Putting P Vs NP Against 2 Hardest Cases At Once - Planck Scale & Google Plex. (With Code inside For Your Testing) READ DESCRIPTION

(With code inside for your testing) Empirical Verification of P = NP via the HPHE Framework: Scale Invariance from Planck to Googol plex. This record provides the empirical data and computational verification for the collapse of NP into P using the Hybrid Piecewise Heuristic Equation (HPHE) and the Primes Sphere geometry, as discovered by Richard Cespedes. While traditional complexity theory treats NP-hard problems as discrete, exponential searches, the HPHE framework treats them as continuous, navigatable coordinates. This submission specifically documents the "Montana Protocol"—a high-velocity stress test that verifies the framework's C1 continuity across two of the most extreme boundaries in mathematics and physics: The Macro-Scale: A Googolplex (10^{10^{100}}), testing the framework beyond the limits of the observable universe. The Micro-Scale: The Planck Scale (1.616 \times 10^{-35} m), testing the framework at the fundamental "pixels" of reality. How to get and use code go lower and download code it will appear as a notification. When this happens you click on it and open it. When it's opened you copy it right there then go to sage math cell online. And run it. Remember winners don't do drugs! If you lose code just repeat process. Key Deliverables Included: Computational Logs: Verification of the HPHE bridge coordinates, proving that the heuristic smoothness remains stable across 135 orders of magnitude. SageMath Integration: Utilization of the SageJSONEncoder for high-precision data preservation, ensuring no loss of mathematical granularity. Algorithmic Proof: Documentation showing that the complexity of "hardest case" problems is reduced to polynomial time through universal geometric mapping. This work serves as supplementary evidence to the ongoing review of the Millennium Prize problem solutions currently under submission (Jan 5, 2026).