Certified Analytical-Numerical Equivalence for 3D Incompressible Navier-Stokes via Dyadic Reformulation (Reproducibility Package)

This dataset accompanies the manuscript “Conditional A-Priori–A-Posteriori Framework for 3D Incompressible Navier–Stokes 3D via Dyadic Reformulation and Verified Analytical Equivalence” (Proietti & Kaczmarczyk, 2025). It provides the complete certified reproducibility package associated with the analytical–numerical equivalence between the reformulated Navier–Stokes system and its classical counterpart. All results, computational scripts, and verification logs are validated, timestamped, and cryptographically sealed for transparent peer evaluation. Contents. The package includes: • The full project archive (NS3D_Conditional_A_Priori_A_Posteriori_Framework_Equivalence.zip), containing configuration, scripts, and results directories; • The final manuscript PDF and analytical certification report; • SHA-256 signatures (ZIP & PDF) ensuring file-level integrity; • License and copyright documentation; • Certified analytical certificates and manifests located under NS3D_equivalent_certificate/seal/. Reproducibility. All verification runs—covering residual balance, energy consistency, and equivalence validation—are executed under the certified a posteriori verification route NS3D_Aposteriori_Equivalence_Verification/. Each computational output (JSON and log) is hashed and cross-verified, enabling full traceability of the analytical–numerical consistency checks. Certification and Timestamp. All digital artifacts were formally sealed and timestamped on 09 October 2025 under verified SHA-256 signatures. This guarantees the permanent authenticity, reproducibility, and certified integrity of the 3D Navier–Stokes conditional framework.