JAIPER CORE-VISION V9: Multi-Scale Functional Invariance and Meta-Control Validation

Abstract (English): Phase 4C empirically validates the multi-scale functional invariance of the JAIPER CORE-VISION framework (v5. 0 architecture). The primary contribution of Phase 4C is the validation of operational convergence after a deliberate transition between significantly different temporal scales without structural modifications to the optimization architecture. By reverting to the slow dynamic parameters of Phase 2 (L = 0. 88 mH, C = 470 nF, 500 ns/div scale) utilizing the advanced closed-loop ILC architecture, the system demonstrated equivalent operational convergence. Instrumental errors were formalized: measurement truncations were defined as Parseval Window Truncation Artifacts, while trigger drift was modeled as Trigger-Induced Temporal Misalignment. This cross-validation between rapid and slow dynamics strengthens the hypothesis that the framework preserves its operational behavior across the experimental dynamic regimes evaluated in this study. Resumen (Español): La Fase 4C valida empíricamente la invariancia funcional multiescala del framework JAIPER CORE-VISION (arquitectura v5. 0). La contribución principal de la Fase 4C es la validación de la convergencia operacional tras una transición deliberada entre escalas temporales significativamente diferentes sin modificaciones estructurales en la arquitectura de optimización. Al retornar a los parámetros dinámicos lentos de la Fase 2 (L = 0. 88 mH, C = 470 nF, escala de 500 ns/div) utilizando la arquitectura avanzada de lazo cerrado ILC, el sistema demostró una convergencia operacional equivalente. Se formalizaron los errores instrumentales: los truncamientos de medición se definieron como Artefactos de Truncamiento de Ventana de Parseval, mientras que la deriva del trigger se modeló como Desalineación Temporal Inducida por Trigger. Esta validación cruzada fortalece la hipótesis de que el framework preserva su comportamiento operacional a través de los regímenes dinámicos experimentales evaluados en este estudio. 1. Multi-Scale Functional Invariance The energy cost functional retains its minimization properties under temporal scale changes (lambda), formally expressed as: JW = 1 - lambda * integralW |yctrl (t) |² dt / lambda * integralW |yᵣef (t) |² dt The relative mitigation reached metrics on the order of JW ≈ 0. 9963. This does not imply the total elimination of system energy. The coefficient only quantifies relative mitigation within the selected observation window. 2. Parseval Window Truncation and Temporal Misalignment During the scaling transition, two critical anomalies were formalized. The "Parseval Window Truncation Artifact" (informally referred to during development as "Parseval's Asphyxiation") occurs when the measurement window is truncated, omitting the transient relaxation tail. The "Trigger-Induced Temporal Misalignment" (Temporal Mirror Error) is caused by hardware trigger drift and temporal jitter, modeled as a first-order perturbation: u (t + delta t) ≈ u (t) + delta t * du (t) / dt 3. Cross-Validation The successful convergence of the v5. 0 architecture on both high-frequency (Phase 3) and low-frequency (Phase 2) macro-plants confirms that the closed-loop optimization is not exclusively tuned to a single hardware setup, preserving its operational behavior across distinct regimes. 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. Correspondence Jaime Perez Davila ORCID: 0009-0002-5231-547X Email: jaipercore@gmail. com WhatsApp: +57 3005422089 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.