`summary`

definition

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module: IndisputableMonolith.Information.Compression
domain: Information
line: 229 · github
papers citing: none yet

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open lean source

IndisputableMonolith.Information.Compression on GitHub at line 229.

browse module

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explainer page

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open explainer

depends on

formal source

 226    3. **Entropy = minimum J-cost**: For faithful representation
 227    4. **Redundancy = excess J-cost**: Can be removed
 228    5. **Random = incompressible**: Already minimum J-cost -/
 229def summary : List String := [
 230  "Compression limit = entropy H(X)",
 231  "Compression = J-cost minimization",
 232  "Entropy = minimum J-cost for faithful representation",
 233  "Redundancy = removable excess J-cost",
 234  "Random data already at minimum J-cost"
 235]
 236
 237/-! ## Falsification Criteria -/
 238
 239/-- The derivation would be falsified if:
 240    1. Compression below entropy achieved
 241    2. J-cost doesn't decrease with compression
 242    3. Random data can be systematically compressed -/
 243structure CompressionFalsifier where
 244  below_entropy : Prop
 245  jcost_not_decreased : Prop
 246  random_compressible : Prop
 247  falsified : below_entropy → False
 248
 249end Compression
 250end Information
 251end IndisputableMonolith

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