JAIPER-1 V7 Phase 3 – High-Frequency Regime Transition and Multi-Scale Ringi

Abstract (English): Phase 3 evaluates the robustness of the JAIPER-CORE geometric shaping framework under high-frequency (HF) dynamic regimes. Utilizing a fast RLC topology (L = 4. 7 uH, C = 100 nF), the system operated within a 20-50 ns/div temporal scale. The transition allowed for clearer modal separation and confirmed the applicability of the V10 mitigation strategy in ultra-fast domains. Crucially, spectral signatures initially identified in the hundreds of MHz were formally reclassified as Moiré optical aliasing and spatial discretization artifacts inherent to the computer vision acquisition process. The phase produced the first formal distinction between physical plant dynamics and image-reconstruction artifacts, establishing a methodological foundation for the subsequent closed-loop adaptive framework. This methodological discovery necessitated the implementation of bounded-band digital filtering, grounding the framework against instrumental aliasing. Resumen (Español): La Fase 3 evalúa la robustez del framework de shaping geométrico JAIPER-CORE bajo regímenes dinámicos de alta frecuencia (HF). Utilizando una topología RLC rápida (L = 4. 7 uH, C = 100 nF), el sistema operó en una escala de 20-50 ns/div. La transición permitió una separación modal más clara y confirmó la aplicabilidad de la estrategia de mitigación V10 en dominios ultrarrápidos. Fundamentalmente, las firmas espectrales identificadas inicialmente en centenas de MHz fueron reclasificadas formalmente como aliasing óptico tipo Moiré y artefactos de discretización espacial inherentes a la adquisición por visión artificial. La fase produjo la primera distinción formal entre las dinámicas físicas de la planta y los artefactos de reconstrucción de imagen, estableciendo una base metodológica para el posterior framework adaptativo de lazo cerrado. Este descubrimiento metodológico requirió la implementación de filtros digitales de banda limitada, blindando el framework contra el aliasing instrumental. 1. High-Frequency Regime Analysis and Experimental Setup 1. 1 Transition from Phase 2 Phase 3 was initiated following the successful validation of the V10 mitigation strategy in Phase 2. The objective was to evaluate whether the geometric shaping framework remained effective when transitioning from a slow macro-RLC regime to a significantly faster dynamic domain. 1. 2 Physical Foundation To evaluate the scalability of the architecture under rapid switching conditions, the plant was replaced with a low-inductance fast RLC circuit configuration: Inductor (L): 4. 7 uH nominal (High-speed ferrite core coil). Capacitor (C): 100 nF (Low-ESR multilayer ceramic). Operating Frequency: Scaled dynamically between 25 kHz and 100 kHz. Oscilloscope Time Base: Set between 20 ns/div and 50 ns/div. Probes: 10X configuration with strict AC coupling. The theoretical macroscopic natural frequency of this rapid circuit configuration is mathematically defined and calculated as: fₘacro = 1 / (2 * pi * sqrt (L * C) ) ≈ 232 kHz 2. Evolution of the V10 Strategy and Quantitative Results 2. 1 Strategy Robustness Operating within this fast dynamic regime, the ecosystem achieved a clear modal separation, allowing the isolation of high-frequency transients. The persistence of mitigation effectiveness after a two-order-of-magnitude reduction in inductance suggests that the shaping strategy is not restricted to a single plant configuration, demonstrating robustness across the tested configurations. 2. 2 Quantitative Results The empirical evaluation of the V10 mitigation signals under the HF regime yielded the following operational metrics: Windowed Coefficient (JW): 0. 58 to 0. 81 Overshoot Reduction: 60% to 85% Ringing Mitigation: Visually confirmed and repeatable across independent runs. Modal Stability: Maintained under bounded conditions. 3. Methodological Discovery: Moiré-Type Optical Aliasing 3. 1 Consequences of the Aliasing Discovery During initial fast-regime testing at 20 ns/div, automated spectral extraction reported severe high-frequency anomalies, plotting false spectral peaks at 633 MHz and 316 MHz. Initially interpreted as potential physical signatures of the system, systematic auditing revealed that these were artifacts of spatial discretization (Moiré-type Optical Aliasing). The physical pixels of the oscilloscope display screen interacted directly with the mathematical sampling steps of the vision script (BMP sampling artifacts). It is extremely important to state that the aliasing discovery represented a methodological correction rather than a physical discovery, demonstrating the experimental self-correction capability of the framework. 3. 2 Formal Definition of the Constrained Functional Space To resolve the reconstruction artifacts, a band-limited functional space (H₂5) was formally introduced into the software kernel: H₂5 = y (t) in L² (R) | Y (w) = 0 for all |w| > 2 * pi * (25 * 10⁶) This constrained spectral space was introduced strictly to prevent non-physical frequencies from contaminating the optimization process, ensuring that the control vector acts solely upon true electromagnetic plant dynamics. 4. Core Contributions and Hardware Constraints To accurately quantify the relative energy mitigation within these specific operational windows, the framework relied on the Windowed Jaiper Coefficient as its mathematical bridge: JW = 1 - integralW |yctrl (t) |² dt / integralW |yᵣef (t) |² dt 4. 1 Core Contribution of Phase 3 Phase 3 demonstrated that the JAIPER shaping framework remained operational under high-frequency conditions while simultaneously revealing the critical distinction between physical dynamics and vision-induced spectral artifacts. 4. 2 Instrumental Constraints in HF At nanosecond scales, trigger synchronization becomes a first-order uncertainty source. Furthermore, the capability is strongly limited by the amplifier rise time, oscilloscope jitter, and the effective bandwidth of the DDS generator. Mandatory Methodological Declarations: Note on Coefficients: The coefficients J and JW represent relative energy mitigation metrics within defined operational windows. They must not be interpreted as absolute reductions in the total physical energy of the system. Experimental Limitations: The system is strictly bounded by ADC/DAC quantization, temporal jitter, optical aliasing, BMP resolution, trigger synchronization, DDS limitations, instrumental bandwidth, and the spatial resolution of the display. Author Note The author is a native Spanish speaker and is available for communication in Spanish. English is used in this document for international accessibility.