plateMotionCert
plain-language theorem explainer
The definition assembles a certificate asserting five plate types and successive velocities on the phi-ladder differing by exactly the golden ratio. Geologists working within Recognition Science would cite it to connect observed tectonic speeds (roughly 1 to 17 cm/yr) to the phi-ladder structure. Construction proceeds by direct field assignment from the cardinality theorem plateTypeCount and the ratio theorem plateVelocityRatio.
Claim. A certificate asserting that the set of plate types has cardinality 5 and that for every natural number $k$ the ratio of velocities at successive rungs satisfies $v(k+1)/v(k) = phi$.
background
The module models plate velocities as lying on the phi-ladder, with observed ratios fastest/slowest approximately 17 matching phi^5 within a factor of 1.5. Five canonical types (continental fast, continental slow, oceanic fast, oceanic slow, collisional) are identified with configDim D = 5. The upstream definition phi_ratio supplies the inverse golden ratio 1/phi as a convex energy proxy minimized at that value. The structure PlateMotionCert packages two properties: the cardinality equality and the universal ratio equality for successive rungs.
proof idea
One-line wrapper that applies plateTypeCount to the five_types field and plateVelocityRatio to the phi_ratio field of the PlateMotionCert structure.
why it matters
The certificate closes the geology module by confirming the RS prediction that plate velocities lie on the phi-ladder. It draws directly on the phi-ratio definition from quasicrystal and the eight-tick octave structure implicit in rung indexing. No downstream theorems are recorded, leaving the certificate as a terminal interface for Earth-science applications within the T0-T8 forcing chain.
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