This release contains the submission version of the manuscript “Compressed Odd Dynamics and a Structural Proof of the Collatz Conjecture.” The paper studies the compressed odd Collatz map and presents a structural reduction framework in which all hypothetical nonconvergent odd orbits are classified into four residual families and then eliminated. The computational appendix is included for bounded verification and reproducibility only and is not part of the logical derivation of the main theorem.
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Four-Family Dynamical Partition
A complete classification of all odd orbits into S, R, H, and C families. -
Finite Residue-Graph Core
A bounded, inspectable model capturing the near-critical region. -
Structural Invariants
Drift, deviation, and valuation geometry used to constrain all possible behaviors. -
Elimination Ladder
A step-by-step structural reduction showing how each family collapses.
OmegaGenesis reframes the Collatz landscape as a finite elimination problem, offering a clear, structured, and historically informed approach to a long-standing mathematical puzzle.
- Canonical documentation
- Diagrams and structural models
- Explanations of the four-family architecture
- Historical and conceptual notes
MIT License (or your preferred license)