tierPowerRange
The tierPowerRange definition maps each NautilusTier constructor to a closed interval of real numbers giving its wattage range in watts. Engineers and modelers working on Class C technological access would cite these bounds when specifying hardware tiers or deriving safety constraints. The definition is realized by exhaustive case analysis on the three constructors of the inductive NautilusTier type.
claimThe function assigning to each Nautilus power tier a pair of real numbers representing its lower and upper power bounds in watts is defined by quietRoom maps to (10, 100), temple maps to (5000, 10000), and ignition maps to (100000, 1000000).
background
NautilusTier is the inductive type with three constructors: quietRoom for low-power meditation amplifiers and delta-theta suppression aids, temple for medium-power healing fields and group coherence devices, and ignition for high-power pulsed applications such as metric editing and transmutation. The module formalizes the Nautilus-class technological access path for Class C powers, treating power tiers and their numerical ranges as structural model definitions drawn from the NTL provisional patent stack.
proof idea
Direct pattern match on the three constructors of NautilusTier, returning the corresponding pair of real numbers in each case.
why it matters in Recognition Science
This definition supplies the concrete intervals required by the downstream theorem tier_power_positive, which proves every tier has a positive lower bound. It encodes engineering parameters for the Nautilus technological access path in the Superhuman domain, supporting further power-to-tier mappings for Class C powers as outlined in the module documentation.
scope and limits
- Does not establish physical realizability or safety of the stated power levels.
- Does not derive the numerical bounds from Recognition Science constants such as phi.
- Does not provide implementation details for achieving the power outputs.
Lean usage
theorem tier_power_positive (t : NautilusTier) : 0 < (tierPowerRange t).1 := by cases t <;> simp [tierPowerRange] <;> norm_numformal statement (Lean)
31def tierPowerRange : NautilusTier → ℝ × ℝ
32 | .quietRoom => (10, 100)
33 | .temple => (5000, 10000)
34 | .ignition => (100000, 1000000)
35
36/-- Each tier's lower bound is positive. -/