KSS Framework for Navier–Stokes Regularity: Enhanced Conditional Proof Architecture and Bridge-Completeness Program (v2) This work presents a strengthened conditional proof architecture for the three-dimensional Navier–Stokes regularity problem within the KSS (Kernel Stream State) framework. The Navier–Stokes carrier-layer is reformulated through a KSS-compatible Stream-state representation supported by the Energy Bridge (EB Block), Dynamic Observation Bridge, and a finite Registry of source-channel interactions (R1–R4). In this version, the external bridge strategy is substantially revised. Pointwise and raw convolution approaches to the near-field contribution are replaced by a principal-value cancellation framework combined with a local oscillation ledger and its admissible absorption mechanism. This resolves previously identified singular-kernel and concentration issues. The analysis is further extended by a coherent-concentration audit, ensuring that any potentially dangerous concentration mode is either absorbed, transferred to an existing KSS ledger (coherence, source, or dynamic observation), or shown to be harmless for the continuation channel. This eliminates the possibility of a hidden fifth continuation mechanism within the proposed architecture. The main result remains conditional: under KSS compatibility, admissible dynamic observation, and source-channel completeness, finite-time structural singularities are excluded. The proof relies on bounded KSS coercivity derived from non-circular source-channel decomposition and on an integrated-affine domination structure for high-strain contributions across near-field, coherence, source, and observation layers. The manuscript establishes a completed and internally reinforced conditional proof framework. However, the transition to a full Clay-level result requires resolving the bridge-completeness problem, including:(1) construction and boundedness of a non-circular dynamic observation operator for all admissible carrier-layers,(2) universal completeness of the source-classifier without hidden channels,(3) derivation of a classical continuation criterion as a consequence of KSS structural closure.
Ferhat Karmil (Sun,) studied this question.