trureturingGitHub MATHEMATICAL ATLAS

Entropy / CONCEPT

Observation-Word and Completion Information Decomposition

Finite observation words obey the Shannon chain rule, and stable completion information is the sum of the later conditional observation entropies.

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DIRECT PREREQUISITES3
DIRECT CONSEQUENCES1
PROOF DEPTH10
DOCUMENT LINKS1
THEOREM

Completion information decomposes along the observation chain

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Entropy and Capacity under Carrier ForgettingEntropy and Capacity underCarrier ForgettingShannon Entropy Is Invariant Under Injective RelabelingShannon Entropy Is InvariantUnder Injective RelabelingGraded Prediction ShiftGraded Prediction ShiftObservation-Word and Completion Information DecompositionObservation-Word and CompletionInformation DecompositionCanonical Completion Information Chain DecompositionCanonical CompletionInformation Chain Decomposition
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Lean sourceResearch workspace
Status
Closed
Depth
10
Layer
D5/S3
Domain
Entropy
Node ID
D5/S3/Entropy/Observation/CompletionInformationChainDecomposition
Repository path
D5/S3/Entropy/Observation/CompletionInformationChainDecomposition.lean
Truth release
sha256:c0d04258d27972c1cf58485e21d64dbcbe336405346ba95133913c64ba2856aa
Source commit
745bf90812f7175f83e1235688249f9495f23bfc
Source tree
143bc6c9ab9054c406f0cdd7f3b296eb38768b5c

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