requiredTier
This definition assigns a minimum Nautilus tier to each Class C power from the canonical list of 27 superhuman powers. Researchers modeling technological requirements for superhuman capabilities cite it to set hardware thresholds for entries such as flight or force fields. The implementation is a direct pattern match on the Power inductive type that returns some tier for the six Class C cases and none otherwise.
claimLet $P$ be the inductive type of the 27 canonical superhuman powers and $N$ the inductive type of Nautilus tiers. The function $r : P → Option(N)$ is defined by $r(flight) = some(ignition)$, $r(invulnerability) = some(temple)$, $r(superStrength) = some(temple)$, $r(forceFields) = some(temple)$, $r(energyProjection) = some(ignition)$, $r(transmutation) = some(ignition)$, and $r(p) = none$ for all other $p ∈ P$.
background
The module formalizes the Nautilus-class technological access path for Class C powers. NautilusTier is the inductive type with three constructors: quietRoom (~10–100 W for meditation amplification), temple (~5–10 kW for healing fields and group coherence), and ignition (>100 kW pulsed for metric editing and flight). Power is the inductive type imported from Core that enumerates the 27 canonical powers drawn from mythology, comics, and folklore, with a subset marked NautilusClass. The module documentation states that power tiers and mappings are MODEL structural definitions while engineering parameters come from the NTL provisional patent stack.
proof idea
This is a definition by exhaustive pattern matching on the Power inductive type. It directly returns the corresponding Option NautilusTier for each of the six Class C constructors and none for the remainder, with no lemmas or tactics applied.
why it matters in Recognition Science
The definition is used by the downstream theorem classC_has_tier, which proves that every power satisfying powerClass p = NautilusClass has (requiredTier p).isSome = true. It supplies the concrete mapping required by the Nautilus architecture parameters section. Within the Recognition Science framework it extends the core structural layer for technological access without touching the T0–T8 forcing chain or the Recognition Composition Law.
scope and limits
- Does not compute numerical wattage values beyond the three tier ranges.
- Does not prove that any given tier is sufficient to realize the associated power.
- Does not address Class A or Class B powers.
- Does not incorporate Gap-45 safety constraints.
Lean usage
theorem flight_requires_ignition : requiredTier .flight = some .ignition := rflformal statement (Lean)
43def requiredTier : Power → Option NautilusTier
44 | .flight => some .ignition
45 | .invulnerability => some .temple
46 | .superStrength => some .temple
47 | .forceFields => some .temple
48 | .energyProjection => some .ignition
49 | .transmutation => some .ignition
50 | _ => none
51
52/-- All Class C powers have a required tier. -/