The 12-Emitter Dodecahedral Resonance Array Exact f0 f_0 f0 Simulation, Watch Logic, Micro-Gap Exploitation, and Burst Envelope Dynamics A Toy Model Validation of the Leedskalnin Equation and CTF Frequency Identity

The 12-Emitter Dodecahedral Resonance Array: Exact f0 f_0 f0 Simulation, Watch Logic, Micro-Gap Exploitation, and Burst Envelope Dynamics — A Toy Model Validation of the Leedskalnin Equation and CTF Frequency Identity

This paper presents the complete numerical implementation and extension of the 12-emitter dodecahedral resonance array described in “The Leedskalnin Equation” (Gurwell, 2026). Using the exact CTF base frequency f0=10373/72≈144.069444… f_0 = 10373/72 \approx 144.069444\ldots f0=10373/72≈144.069444… Hz (the recursive lock form of (1442+10)/144≈53e (144^2 + 10)/144 \approx 53e (1442+10)/144≈53e), the simulation reproduces the reported load modulation (mean geff≈0.72 g_\text{eff} \approx 0.72 geff≈0.72, minimum geff≈0.18 g_\text{eff} \approx 0.18 geff≈0.18) at peak performance.

The model incorporates: 12 emitters in dodecahedral geometry (30° phase increments), watch logic (top-4 reinforcing emitters selected each timestep), burst envelope (9 cycles ON / 27 OFF, 12% duty cycle), asymmetric amplitude taper, and nonlinear threshold coupling. Performance peaks sharply at the exact recursive lock value and degrades rapidly outside ±0.002 Hz, confirming sub-millihertz sensitivity. Micro-gap exploitation ($\delta \approx 0.000507536$ Hz) is explicitly demonstrated via phase-drift in watch logic. All Leedskalnin inscription parameters (15–53–15 burst gates, 7129/2971 scaling, 16th prime symmetry break, micro-gap $\delta$) map directly onto simulation architecture.

This is a toy model (explicitly nonlinear/threshold-driven) with no physical mechanism claimed. Full source code, parameters, plots, and frequency-sweep tables are provided in the paper for complete reproducibility. The simulation validates the engineering synthesis step of the CTF Frequency Identity and closes the loop between the Leedskalnin inscription, the 144-lattice, and the 12-emitter experimental protocol.