PlanetStratum
The PlanetStratum abbreviation defines the type of planetary strata as the disjoint union of three five-element inductive types for atmospheric, Earth, and ocean layers. Cross-domain researchers in Recognition Science cite this to formalize the total of fifteen radial shells in the C2 stratification claim. The definition is a direct abbreviation that encodes the sum type for immediate use in cardinality arguments.
claimLet $A$ be the inductive type of atmospheric layers with five constructors (troposphere through exosphere), $E$ the inductive type of Earth layers with five constructors (inner core through crust), and $O$ the inductive type of ocean layers with five constructors (surface through abyssal). The planetary stratum type is the disjoint union $A + E + O$.
background
The module CrossDomain.PlanetStratification sets out the structural claim C2 that three nested D=5 stratifications cover Earth, expressed as the disjoint sum AtmosphericLayer ⊕ EarthLayer ⊕ OceanLayer = 5 + 5 + 5 = 15. The sum is required rather than a product because the strata occupy distinct radial shells and cannot coincide at the same radius. Each component is an inductive type equipped with DecidableEq, Repr, BEq, and Fintype, so each carries cardinality 5.
proof idea
As an abbreviation the definition is a direct one-line encoding of the sum type AtmosphericLayer ⊕ EarthLayer ⊕ OceanLayer. No lemmas or tactics are invoked; the abbreviation simply aliases the disjoint union for downstream use in Fintype.card calculations.
why it matters in Recognition Science
PlanetStratum supplies the type for PlanetStratificationCert, which records the cardinality 15, the identity 15 = 3 * 5, and the three proper-subset inequalities. It likewise supports planetStratumCount and the three subset theorems. In the Recognition framework it realizes the combinatorial structure for wave 62 cross-domain stratification; the empirical prediction that atmospheric and seismic velocities obey a φ-ladder ratio lies outside the formalization.
scope and limits
- Does not establish physical nesting or radial ordering of the layers.
- Does not prove wave-speed or phase-velocity relations.
- Does not derive φ-ladder ratios from the Recognition functional equation.
- Does not address uniqueness or minimality of the five-layer division per domain.
formal statement (Lean)
41abbrev PlanetStratum : Type := AtmosphericLayer ⊕ EarthLayer ⊕ OceanLayer
proof body
Definition body.
42