trureturingGitHub MATHEMATICAL ATLAS

Entropy / CONCEPT

Entropy and Capacity under Carrier Forgetting

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

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DIRECT PREREQUISITES2
DIRECT CONSEQUENCES20
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 ForgettingFull-Support Native Window Laws and Actual Null ContinuationFull-Support Native Window Lawsand Actual Null ContinuationTranslation Loss under PostprocessingTranslation Loss underPostprocessingInformation Cost of Concept CompletionInformation Cost of ConceptCompletionKullback-Leibler Loss under Deterministic ForgettingKullback-Leibler Loss underDeterministic ForgettingCharge-sector normalization refutes majorization preservationCharge-sector normalizationrefutes majorizationpreservationConditional Entropy under Completion FactorizationConditional Entropy underCompletion FactorizationConditional Information PostprocessingConditional InformationPostprocessingEquality and Strict Loss under Deterministic ForgettingEquality and Strict Loss underDeterministic ForgettingPushforward CompositionPushforward CompositionEntropy Telescoping along Deterministic TrajectoriesEntropy Telescoping alongDeterministic TrajectoriesFusion State EntropyFusion State EntropyThe entropic Glibichuk–Konyagin conjectureThe entropic Glibichuk–KonyaginconjectureObservation-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 EntropyThe qutrit complementary-entropy frontierThe qutrit complementary-entropy frontierThe global ZZ gate-time upper boundThe global ZZ gate-time upperboundStatistical strength of the two-singlet magic squareStatistical strength of thetwo-singlet magic square
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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
sha256:76a8db6a0f78609b1b9d4a959c8392f2752f2daaddc1930e046e34ce07d0f608
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b52262a023c4db9bb30a128ebfd80ea4ef4c1a53
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37a24ddf3b9983bdabf0acbfd9b32b06c35c28d3

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