1. França, C. R. (2025 p1). Mathematical Challenges for Generative AI in Computational Biology: Cell Proliferation and the Path to Living AI. Zenodo. https://doi.org/10.5281/zenodo.15033127 2. França, C. R. (2025 p2). Grok 3 and the Authorial and Unpublished Mathematical Formulas as a learning tool for Generative AIs: Reactions and developments in the face of advanced calculations. Zenodo. https://doi.org/10.5281/zenodo.15066761 3. França, C. R. (2025 p3). Advanced computational mathematics and future point modeling of a predictive system: A collaborative scientific research between a human and a Generative AI. Zenodo. https://doi.org/10.5281/zenodo.15083825 4. França, C. R. (2025 p4). Heru Technologies: Modeling Escape Trajectories of a Probe Trapped in an Asteroid's Gravitational Field Using SRMs and Human-GenAI Collaboration. Zenodo. https://doi.org/10.5281/zenodo.15151423 5. França, C. R. (2025 p5). SRMs and GenAI applied to the stock market: Predictive system and projections of future points for industrial expansion and finance. Zenodo. https://doi.org/10.5281/zenodo.15252352 6. França, C. R. (2025). Predictive analytics in the Swiss pharmaceutical sector: SRMs are the right amount of mathematics for GenAIs. Zenodo. https://doi.org/10.5281/zenodo.15272636 7. França, C. (2025). Beyond Binary Trees: A Paradigm Shift in Data Search Efficiency via SRMs-Based Structures. Zenodo. https://doi.org/10.5281/zenodo.15602787 8 – Citation CAP 10 – LIVRO FUCAP NO ZENODO França, C. R. (2025). Método de criptografia Heru Technologies: único do mundo que utiliza fórmulas matemáticas inéditas autorais e que criptografa com perturbações binárias. Zenodo. https://doi.org/10.5281/zenodo.15653585 9 - França, C. R. (2025, junho 23). Heru Technologies encryption method: unique in the world that uses unpublished mathematical formulas and encrypts with binary disturbances. https://doi.org/10.5281/zenodo.15717868 10 - França, C. R. (2025). SRMs and GenAIs: Bridges between Infinite Series with Multiple Ratios, Generative Intelligence and Quantum Computing (Second version). Zenodo. https://doi.org/10.5281/zenodo.16888353 12 - França, C. R. (2025). GenAIs and SRMs: A Guide to Conceptual Bridges and Practical Applications in Quantum Computing. Zenodo. https://doi.org/10.5281/zenodo.17042186 13 - França, C. R. (2025). SRMs and the Middle Path: Bridging Relativity and Quantum Mechanics. Zenodo. https://doi.org/10.5281/zenodo.17069526 14 - França, C. R. (2025). Quaternary Quantum Dynamics and SRM Algorithms: A Middle-Path Framework Beyond Qubits. Zenodo. https://doi.org/10.5281/zenodo.17095495 15 - França, C. R. (2025). ACH – A Quantum Inspired Annealing Cloud Application Powered by SRMs & GenAIs. Zenodo. https://doi.org/10.5281/zenodo.17163200 16 - França, C. R. (2025). Quantum Biology Based on SRMs: From Cell Proliferation to Cyclical Spheres of Preventive Health. Zenodo. https://doi.org/10.5281/zenodo.17188874 17 - França, C. R. (2025). Pipeline SRMs and GenAIs: Nonlinear Predictive Frameworks for Drone Swarms and Mobility in Defense. Zenodo. https://doi.org/10.5281/zenodo.17220829

If Schrödinger had had a ruler in 1926 that was already multiscale, he would probably have derived discretizations that reconcile phase coherence and nonlocality with fewer points. Infinite Series with Multiple Ratios (SRMs) provide such a ruler: a scheme with multiple coupling steps that preserves unitarity and introduces controlled homologous connections - a fertile ground for studying entanglement as a structural regularity under uncertainty. We propose SRM-Schr, a multiscale scheme for the time-dependent Schrödinger Equation that replaces the classical Laplacian with a SRM Laplacian (stencils with multiple ratios) and introduces a homologous coupling operator that induces calibratable nonlocal correlations. The evolution is done by unitary split-step (Crank–Nicolson/Strang), ensuring conservation of probability. The choice of SRM ratios is guided by physical scaling relations. (E = hf, λ = h/p), to align resonance and phase coherence without "forcing" determinism: we maintain the probabilistic nature but organize the multiscale structure of the wavefield. In 1D tests (free particle, oscillator, double barrier), SRM-Schr reduces dispersion and phase error compared to uniform discretizations at the same cost. In two-body models, an SRM "pulse" smoothly controls entanglement (von Neumann entropy). Results suggest that SRMs form a natural basis for simulating interference and entanglement with fewer points and greater fidelity.