coherenceLevel
Coherence level is defined as the reciprocal of one plus J-cost for any positive real input. Safety interlock results in the Superhuman module cite this definition to derive positivity, maximality at the balance point, and strict reduction under deviation. The declaration is a direct definition that inverts the non-negative J-cost function.
claimFor any real number $x > 0$, the coherence level equals $1 / (1 + J(x))$, where $J$ denotes the J-cost function.
background
The Safety Interlock module shows that the Gap-45 uncomputability barrier together with σ-conservation produces a fundamental safety interlock for high-coherence operation. The J-cost function, drawn from the Cost module, returns a nonnegative real that vanishes only at the unit argument and is strictly positive elsewhere. The coherence level definition directly encodes the module comment that coherence is inversely related to J-cost, with the input parameter x serving as the normalized σ level whose balance point is 1.
proof idea
The declaration is a direct definition that sets coherence level to the reciprocal of one plus J-cost of the input.
why it matters in Recognition Science
This definition supplies the central quantity for the safety interlock theorems. It is used by coherenceLevel_pos to establish positivity, by max_coherence_at_balance to fix the value 1 at x=1, by power_ethics_same_axis to prove that any deviation from 1 strictly lowers coherence, and by weaponization_structurally_impossible to conclude that weaponization cannot achieve maximum coherence. It thereby supports the module claim that power requires ethics within the Gap-45 and σ-constraint framework.
scope and limits
- Does not prove nonnegativity of J-cost.
- Does not establish the maximum value of coherence.
- Does not incorporate Gap-45 coprimality or lcm facts.
- Does not derive weaponization impossibility.
formal statement (Lean)
48def coherenceLevel (x : ℝ) (_ : 0 < x) : ℝ := 1 / (1 + Jcost x)
proof body
Definition body.
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