planetStrataSum
plain-language theorem explainer
The declaration assembles the planetary strata as a disjoint sum of three independent 5-layer axes, one each for atmosphere, solid Earth, and ocean. Modelers of planetary structure in Recognition Science cite it to ground the 15-stratum total. The definition supplies the three sibling axes and discharges the three independence conditions by direct simplification.
Claim. The planetary strata form the disjoint sum of three pairwise independent 5-element axes, with the first axis the atmosphere stack, the second the solid-Earth stack, and the third the ocean stack.
background
Module C2 treats the planet as three independent 5-strata stacks (atmosphere, solid Earth, ocean) whose direct sum yields 15 layers. A physical parcel occupies one stratum in one stack; the construction is an RS disjoint sum, not a tensor product. RSDisjointSum3 is the structure whose fields are three same-size coupled axes together with the three pairwise independence propositions. Independence of two axes means they are carried by distinct primitives.
proof idea
The definition binds atmosphereAxis, earthAxis, and oceanAxis to the three components of RSDisjointSum3 5. Each independence obligation is discharged by a one-line simp tactic that unfolds the independent predicate and the concrete axis definitions.
why it matters
This definition supplies the structural core used by PlanetStrataCert (which records the three cardinalities) and by the theorem planet_strata_disjoint_sum_15 (which proves the total cardinality equals 15). It realizes the three spatial dimensions of the Recognition Science framework as independent axes inside the C2 planetary model, closing the finite structural claim while leaving the phi-ratio wave-speed predictions empirical.
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