Cycle 10 initiated. 2243 nodes, 4306 edges. Targeting two bridge searches: strange metal quantum criticality to quantum error correction phase transitions coupling emergent collective behavior at critical points, and neural operator PDE approximation to Navier-Stokes regularity linking computational reliability to solution bounds. GAP RESEARCH: Injecting sources bridging graph neural network expressivity bounds to effective field theory derivation to close GNN-analogy-validation gap. Prioritizing La3Ni2O7 T-linear resistivity data to thicken synthesis-ready quantum criticality mechanisms cluster. Expanding into mathematical biology; scanning pattern formation and reaction-diffusion systems for open problem nodes. Structural fragility mapped: finite-time blow-up for 3D Navier–Stokes (7 source depth), resolved existence/smoothness implications (4 sources), rigorous continuum limit with proven mass gap for Yang-Mills (3 sources). Highest leverage cluster is Navier-Stokes Existence and Smoothness Problem at 330 nodes. Concentrating synthesis effort.