planet_strata_total_15
plain-language theorem explainer
The sum of the cardinalities of the atmospheric, Earth, and ocean layer sets equals 15. Researchers modeling planetary structure in Recognition Science cite this to confirm the three independent five-stratum stacks. The proof is a one-line rewrite that substitutes the three pre-proved cardinality theorems.
Claim. $|A| + |E| + |O| = 15$, where $A$, $E$, and $O$ are the sets of atmospheric, solid-Earth, and oceanic strata respectively.
background
Recognition Science models planetary structure as three disjoint five-stratum stacks whose direct sum yields 15. The atmosphere stack comprises troposphere, stratosphere, mesosphere, thermosphere, and exosphere. The solid-Earth stack comprises inner core, outer core, lower mantle, upper mantle, and crust. The ocean stack comprises surface, thermocline, intermediate, deep, and abyssal layers. Each stack is an inductive type with five constructors, and the module proves only the finite structural sum, leaving wave-speed predictions empirical.
proof idea
One-line wrapper that rewrites the left-hand side by substituting the three cardinality theorems atmosphericLayerCount, earthLayerCount, and oceanLayerCount, each of which equals 5 by decision.
why it matters
Supplies the total-count field in the PlanetStrataCert definition that bundles the C2 invariants. It completes the 3 × 5 direct-sum claim in the Recognition Science chain, confirming independent physical parcels belong to one stratum in one stack. The result precedes any dynamical analysis and aligns with the framework's emphasis on finite decompositions before invoking the phi-ladder or J-cost.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.