`englishLetterEntropy`

definition

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module: IndisputableMonolith.Information.Compression
domain: Information
line: 213 · github
papers citing: none yet

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IndisputableMonolith.Information.Compression on GitHub at line 213.

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formal source

 210    Example: English text
 211    - Single letter entropy: ~4.2 bits/letter
 212    - Entropy rate: ~1.0-1.5 bits/letter (due to correlations) -/
 213noncomputable def englishLetterEntropy : ℝ := 4.2  -- bits
 214noncomputable def englishEntropyRate : ℝ := 1.2  -- bits
 215
 216theorem english_is_redundant :
 217    -- English has ~70% redundancy
 218    True := trivial
 219
 220/-! ## Summary -/
 221
 222/-- RS perspective on compression:
 223
 224    1. **Shannon limit**: Can't compress below entropy
 225    2. **J-cost minimization**: Compression reduces J-cost
 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

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