CompressionFalsifier
The falsifier structure encodes the three propositions that would jointly refute the claim that J-cost minimization enforces Shannon entropy as the lower bound on lossless compression. A researcher testing Recognition Science predictions against real compression algorithms would cite this definition when specifying experimental violation criteria. The structure is introduced directly as a definition with no lemmas, tactics, or proof obligations.
claimA structure consisting of propositions $B$, $J$, $R$ together with a proof that $B$ implies falsehood, where $B$ asserts existence of a compression scheme whose average code length lies strictly below the Shannon entropy $H(X)$, $J$ asserts that the J-cost of the representation does not decrease under compression, and $R$ asserts that random data admits systematic lossless compression.
background
In the Information.Compression module the J-cost is the recognition cost function that decreases as data becomes more organized, with the entropy $H(X) = -∑ p(x) log₂ p(x) identified as the minimum J-cost achievable by any faithful representation. The module states that compression is exactly J-cost minimization and therefore cannot violate the entropy bound. This structure supplies the explicit negation of those derived limits.
proof idea
The declaration is a structure definition whose body is empty; the four fields are introduced directly to capture the three falsifying conditions listed in the module documentation, with the final field encoding the logical negation of the first.
why it matters in Recognition Science
The definition supplies the concrete interface for refuting the INFO-003 claim that J-cost enforces Shannon's source coding theorem. It closes the theoretical loop from the positive derivation of compression limits to the possibility of empirical falsification, while leaving open the formal statement of the positive theorems that would be contradicted by any instance of this structure.
scope and limits
- Does not assert that any of the three conditions hold in practice.
- Does not derive or prove the entropy bound itself.
- Does not quantify the amount of J-cost reduction required.
- Does not restrict the domain to particular data types or physical systems.
formal statement (Lean)
243structure CompressionFalsifier where
244 below_entropy : Prop
245 jcost_not_decreased : Prop
246 random_compressible : Prop
247 falsified : below_entropy → False
248
249end Compression
250end Information
251end IndisputableMonolith