ErrorCorrectionFalsifier
This structure bundles three propositions that would falsify the Recognition Science error correction derivation together with a contradiction for the Shannon-exceedance case. An information theorist testing RS predictions against channel capacity would cite it to mark the boundary between the framework and empirical failure. The definition is a direct packaging of the conditions with no lemmas or reductions.
claimLet $E$ be the proposition that error correction exceeds the Shannon limit, $N$ the proposition that the 8-tick structure supplies no redundancy, and $Q$ the proposition that quantum error correction fails. Then ErrorCorrectionFalsifier is the structure whose fields are $E$, $N$, $Q$, and a proof of $E → ⊥$.
background
Module INFO-005 derives error correction bounds from the 8-tick structure. Shannon's channel capacity theorem states the maximum rate at which information can be transmitted reliably over a noisy channel. In Recognition Science the eight-tick octave (period $2^3$) supplies phase correlations that act as natural redundancy, allowing recovery of corrupted data without external coding overhead.
proof idea
This is a structure definition that directly packages the three propositions and the implication $E → ⊥$. No tactics or upstream lemmas are invoked; the body is the record constructor itself.
why it matters in Recognition Science
The declaration supplies the falsification interface for the error-correction bounds obtained from the eight-tick octave (T7). It sits in the Information domain and makes explicit the conditions under which the RS mechanism would violate Shannon capacity or fail in the quantum regime. No downstream theorems are recorded yet, leaving the concrete bounds (Hamming, singleton) as open derivations.
scope and limits
- Does not derive any explicit error-correction bound from the 8-tick phases.
- Does not prove that the 8-tick structure respects the Shannon limit.
- Does not specify the encoding map that realizes redundancy across ticks.
- Does not address classical versus quantum noise models beyond the listed propositions.
formal statement (Lean)
231structure ErrorCorrectionFalsifier where
232 exceeds_shannon : Prop
233 no_8tick_redundancy : Prop
234 qec_fails : Prop
235 falsified : exceeds_shannon → False
236
237end ErrorCorrectionBounds
238end Information
239end IndisputableMonolith