planetStratum_three_D
plain-language theorem explainer
The arithmetic identity 15 equals three times five is recorded to certify the total count arising from three nested planetary layers each carrying stratification depth five. Cross-domain researchers in Recognition Science reference the result when assembling the PlanetStratificationCert bundle. The proof is a single decision tactic that evaluates the equality directly.
Claim. $15 = 3 × 5$, where the factor of five is the stratification depth assigned to each of the three nested layers (atmosphere, solid earth, ocean).
background
The module models Earth as three nested strata—AtmosphericLayer, EarthLayer, OceanLayer—occupying distinct radial shells, so their combination is a disjoint sum rather than a product. Each stratum is assigned the same depth parameter D = 5, producing the combinatorial total 15. This is the C2 structural claim of Wave 62 Cross-Domain; the module states that wave-speed ratios at the boundaries should later obey a phi-ladder relation, but the Lean declaration only records the count.
proof idea
The proof is a one-line wrapper that applies the decide tactic to the decidable arithmetic proposition 15 = 3 * 5.
why it matters
The result populates the three_D field inside planetStratificationCert, which also records the stratum count and the three proper-subset relations. It supplies the combinatorial half of the C2 claim, consistent with the framework’s T8 assignment of spatial dimension three while treating the per-layer depth five as an independent structural parameter. No open scaffolding question is closed here.
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