lossyCompression
plain-language theorem explainer
The lossyCompression definition supplies a string label for approximate reconstruction that accepts distortion, allowing rates below source entropy. Information theorists cite it when extending Shannon limits to rate-distortion trade-offs inside the Recognition Science J-cost framework. The realization is a direct string assignment with no computation or lemmas.
Claim. Lossy compression is defined as approximate reconstruction that accepts distortion $D$, permitting a rate $R(D)$ below the entropy $H(X)$ by discarding high $J$-cost information.
background
The Information.Compression module derives compression limits from J-cost. Shannon's source coding theorem requires average code length at least $H(X) = -∑ p(x) log₂ p(x)$. In Recognition Science, every recognition event carries nonnegative J-cost, and compression lowers total J-cost by increasing organization.
proof idea
Direct string definition assigning the literal value. No lemmas from upstream cost definitions or forcing structures are invoked; the body is a one-line string literal.
why it matters
This definition completes the lossy case inside INFO-003 on data compression limits from J-cost. It supports the module claim that compression equals J-cost minimization and prepares extensions toward rate-distortion theory while remaining consistent with the Recognition Composition Law.
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