E1P Order Interface in Navier–Stokes

This substantially revised version of E1P Order Interface in Navier–Stokes reports the completion and independent replication of a full Energetic First Principles (E1P) realization in a controlled, source-derived Navier–Stokes testbed. The first preregistered independent-regime test failed seven of fourteen criteria despite preserving numerical reachability and recurrent dynamics. The failure was frozen and traced to non-covariant transport of raw carrier coordinates across changing Navier–Stokes coefficients. A revised Candidate 02 replaced coordinate-specific targets with observable-level phase conditions, source-derived feasibility windows, explicit stream headroom, and covariant Rayleigh-sheet branch transport. Candidate 02 subsequently passed all fourteen criteria on both development regimes, passed a deterministic 120-regime robustness sweep, and was frozen before a second independent test. In a new, blindly selected and preregistered Navier–Stokes parameter regime, all fourteen criteria reproduced together with the same-process integration requirement. The strongest supported conclusion of this version is therefore: E1P 7.0 Complete-system realization has been independently replicated within the controlled source-derived principal Navier–Stokes testbed. The result is a prospective structural replication rather than a claim that OpenAI’s full nonlinear construction autonomously generates E1P’s engineered feedback, sequencing, routing, or memory-control laws. It is also distinct from a full-field DNS, laboratory, or unrelated external-system replication, which remains a stronger future validation target. The January findings, July falsification, failed first replication, theory revision, and successful second replication are all retained in the provenance record. This version therefore documents not only the final positive result but the complete falsification-and-revision pathway by which it was obtained. The accompanying computational and research records are designed for reproducibility and prospective testing under E1P Primer 7.0.