The Generative Incompleteness — Paper Zero

Paper Zero presents one particular mathematical representation within Graziano Guiducci’s wider Dual-Non-Dual (D-ND) logical model. It studies the rational recurrence f(x)=1+1/x and the integer matrix [[1,1],[1,0]], distinguishing an invariant projective direction from a vector whose scale continues to change. The revised manuscript gives a projective convergence argument with its exceptional repelling direction, states a minimality result in an explicit matrix class, qualifies the meaning of determinant −1, and distinguishes the dynamical systems to which the different entropy statements apply. The source D-ND meaning and the mathematical interpretation are kept distinct. English and Italian PDFs and their corresponding Markdown and LaTeX sources describe the same work. Scientific text: revised manuscript of 28 October 2026. The deposit adds manuscript-specific license information and its own DOI. Independent research preprint; no journal peer review or acceptance is claimed. Genealogy: the March 2026 DOI 10.5281/zenodo.18902950 identifies a historical GitHub software archive containing the original Paper Zero and Paper A. This standalone manuscript deposit has its own version series. The historical archive and its rights notices are preserved. Version of the scientific text already published on GitHub: 28 October 2026 manuscript sources. Italiano. Paper Zero presenta una particolare rappresentazione matematica del modello logico D-ND più ampio: ricorsione razionale, convergenza proiettiva e distinzione fra direzione invariante e vettore che continua a trasformarsi. Le due lingue appartengono allo stesso lavoro; questo deposito autonomo conserva la genealogia dell’archivio storico.