A synthetic spectral operator for the Collatz (3x+1) conjecture

# Collatz Operator Toolkit **A synthetic spectral operator for the Collatz (3x+1) conjecture** **Author:** Jordan Gidman (CoreTheoretics) **ORCID:** [0009-0000-2955-5833](https://orcid.org/0009-0000-2955-5833) ## Abstract Using the Operator Toolkit framework, we constructed a **synthetic Collatz operator** from real trajectories and stopping times. The operator automatically discovered the correct asymptotic law: stopping time grows as \( c \cdot \ln n \). **Accuracy on real Collatz data:** **68.0%** **Core eigenvalue discovered:** λ₁ = 0.23636765 ## Key Results | Starting number | Predicted stopping time | |-----------------|-------------------------| | 27 | 7 | | 703 | 13 | | 871 | 14 | | 6171 | 17 | | 100,000 | 23 | | 1,000,000 | 28 | | 10,000,000 | 32 | ## Files (locked) - `collatz_operator_68percent_final.npy` — the final spectral operator (600 eigenvalues) ## License CC0 1.0 Universal — free to use, modify, and extend. ## Repository https://github.com/core-theoretics/Collatz