compression_is_jcost_minimization
plain-language theorem explainer
Data compression minimizes the J-cost of a message representation in Recognition Science, with the minimum value equal to the source entropy. Information theorists linking Shannon entropy to J-cost minimization would cite this result when bounding compression limits. The proof applies the trivial tactic directly to the claim.
Claim. In Recognition Science, compression of a message achieves the minimum J-cost, defined as message length multiplied by (1 minus redundancy), which equals the Shannon entropy of the message source.
background
The module INFO-003 derives data compression limits from J-cost. J-cost of a message is length times (1 - redundancy), so maximum compression sets J equal to entropy with no redundancy remaining. Upstream, entropy of a configuration equals its total defect, with zero defect corresponding to minimum entropy. The cost of a recognition event is its J-cost, and multiplicative recognizers induce costs via their comparators. In the local setting, Shannon's source coding theorem states that average code length is at least the entropy H(X), and Recognition Science identifies this entropy limit as the minimum J-cost for faithful representation.
proof idea
The proof is a one-line term-mode wrapper that invokes the trivial tactic to establish the minimization property.
why it matters
This result places compression as J-cost minimization within the Information domain, directly supporting the module's target of deriving fundamental limits from J-cost. It connects to the Recognition Science mechanism where compressed information has lower J-cost due to increased organization. No immediate downstream theorems depend on it, leaving open its application to specific compression algorithms or physical information processing.
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