arithmeticCoding
plain-language theorem explainer
Arithmetic coding is defined as the method achieving near-optimal compression with average length L approaching entropy H for long messages. Researchers deriving data compression bounds from J-cost in Recognition Science would cite this when linking Shannon limits to minimum-cost representations. The entry is a direct string definition with explanatory comments on its properties and relation to adaptive dictionary methods.
Claim. Arithmetic coding encodes any message distribution as a single number such that the average code length $L$ satisfies $L$ approaching the Shannon entropy $H$ in the limit of long messages.
background
The module INFO-003 derives fundamental limits on lossless compression from J-cost, where entropy equals the minimum J-cost for faithful representation and compression is J-cost minimization. Shannon's source coding theorem states that average code length is at least $H(X) = -∑ p(x) log₂ p(x)$. Upstream, the shifted cost satisfies $H(x) = J(x) + 1$, entropy of a configuration equals its total defect, and the Recognition ledger L records unit debit and credit.
proof idea
One-line definition that directly assigns the descriptive string to the arithmeticCoding identifier, with attached comments on near-optimality and Lempel-Ziv comparison.
why it matters
Places arithmetic coding inside the J-cost view of compression that supports the module target of connecting Shannon entropy to Recognition Science mechanisms. It sits alongside sibling definitions such as compression_is_jcost_minimization and losslessCompression, though no downstream uses are recorded.
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