CTT Algorithm
Abstract
CTT Project - Hwang Joon This paper was written using GPT-5.6sol,GPT-6 Astra model of OpenAI. Abstract CTT is a computational research framework developed for large-scale hierarchical computation and structure-aware analysis across multiple scientific and engineering domains. The numerical CTT implementation has been evaluated on billion- and trillion-scale logical workloads. In a recorded experiment on a ten-core MacBook Air M5, CTT processed a logical hierarchy containing 2^30=1,073,741,824 leaves and 1,073,741,823 local recovery operations in approximately 67.66 seconds, with zero failed local recoveries and an effective throughput of approximately 31.74 million logical links per second. Subsequent GPU-based experiments extended numerical stress testing to approximately 2^42-scale local evaluations. CTT-LLM applies CTT to the analysis of large language models. Completed experiments have covered billion-parameter, 10-billion-parameter, and 120-billion-parameter model scales. A GPT-OSS-120B experiment generated 77,184 perturbation-response measurements over 2,412 measured targets and recovered 2,351 of 2,351 evaluated structural pairs in approximately 375.79 seconds using two NVIDIA RTX PRO 6000 Blackwell GPUs. A separate KORMo-10B experiment covered 1,760 targets using a single RTX PRO 6000-class GPU. CTT-BIO applies CTT to phylogenomics and ancestral-state reconstruction. A Neoaves production experiment processed 363 taxa and 63,430 loci, representing approximately 63.43 million modeled ancestral sites, with 362 of 362 tested local branch recoveries completed. In a controlled ground-truth experiment, CTT-assisted reconstruction achieved 98.01784% MAP accuracy, compared with 47.16168% for the corresponding ordinary JC69 baseline under the tested conditions. CTT-SAT applies CTT to Boolean and finite-domain constraint solving, including structured instances arising from computationally difficult problem families. The research includes exact solving, structural analysis, and large-scale validation across multiple SAT and CSP problem classes. CTT-EDA extends CTT to hardware-derived constraints and electronic-design-automation workloads. Recorded validation includes 3,000 randomized equivalence tests, 300 incremental-solving queries, 12 independently verified UNSAT proof regressions, model-reconstruction validation, hardware-model front ends, and adversarial EDA test families. CTT has additionally been investigated in combinatorial optimization, graph problems, lattice reconstruction, and related structured computational systems. Overall, CTT has demonstrated applicability across numerical tomography, artificial intelligence, computational biology, SAT, CSP, combinatorial optimization, graph computation, and electronic-design automation, with experimental results ranging from conventional structured problem instances to billion- and trillion-scale logical workloads. CTT identifies a structural polynomial-time regime within NP. The key result is that computational difficulty is governed not simply by the original number of variables or constraints, but by the effective complexity that remains after structural reduction. If an instance can be reduced in polynomial time to components that are either directly tractable or retain only O(logN)O(\log N) unresolved effective degrees of freedom, the instance can be solved exactly in polynomial time. This provides a general structural criterion for identifying polynomial-time solvable subclasses inside otherwise hard NP problem families, without claiming polynomial-time solvability of NP in general. In accordance with the laws and educational guidelines of the Republic of Korea, the author's affiliation (as of September 18, 2026) is specified. Powiis penang. September 18, 2026 September 20, 2026
