losslessCompression
plain-language theorem explainer
Lossless compression is defined as exact reconstruction of the source with average code length bounded below by entropy. Information theorists working in the Recognition Science setting cite it when linking Shannon limits to J-cost minimization. The entry is a direct string definition that encodes the RS view of preserving all ledger information.
Claim. Lossless compression permits exact reconstruction of the original message, with the minimal average code length equal to the Shannon entropy $H(X) = -∑ p(x) log₂ p(x)$.
background
The Information.Compression module derives fundamental limits on data compression from J-cost. J-cost is the recognition cost of a state; the shifted function H(x) = J(x) + 1 satisfies the d'Alembert equation H(xy) + H(x/y) = 2 H(x) H(y). Entropy of a configuration is defined as its total defect, vanishing only at the minimum-entropy state. Upstream results supply the cost induced by multiplicative recognizers and the cost of recognition events, together with the Boltzmann entropy expressed via average energy and partition function.
proof idea
One-line definition that assigns the string literal 'Exact reconstruction, limit = entropy' to losslessCompression.
why it matters
The definition supplies the RS-native statement of the lossless limit inside the INFO-003 development. It anchors the claim that entropy equals minimum J-cost for faithful representation and prepares the contrast with lossy compression that discards high-J-cost information. It aligns with the Recognition Composition Law and the interpretation of compression as J-cost minimization.
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