ConsistentConfig
ConsistentConfig pairs a proposition P with a positive real ratio to model a non-contradictory state that can stabilize under cost minimization. Researchers deriving logic from J-cost landscapes cite it as the canonical object for single propositions that reach defect zero. The declaration is a bare structure with three fields and no proof obligations.
claimA consistent configuration consists of a proposition $P$ and a positive real ratio $r > 0$.
background
The LogicFromCost module shows that logical consistency arises as the minimum of the J-cost function on configurations. A configuration stabilizes when its defect vanishes, which occurs precisely when the ratio equals 1; contradictions force at least one component to diverge and therefore incur positive or infinite cost. ConsistentConfig encodes a single proposition without its negation, using the cost definition imported from ObserverForcing where cost of a recognition event equals Jcost of its state.
proof idea
The declaration is a direct structure definition that introduces the fields P, ratio, and ratio_pos with no tactics or lemmas applied.
why it matters in Recognition Science
ConsistentConfig supplies the type for the central theorems logic_from_cost and why_logic_is_real, which establish that only non-contradictory configurations can achieve zero defect. It realizes the module claim that logic is the structure of cost-minimizing states and feeds the summary table contrasting contradiction cost with consistency cost. The structure closes the step from cost minima to the emergence of logical stability in the Recognition Science forcing chain.
scope and limits
- Does not derive classical logic from cost; it works inside Lean's classical metalanguage.
- Does not represent propositions that carry negative ratios or infinite defect.
- Does not claim to enumerate all possible configurations; only those with positive ratios are admitted.
- Does not address physical embedding of propositions in spacetime or quantum measurement.
Lean usage
example : ConsistentConfig := ⟨True, 1, by norm_num⟩formal statement (Lean)
182structure ConsistentConfig where
183 /-- The proposition P -/
184 P : Prop
185 /-- The ratio for P -/
186 ratio : ℝ
187 /-- Ratio is positive -/
188 ratio_pos : ratio > 0
189
190/-- The cost of a consistent configuration. -/