Ghost Numbers Dataset

This dataset contains the numerical results of the 'Ghost Numbers' verification suite, confirming the properties of the factorial-power crossover sequence $C(k) = \min\{n \in \mathbb{N} : n! > n^k\}$. This record includes the generated list of ghost numbers, crossover intervals, and milestone ratios up to $k = 10^9$. The data was generated using the optimized sequential $O(1)$ algorithm described in the associated manuscript, "Ghost Numbers: Skipped Integers in the Factorial-Power Crossover." Data Structure: The file Ghosts.txt is structured as a pipe-delimited text file. Columns: g_i (Ghost number) a_i + i + 2 (Linear Invariant verification) Crossover_k (Interval) g_Gap (n_gap) a_Gap (k_gap) Law_Diff (n_gap - k_gap) m_j/m_{j-1} (Ratio) |e - Ratio| (Absolute distance from Euler's number)