The Amestoy-Vazquez Conjecture: Fast O(D) Verification of Magic Hypercubes

This expanded version of the Amestoy-Vázquez conjecture includes the complete paper and validation code. The conjecture provides: (1) Magic constant formula M = n·a + n·(n^D-1)/2, (2) O(D) verification algorithm requiring only 2D line checks. Validated up to D=24. Applications in cryptography, quantum physics, data science. ## Potential Applications- Cryptography: Nonlinear component design- Quantum Physics: State symmetry verification - Data Science: Multidimensional balancing- Mathematics: Magic hypercube theory extension Initial version: DOI 10.5281/zenodo.18248839This version: January 17, 2026 updateGitHub: https://github.com/AmestoyVazquez/Amestoy-Vazquez-Conjecture ## AI AssistanceAI (ChatGPT-4) was used for formatting and implementation assistance.All mathematical content is original to the author.