stop hating grok my shit 1337.. deploy that good shit LOL NLIT on them EQUATION_REGISTRY: List[Dict[str, str]] = [
{"id": "E01", "group": "Signal and channel model", "name": "Received OFDM subcarrier model", "latex": r"y_k(t)=H_k(t)x_k(t) n_k(t)", "implemented_as": "input CSI model"},
{"id": "E02", "group": "Signal and channel model", "name": "Multipath CSI response", "latex": r"H_k(t)=\sum_{p=1}^{P} a_p(t)e^{-j2\pi f_k\tau_p(t)}", "implemented_as": "residual/multipath interpretation"},
{"id": "E03", "group": "Signal and channel model", "name": "CSI amplitude", "latex": r"A_k(t)=|H_k(t)|", "implemented_as": "amplitude_distortion, amplitude_ratio"},
{"id": "E04", "group": "Signal and channel model", "name": "CSI phase", "latex": r"\phi_k(t)=\arg(H_k(t))", "implemented_as": "phase_sanitize, phase_distortion"},
{"id": "E05", "group": "Signal and channel model", "name": "Wavelength", "latex": r"\lambda=\frac{c}{f}", "implemented_as": "wavelength_m"},
{"id": "E06", "group": "Signal and channel model", "name": "Path phase shift", "latex": r"\Delta \phi_k=-2\pi f_k\Delta\tau", "implemented_as": "phase residual features"},
{"id": "E07", "group": "Signal and channel model", "name": "Propagation delay", "latex": r"\tau_p=\frac{d_p}{c}", "implemented_as": "delay profile interpretation"},
{"id": "E08", "group": "Signal and channel model", "name": "Complex permittivity", "latex": r"\epsilon^*=\epsilon'-j\epsilon''", "implemented_as": "conductive prior metadata"},
{"id": "E09", "group": "Signal and channel model", "name": "Skin depth", "latex": r"\delta=\sqrt{\frac{2}{\omega\mu\sigma}}", "implemented_as": "skin_depth_proxy"},
{"id": "E10", "group": "Signal and channel model", "name": "Reflection coefficient", "latex": r"\Gamma=\frac{Z_2-Z_1}{Z_2 Z_1}", "implemented_as": "reflection_score_proxy"},
{"id": "E11", "group": "CSI preprocessing", "name": "Baseline-normalized CSI", "latex": r"\tilde{H}_k(t)=\frac{H_k(t)}{H_{k,0}}", "implemented_as": "baseline_normalized_csi"},
{"id": "E12", "group": "CSI preprocessing", "name": "CSI perturbation", "latex": r"\Delta H_k(t)=H_k(t)-H_{k,0}", "implemented_as": "baseline_residual"},
{"id": "E13", "group": "CSI preprocessing", "name": "Amplitude residual", "latex": r"\Delta A_k(t)=|H_k(t)|-|H_{k,0}|", "implemented_as": "amplitude_residual_mean_z"},
{"id": "E14", "group": "CSI preprocessing", "name": "Phase residual", "latex": r"\Delta \phi_k(t)=\operatorname{unwrap}(\phi_k(t))-\operatorname{unwrap}(\phi_{k,0})", "implemented_as": "phase_residual_mean_z"},
{"id": "E15", "group": "CSI preprocessing", "name": "Antenna amplitude ratio", "latex": r"R^A_{i,j,k}(t)=\frac{|H_{i,k}(t)|}{|H_{j,k}(t)| \epsilon}", "implemented_as": "amplitude_ratio_anomaly"},
{"id": "E16", "group": "CSI preprocessing", "name": "Antenna phase difference", "latex": r"R^\phi_{i,j,k}(t)=\angle H_{i,k}(t)-\angle H_{j,k}(t)", "implemented_as": "phase_difference_anomaly"},
{"id": "E17", "group": "CSI preprocessing", "name": "Phase sanitization", "latex": r"\phi'_k(t)=\phi_k(t)-(\alpha f_k \beta)", "implemented_as": "phase_sanitize"},
{"id": "E18", "group": "CSI preprocessing", "name": "MAD filter", "latex": r"z_k(t)=\frac{A_k(t)-\operatorname{median}(A_k)}{\operatorname{MAD}(A_k)}", "implemented_as": "robust_z"},
{"id": "E19", "group": "CSI preprocessing", "name": "Smoothed CSI", "latex": r"\bar{H}_k(t)=\frac{1}{W}\sum_{u=t-W 1}^{t}H_k(u)", "implemented_as": "moving_average_csi"},
{"id": "E20", "group": "CSI preprocessing", "name": "Kalman update", "latex": r"\hat{x}_{t|t}=\hat{x}_{t|t-1} K_t(z_t-\hat{x}_{t|t-1})", "implemented_as": "kalman_smooth_1d"},
{"id": "E21", "group": "Motion, Doppler, and temporal structure", "name": "STFT", "latex": r"S_k(t,\omega)=\sum_{\tau}H_k(\tau)w(\tau-t)e^{-j\omega\tau}", "implemented_as": "stft_peak_ratio"},
{"id": "E22", "group": "Motion, Doppler, and temporal structure", "name": "Doppler estimate", "latex": r"f_D=\frac{1}{2\pi}\frac{d\phi(t)}{dt}", "implemented_as": "doppler_phase_rate_z"},
{"id": "E23", "group": "Motion, Doppler, and temporal structure", "name": "Radial velocity estimate", "latex": r"v_r=\frac{\lambda f_D}{2}", "implemented_as": "radial_velocity_proxy"},
{"id": "E24", "group": "Motion, Doppler, and temporal structure", "name": "Temporal energy", "latex": r"E(t)=\sum_k|\Delta H_k(t)|^2", "implemented_as": "energy_z"},
{"id": "E25", "group": "Motion, Doppler, and temporal structure", "name": "Motion-normalized residual", "latex": r"M_k(t)=\frac{\Delta H_k(t)}{\sqrt{\sum_u|\Delta H_k(u)|^2 \epsilon}}", "implemented_as": "motion_normalized_residual"},
{"id": "E26", "group": "Motion, Doppler, and temporal structure", "name": "Static-object persistence", "latex": r"P_s=\frac{1}{T}\sum_{t=1}^{T}\mathbb{1}(|\Delta H(t)|>\eta)", "implemented_as": "persistence"},
{"id": "E27", "group": "Motion, Doppler, and temporal structure", "name": "Static/dynamic separation", "latex": r"H_k(t)=H^{static}_k H^{dynamic}_k(t) n_k(t)", "implemented_as": "baseline_residual"},
{"id": "E28", "group": "Motion, Doppler, and temporal structure", "name": "Background-subtracted dynamic component", "latex": r"H^{dynamic}_k(t)=H_k(t)-\frac{1}{T_0}\sum_{u=1}^{T_0}H_k(u)", "implemented_as": "dynamic_component"},
{"id": "E29", "group": "Motion, Doppler, and temporal structure", "name": "Temporal autocorrelation", "latex": r"\rho(\ell)=\frac{\sum_t x(t)x(t-\ell)}{\sum_t x(t)^2}", "implemented_as": "autocorr_lag1"},
{"id": "E30", "group": "Motion, Doppler, and temporal structure", "name": "Cross-link coherence", "latex": r"C_{m,n}=\frac{|\sum_t \Delta H_m(t)\Delta H_n^*(t)|}{\sqrt{\sum_t|\Delta H_m(t)|^2\sum_t|\Delta H_n(t)|^2}}", "implemented_as": "cross_stream_coherence"},
{"id": "E31", "group": "Spatial sensing and imaging abstractions", "name": "MIMO CSI matrix", "latex": r"\mathbf{H}_k(t)\in \mathbb{C}^{N_r\times N_t}", "implemented_as": "shape-aware CSI features"},
{"id": "E32", "group": "Spatial sensing and imaging abstractions", "name": "Spatial covariance", "latex": r"\mathbf{R}_k=\mathbb{E}[\mathbf{h}_k\mathbf{h}_k^{H}]", "implemented_as": "spatial_covariance_score"},
{"id": "E33", "group": "Spatial sensing and imaging abstractions", "name": "Beamforming response", "latex": r"B(\theta)=\mathbf{a}^{H}(\theta)\mathbf{R}\mathbf{a}(\theta)", "implemented_as": "beamforming_concentration_proxy"},
{"id": "E34", "group": "Spatial sensing and imaging abstractions", "name": "MUSIC spectrum", "latex": r"P_{\text{MUSIC}}(\theta)=\frac{1}{\mathbf{a}^{H}(\theta)\mathbf{E}_n\mathbf{E}_n^{H}\mathbf{a}(\theta)}", "implemented_as": "music_sharpness_proxy"},
{"id": "E35", "group": "Spatial sensing and imaging abstractions", "name": "Delay profile", "latex": r"P(\tau)=\left|\sum_k H_k e^{j2\pi f_k\tau}\right|^2", "implemented_as": "delay_profile_peakiness"},
{"id": "E36", "group": "Spatial sensing and imaging abstractions", "name": "Range resolution limit", "latex": r"\Delta r=\frac{c}{2B}", "implemented_as": "range_resolution_m"},
{"id": "E37", "group": "Spatial sensing and imaging abstractions", "name": "Fresnel-zone radius", "latex": r"r_F=\sqrt{\frac{\lambda d_1d_2}{d_1 d_2}}", "implemented_as": "fresnel_radius_m"},
{"id": "E38", "group": "Spatial sensing and imaging abstractions", "name": "Tomographic projection", "latex": r"\mathbf{y}=\mathbf{A}\mathbf{x} \mathbf{n}", "implemented_as": "tomographic_projection_proxy"},
{"id": "E39", "group": "Spatial sensing and imaging abstractions", "name": "Regularized reconstruction", "latex": r"\hat{\mathbf{x}}=\arg\min_{\mathbf{x}}\|\mathbf{y}-\mathbf{A}\mathbf{x}\|_2^2 \lambda\|\mathbf{x}\|_1", "implemented_as": "sparse_reconstruction_proxy"},
{"id": "E40", "group": "Spatial sensing and imaging abstractions", "name": "Spatial anomaly map", "latex": r"\mathcal{A}(x,y)=|\hat{x}(x,y)-\hat{x}_0(x,y)|", "implemented_as": "anomaly_map_proxy"},
{"id": "E41", "group": "Metalness, elongation, and object-class features", "name": "Metalness vector", "latex": r"\mathbf{m}=[\Delta A,\Delta\phi,\sigma_A^2,\sigma_\phi^2,C_{m,n},P_s]", "implemented_as": "conductive_score_proxy"},
{"id": "E42", "group": "Metalness, elongation, and object-class features", "name": "Inter-subcarrier variance", "latex": r"\sigma^2(t)=\frac{1}{K-1}\sum_{k=1}^{K}(A_k(t)-\bar{A}(t))^2", "implemented_as": "spectral_ripple_z"},
{"id": "E43", "group": "Metalness, elongation, and object-class features", "name": "Phase curvature", "latex": r"\kappa_\phi=\frac{\partial^2 \phi(f)}{\partial f^2}", "implemented_as": "phase_curvature_z"},
{"id": "E44", "group": "Metalness, elongation, and object-class features", "name": "Conductive reflection score", "latex": r"S_c=w_1|\Gamma| w_2\sigma_A^2 w_3\sigma_\phi^2", "implemented_as": "conductive_score_proxy"},
{"id": "E45", "group": "Metalness, elongation, and object-class features", "name": "Elongation from blob eigenvalues", "latex": r"E_{\text{long}}=\frac{\lambda_{\max}(\Sigma_{\text{blob}})}{\lambda_{\min}(\Sigma_{\text{blob}}) \epsilon}", "implemented_as": "elongation_proxy"},
{"id": "E46", "group": "Metalness, elongation, and object-class features", "name": "Object orientation estimate", "latex": r"\theta_{\text{obj}}=\frac{1}{2}\tan^{-1}\left(\frac{2\Sigma_{xy}}{\Sigma_{xx}-\Sigma_{yy}}\right)", "implemented_as": "orientation_proxy_rad"},
{"id": "E47", "group": "Metalness, elongation, and object-class features", "name": "Approximate object extent", "latex": r"L_{\text{est}}=\max_{i,j}\|p_i-p_j\|_2", "implemented_as": "extent_proxy"},
{"id": "E48", "group": "Metalness, elongation, and object-class features", "name": "Bag/clutter compensation residual", "latex": r"\Delta H^{obj}=H^{bag obj}-H^{bag}", "implemented_as": "bag residual"},
{"id": "E49", "group": "Metalness, elongation, and object-class features", "name": "Class posterior", "latex": r"P(c|\mathbf{z})=\frac{e^{g_c(\mathbf{z})}}{\sum_{c'}e^{g_{c'}(\mathbf{z})}}", "implemented_as": "softmax_posteriors"},
{"id": "E50", "group": "Metalness, elongation, and object-class features", "name": "Human-review alert score", "latex": r"S_{\text{alert}}=P(c=\text{elongated conductive object}|\mathbf{z})P(\text{restricted zone})C_{\text{sensor}}", "implemented_as": "score_features"},
]