity and cannot increase Shannon entropy.

Closed Authored exposition
DIRECT PREREQUISITES2
DIRECT CONSEQUENCES13
PROOF DEPTH5
DOCUMENT LINKS1
THEOREM

Deterministic forgetting lowers entropy and capacity

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Conditional Entropy and Its Chain RuleConditional Entropy and ItsChain RuleNonnegativity of Finite EntropyNonnegativity of Finite EntropyEntropy and Capacity under Carrier ForgettingEntropy and Capacity underCarrier ForgettingTranslation Loss under PostprocessingTranslation Loss underPostprocessingInformation Cost of Concept CompletionInformation Cost of ConceptCompletionKullback-Leibler Loss under Deterministic ForgettingKullback-Leibler Loss underDeterministic ForgettingConditional Entropy under Completion FactorizationConditional Entropy underCompletion FactorizationConditional Information PostprocessingConditional InformationPostprocessingEquality and Strict Loss under Deterministic ForgettingEquality and Strict Loss underDeterministic ForgettingEntropy Telescoping along Deterministic TrajectoriesEntropy Telescoping alongDeterministic TrajectoriesFusion State EntropyFusion State EntropyObservation-Word and Completion Information DecompositionObservation-Word and CompletionInformation DecompositionMulti-Target Information ChainMulti-Target Information ChainEntropy of a Commonly Determined StateEntropy of a CommonlyDetermined StatePredictive Memory under Deterministic RefinementPredictive Memory underDeterministic RefinementPrediction Stability from Zero Conditional EntropyPrediction Stability from ZeroConditional Entropy
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Lean sourceResearch workspace
Status
Closed
Depth
5
Layer
D5/S3
Domain
Entropy
Node ID
D5/S3/Entropy/Forgetting/CapacityMonotone
Repository path
D5/S3/Entropy/Forgetting/CapacityMonotone.lean
Truth release
sha256:c0d04258d27972c1cf58485e21d64dbcbe336405346ba95133913c64ba2856aa
Source commit
745bf90812f7175f83e1235688249f9495f23bfc
Source tree
143bc6c9ab9054c406f0cdd7f3b296eb38768b5c

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