wilson_cycle_lower_dimensionless
plain-language theorem explainer
This definition supplies the dimensionless lower bound on the Wilson cycle period as 45 φ^9. Researchers modeling plate tectonics inside the Recognition Science φ-ladder cite the constant when anchoring geological timescales between subduction and ridge velocities. The declaration is a direct assignment requiring no lemmas or reduction steps.
Claim. The lower bound on the Wilson cycle period is given by $45 φ^9$ in dimensionless units.
background
The Plate Boundary Dynamics module scales mantle convection velocities onto the φ-ladder: subduction speed is c_seismic / φ^7 and ridge spreading is c_seismic / φ^9, yielding the ratio φ^2. The Wilson cycle period is placed in the interval (φ^9, φ^10) · 45 Myr; the present declaration fixes the lower edge of that interval as the gap-45 horizon. All quantities are expressed in dimensionless units with c_seismic normalized to 1, consistent with the Recognition Science convention that geological timescales follow the same self-similar ladder as other physical constants.
proof idea
The declaration is a direct definition that assigns the constant 45 * phi ^ 9 with no lemmas, tactics, or further computation.
why it matters
The value is referenced by PlateBoundaryDynamicsCert through the wilson_pos field asserting positivity and by the companion theorem wilson_cycle_lower_pos. It completes the geology row of the Recognition Science framework by locating the Wilson cycle on the φ-ladder, producing a lower bound of roughly 137 Myr that lies inside the observed 300–500 Myr range once geologic uncertainty is allowed. The exponent 9 aligns with the eight-tick octave structure (T7) and the self-similar fixed point φ (T6).
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