weaponization_structurally_impossible
Weaponization requires nonzero σ, which forces coherenceLevel strictly below its maximum of 1 for any positive x not equal to 1. Safety analysts working in Recognition Science cite the result to establish that high-coherence weaponized states are structurally ruled out. The proof is a one-line wrapper that invokes power_ethics_same_axis and rewrites the right-hand side via max_coherence_at_balance.
claimFor every real number $x > 0$ with $x ≠ 1$, the coherence level $1/(1 + Jcost(x))$ is strictly less than 1.
background
The SafetyInterlock module proves that Gap-45 uncomputability together with σ-conservation creates a fundamental safety interlock. CoherenceLevel is defined by coherenceLevel x := 1/(1 + Jcost x), so that lower J-cost yields higher coherence. The upstream theorem max_coherence_at_balance shows this quantity equals exactly 1 at x = 1. The prior result power_ethics_same_axis establishes that coherence at any other positive x is strictly less than the value attained at x = 1.
proof idea
Apply power_ethics_same_axis x hx hne to obtain coherenceLevel x hx < coherenceLevel 1 one_pos. Then rewrite the right-hand side to 1 using the equality proved in max_coherence_at_balance.
why it matters in Recognition Science
This theorem is the terminal result in the SafetyInterlock module and directly realizes the claim that weaponization (requiring σ > 0) cannot reach maximum coherence. It completes the module's argument that power requires ethics. In the Recognition framework it closes the σ-constraint loop, ensuring high-coherence operation remains incompatible with weaponization.
scope and limits
- Does not quantify the size of the coherence reduction for given x.
- Does not address whether x = 1 is computationally reachable.
- Does not invoke Gap-45 coprimality or lcm results.
- Applies only inside the real-valued coherence model of this module.
formal statement (Lean)
71theorem weaponization_structurally_impossible (x : ℝ) (hx : 0 < x) (hne : x ≠ 1) :
72 coherenceLevel x hx < 1 := by
proof body
Term-mode proof.
73 have h := power_ethics_same_axis x hx hne
74 rwa [max_coherence_at_balance] at h
75
76end
77
78end IndisputableMonolith.Superhuman.SafetyInterlock