This archive contains the final public AssemblyNS proof dossier presenting the author’s claimed proof of global regularity and smoothness for the three-dimensional incompressible Navier–Stokes equations. The work originated from the broader research framework called System of Streams / KSS. In this framework, a Stream is understood as a dynamic state of a binary field. System of Streams / KSS is an authorial structural system for studying dynamic systems through organized streams, localization, residual interactions, defect channels, closure mechanisms, and the transition from local structures to a global conclusion. In the present project, KSS served as an initial structural and methodological framework for identifying how a possible singular scenario could be localized, controlled, and ultimately excluded. The final AssemblyNS package presented here is not dependent on accepting System of Streams / KSS as a philosophical or heuristic foundation. The proof chain has been translated into an autonomous PDE-oriented format. The final dossier is organized in terms of PDE analysis, localization, admissible selection, pressure-free residual interfaces, pressure reconstruction, compactness, no-defect closure, contraction and endpoint telescoping, zexit–Liouville contradiction, and the final transition to the main theorem. The archive contains the main manuscript, the full formula chain from the initial PDE setup to the final conclusion, Pre-Appendix A, Appendices A–E, a claim boundary document, a cover note, and a reading guide. The main manuscript states the central claim and the accepted boundaries of the result. The full proof chain records the dependency order of the key formulas and proof transitions. Pre-Appendix A and Appendix A provide the local foundation, admissible selection, pressure-free residual interface, and the initial export mechanism. Appendix B develops the pressure envelope and downstream pressure reconstruction. Appendix C contains the no-defect closure. Appendix E provides the contraction and endpoint telescoping mechanism. Appendix D completes the zexit–Liouville contradiction and exports the result to the main theorem. The claim boundary, cover note, and reading guide are included to assist independent readers and external mathematical reviewers in navigating the proof dossier. The archive includes both editable DOCX files and corresponding PDF versions. The DOCX files preserve the original document structure and formula layer, while the PDF files provide stable reading versions for citation, review, and independent examination. Because this is an authorial proof dossier intended for public access and independent mathematical review, minor technical, typographical, formula-formatting, or editorial errors may still be identified during subsequent examination. Such possible errors are not intended as part of the mathematical mechanism itself and may be corrected by the author in later versions after additional checking, external comments, or expert review. The purpose of this publication is to openly register the complete authorial AssemblyNS proof dossier, provide a stable citable version of the current work, and make the material available for independent mathematical scrutiny. Publication of this archive is an act of scholarly disclosure and preservation of the author’s work; it is not journal peer review, official acceptance, or external validation of the claimed mathematical result. All materials in this archive are authored by Ferhat Karmil. Any use, citation, discussion, or reference to this material should acknowledge the author, the title of the package, the version, and the DOI of the record. The proof dossier, its structure, formula chain, proof blocks, and authorial presentation must not be represented as the independent work of another author. Unless otherwise stated in the record, the materials are intended to be distributed under the CC BY-NC-ND 4.0 license: non-commercial sharing is allowed with proper attribution, while commercial use and distribution of modified derivative versions are not permitted without the author’s permission. This archive is published as a complete AssemblyNS proof dossier for independent expert review.
Ferhat Karmil (Sat,) studied this question.