huffmanCoding
plain-language theorem explainer
Huffman coding is defined as the optimal prefix-free code whose average length L satisfies L ≤ H + 1. Researchers deriving compression bounds from J-cost in Recognition Science would reference this label when connecting classical information theory to the module's entropy-minimization claim. The entry is a direct string constant with no computation or lemmas.
Claim. Huffman coding supplies an optimal prefix-free code satisfying $L ≤ H + 1$, where $H$ is the Shannon entropy and $L$ the mean code length.
background
Module INFO-003 derives fundamental limits on lossless compression from J-cost, stating that average code length is bounded below by entropy and that compression equals J-cost minimization. Shannon entropy is $H(X) = -∑ p(x) log₂ p(x)$. The upstream definition H(x) = J(x) + 1 = ½(x + x⁻¹) reparametrizes the Recognition Composition Law into d'Alembert form. Local setting treats entropy as the minimum J-cost for faithful representation.
proof idea
One-line definition that directly assigns the descriptive string literal. No lemmas or tactics are invoked; the body is the constant value itself.
why it matters
The definition supplies the classical bound that the module uses to align Shannon limits with the Recognition Science view of entropy as minimum J-cost. It sits inside the information domain but has no recorded downstream uses. It touches the J-cost mechanism without invoking the forcing chain or phi-ladder.
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