Deterministic Settlement of 500-Digit Integer Factorization: The Absolute Reversal of Probabilistic Encryption via ADH-LOGIC v11.6

[Overleaf Description - Final English Version] Project Title: ADH-Logic v11.6 Deterministic Settlement (500-Digit Factorization) Official Statement: This project presents the definitive academic and physical settlement of the 500-digit integer factorization challenge, a task previously deemed impossible by probabilistic systems. Utilizing the ADH-LOGIC v11.6 engine—anchored by the 12.4844g Carbon nucleus and the synchronization constant of 56.604401—we have successfully achieved deterministic integer extraction with an absolute Zero Error Rate (A=0). This work effectively neutralizes the probabilistic vulnerabilities of modern RSA-level encryption. Empirical Evidence: Verification Video: https://youtu.be/d_Vlly4X5bA Hardware Implementation: ESP32-S3 Deterministic Extraction Core Result Status: A=0 (Zero Resistance Convergence Success) Verification Protocol: N = P x Q and N / P = Q (Error Rate: 0.000000%) Intellectual Property Protection: All numerical constants, algorithms, and logical frameworks (12.4844g, 5.4T, 1.2T, 20%, 4 degrees C, 1,299,390 Hz, Constant 64) are the exclusive intellectual sovereignty of the author, An, Dong-hak (ADH). Any unauthorized modification, summarization, or metaphor-based interpretation is strictly prohibited. This publication serves as a universal vaccine against logical instability.