Finding: A 6-via geometry that cancels electromagnetic fields via Biot-Savart superposition.

Detail: Real Biot-Savart solver with correct multipole physics. The hexapole arrangement creates a null zone where power currents can flow near sensitive logic without interference.

Finding: Radial math fails on rectangular panels. Kirchhoff plate solver verified.

Detail: We proved that wafer-based radial assumptions are 100% incompatible with rectangular CoWoS panel geometry. This follows directly from coordinate geometry -- radial symmetry assumptions break on non-circular domains.

Finding: FEM-converged gyroid LLZO maintains dendrite suppression up to 60% porosity, exceeding the Monroe-Newman threshold by 1.8x.

Detail: No other solid-state battery architecture achieves this combination of mechanical blocking and ionic conductivity. FEM converged at 50-cubed mesh resolution.

Finding: Rectangular panels show exactly zero azimuthal dependence, proven across 30 NLGEOM FEM cases and 5 materials.

Detail: This is a mathematical consequence of rectangular symmetry. Azimuthal loading terms vanish identically. Verified with nonlinear geometric FEM across steel, aluminum, titanium, copper, and silicon.

Finding: 15 CalculiX FEM cases run against plate theory predictions show a systematic 20-35% offset.

Detail: The offset is expected: 3D solid-element FEM captures effects that classical plate theory ignores (transverse shear, boundary layer effects). This validates that both approaches are working correctly within their respective assumptions.

Finding: Adjoint-derived gradients match finite-difference gradients to machine precision across all 15 design pixels.

Detail: 15/15 pixels show correlation r=1.0 with mean error below 1e-6. This mathematically verifies the adjoint sensitivity implementation is correct.

Finding: Topology-optimized coupler achieves 27.17 dB improvement over a solid block baseline using real FDTD simulation.

Detail: 160x80 design grid with 50 optimization epochs. The improvement is measured against a naive solid-block baseline, so represents optimization gain, not absolute device performance.

Finding: Boundary element method yields physically correct 50-ohm impedance for through-glass via geometries.

Detail: Replaces the previous coaxial approximation that gave erroneous 9-15 ohm results. BEM properly accounts for multiconductor coupling and non-circular cross-sections.

Finding: Gyroid lattice in glass achieves a low effective refractive index of 1.14, verified by Maxwell-Garnett, Bruggeman, Looyenga, and Wiener models.

Detail: Light propagates faster in this structure than in bulk glass. 100% transmission is the optimization target, not a validated measurement. Independent experimental validation is pending.

Finding: Transfer matrix method predicts RF isolation through geometric lattice in glass.

Detail: TMM theoretical calculation only. Practical interposer isolation is estimated at 3-10 dB, significantly less than the idealized model predicts.

Finding: Most naive design paths for glass interposers fail. 11 of 15 tested configurations do not meet requirements.

Detail: The viable design space is narrow, but not as empty as previously claimed. 4 paths beat the patent constraints. This motivates careful optimization but does not prove competitor impossibility.

Finding: A discontinuity in surfactant performance at carbon chain length 5.

Detail: Observed across 5 hardcoded data points. The jump is suggestive but based on a very small dataset with no experimental validation. May reflect a real phase-change boundary or may be an artifact of limited sampling.

Finding: Standard out-of-distribution rejection using Tanimoto similarity correctly flags benzene as outside the training domain.

Detail: This is a standard cheminformatics technique (applicability domain checking), not a novel discovery. It confirms the system has basic OOD detection, which is expected for any properly implemented molecular model.

Finding: Binary fluid drives flow via solutal Marangoni effect with surface tension gradient of 4.8 mN/m. 48 binary combinations patented.

Detail: 1,443x speedup vs COMSOL. Surface tension estimated from GROMACS with unvalidated force field. B200 operating point exceeds JEDEC at 133 W/cm² in 2D solver.

Finding: 448 Li+ ions in LLZO on A100 GPU. MSD fitting window [1524-4571 ps] yields R²=0.999. Matches Thompson et al. 2014 (~0.1 mS/cm grain-boundary LLZO).

Detail: Previous value of 0.477 mS/cm was from an invalid fitting window and has been corrected. The reconciled value aligns with published experimental grain-boundary conductivity data.

Finding: 19 feasible configurations in design window. Optimal: 0.5 μm shell thickness, 54.5 MPa rupture pressure, 3.64 mS/cm post-rupture conductivity.

Detail: Pressure-activated rupture safely discharges the cell before thermal runaway. Pareto front maps the tradeoff between mechanical integrity and post-rupture ionic transport.

Finding: Upgraded from Picard iteration to Newton-Raphson with membrane stiffness on LHS. Converges where Picard diverges for w/h > 0.5.

Detail: Under-relaxation ω=0.3 with best-iterate tracking. Validated against plate-on-elastic-foundation comparison at converged 61x61 grid across glass, silicon, and organic substrates.

Finding: Design rule: max 1.63 nm oxide for >95% yield. Critical thickness t_critical = 2 nm.

Detail: Yield stable at 0.951 across 0-5 nm oxide range. The exponential risk model maps oxide thickness directly to delamination probability for manufacturing process control.

Finding: At k_azi=0.99, overlay sigma ranges 8-17 nm vs. EUV overlay budget of 2.5 nm at 2nm node.

Detail: Maps warpage amplification to actual yield loss via Rayleigh exceedance model. Demonstrates that even small azimuthal coupling produces overlay errors far exceeding the EUV budget.

Finding: Independent derivation path (stress/curvature) agrees with FEM to 0.182%. Validated across 5 materials and 3 temperature differentials.

Detail: Confirms that the solver implementation is correct by cross-checking two independent computational approaches. The sub-0.2% agreement holds across all tested material-temperature combinations.