{ "A": { "imports": [ "__future__.annotations", "dataclasses.asdict", "dataclasses.dataclass", "dataclasses.field", "dataclasses.replace", "litholab.forward.optics.AerialImager", "litholab.theory.certified_optimality._fista_fw", "litholab.theory.certified_optimality.bandlimit_epe_floor", "litholab.theory.certified_optimality.boxqp_lagrangian_lower_bound", "litholab.theory.certified_optimality.socs_linear_operator", "litholab.theory.infeasibility.line_space_target", "litholab.theory.reachability_floor.split_target_band", "litholab.unprintable.floor.FEASIBLE_DEMONSTRATED", "litholab.unprintable.floor.PROVABLY_UNPRINTABLE", "litholab.unprintable.floor.REFUSED", "litholab.unprintable.floor.SOUNDNESS_VIOLATION", "litholab.unprintable.floor.UnprintabilityCertificate", "litholab.unprintable.floor.certified_floor", "litholab.unprintable.floor.pw_weight_family", "litholab.unprintable.floor.relative_residual", "litholab.unprintable.floor.stacked_operator", "litholab.unprintable.relax.Axis", "litholab.unprintable.relax.RELAX_LATTICE", "litholab.unprintable.relax.RelaxationReport", "litholab.unprintable.relax.attribute_bottleneck", "litholab.unprintable.relax.bisection_minimal_step", "litholab.unprintable.relax.design_rule_scan", "litholab.unprintable.relax.minimal_relaxation", "litholab.unprintable.relax.monotonicity_audit", "litholab.unprintable.relax.relaxed", "litholab.unprintable.spec.Feature", "litholab.unprintable.spec.MASK_ALT_PSM", "litholab.unprintable.spec.MASK_ATT_PSM_6PCT", "litholab.unprintable.spec.MASK_CHROME", "litholab.unprintable.spec.MaskClass", "litholab.unprintable.spec.PrintSpec", "litholab.unprintable.spec.ProcessWindow", "litholab.unprintable.spec.SpecRefusal", "litholab.utils.config.LithoConfig" ], "oob_rho": 0.09341066828196307, "point_masses": [ 0.3666338450743034, 0.36670880095957925, 0.36677771070369103, 0.36670880095957925, 0.3666338450743034 ], "stacked_vs_committed": [ { "abs_diff": 0.0, "committed_rho": 0.3666338450743034, "kept_nodes": [ -60.0 ], "stacked_rho": 0.3666338450743034, "z_nm": -60.0 }, { "abs_diff": 0.0, "committed_rho": 0.36670880095957925, "kept_nodes": [ -30.0 ], "stacked_rho": 0.36670880095957925, "z_nm": -30.0 }, { "abs_diff": 0.0, "committed_rho": 0.36677771070369103, "kept_nodes": [ 0.0 ], "stacked_rho": 0.36677771070369103, "z_nm": 0.0 }, { "abs_diff": 0.0, "committed_rho": 0.36670880095957925, "kept_nodes": [ 30.0 ], "stacked_rho": 0.36670880095957925, "z_nm": 30.0 }, { "abs_diff": 0.0, "committed_rho": 0.3666338450743034, "kept_nodes": [ 60.0 ], "stacked_rho": 0.3666338450743034, "z_nm": 60.0 } ] }, "B": { "n_random_masks_per_spec": 300, "pw_weighting_gain": [ { "best_multi_node": 0.4835990085210983, "best_point_mass": 0.4835990085210983, "gain": 0.0, "kind": "line_space", "spec_pitch_nm": 24.0 }, { "best_multi_node": 0.3666926005542913, "best_point_mass": 0.36677771070369103, "gain": -8.511014939971417e-05, "kind": "line_space", "spec_pitch_nm": 32.0 }, { "best_multi_node": 0.2618966998444968, "best_point_mass": 0.2618966998444968, "gain": 0.0, "kind": "line_space", "spec_pitch_nm": 40.0 }, { "best_multi_node": 0.23066271429374752, "best_point_mass": 0.2306627142937475, "gain": 2.7755575615628914e-17, "kind": "line_space", "spec_pitch_nm": 48.0 }, { "best_multi_node": 0.3445730124370436, "best_point_mass": 0.3445730124370435, "gain": 5.551115123125783e-17, "kind": "line_space", "spec_pitch_nm": 32.0 }, { "best_multi_node": 0.6089219331807733, "best_point_mass": 0.60940082989075, "gain": -0.000478896709976695, "kind": "contact_array", "spec_pitch_nm": 32.0 } ], "rows": [ { "best_any_rho": 0.4835999377131339, "best_random_rho": 0.530763321038066, "n_random_masks": 300, "ratio": 1.0000019214101337, "rho_floor": 0.4835990085210983, "spec": { "feature": { "duty": 0.5, "kind": "line_space", "pitch_nm": 24.0 }, "field_band_edge_cyc_per_nm": 0.044000000000000004, "grid": 128, "grid_nyquist_cyc_per_nm": 0.5, "mask": { "hi": 1.0, "lo": 0.0, "name": "chrome_or_absorber", "rationale": "amplitude in [0,1]; contains every binary mask" }, "na": 0.33, "pixel_nm": 1.0, "pw": { "defocus_half_nm": 60.0, "n_nodes": 5, "nodes_nm": [ -60.0, -30.0, 0.0, 30.0, 60.0 ] }, "rho_max": 0.28, "sigma_in": 0.4, "sigma_out": 0.8, "wavelength_nm": 13.5 }, "verdict": "PROVABLY_UNPRINTABLE" }, { "best_any_rho": 0.36677771070369103, "best_random_rho": 0.4980932962647433, "n_random_masks": 300, "ratio": 1.0, "rho_floor": 0.36677771070369103, "spec": { "feature": { "duty": 0.5, "kind": "line_space", "pitch_nm": 32.0 }, "field_band_edge_cyc_per_nm": 0.044000000000000004, "grid": 128, "grid_nyquist_cyc_per_nm": 0.5, "mask": { "hi": 1.0, "lo": 0.0, "name": "chrome_or_absorber", "rationale": "amplitude in [0,1]; contains every binary mask" }, "na": 0.33, "pixel_nm": 1.0, "pw": { "defocus_half_nm": 60.0, "n_nodes": 5, "nodes_nm": [ -60.0, -30.0, 0.0, 30.0, 60.0 ] }, "rho_max": 0.28, "sigma_in": 0.4, "sigma_out": 0.8, "wavelength_nm": 13.5 }, "verdict": "PROVABLY_UNPRINTABLE" }, { "best_any_rho": 0.2618966999168345, "best_random_rho": 0.5091231042958555, "n_random_masks": 300, "ratio": 1.000000000276207, "rho_floor": 0.2618966998444968, "spec": { "feature": { "duty": 0.5, "kind": "line_space", "pitch_nm": 40.0 }, "field_band_edge_cyc_per_nm": 0.044000000000000004, "grid": 128, "grid_nyquist_cyc_per_nm": 0.5, "mask": { "hi": 1.0, "lo": 0.0, "name": "chrome_or_absorber", "rationale": "amplitude in [0,1]; contains every binary mask" }, "na": 0.33, "pixel_nm": 1.0, "pw": { "defocus_half_nm": 60.0, "n_nodes": 5, "nodes_nm": [ -60.0, -30.0, 0.0, 30.0, 60.0 ] }, "rho_max": 0.28, "sigma_in": 0.4, "sigma_out": 0.8, "wavelength_nm": 13.5 }, "verdict": "FEASIBLE_DEMONSTRATED" }, { "best_any_rho": 0.2306627142937475, "best_random_rho": 0.5276816076454177, "n_random_masks": 300, "ratio": 0.9999999999999999, "rho_floor": 0.23066271429374752, "spec": { "feature": { "duty": 0.5, "kind": "line_space", "pitch_nm": 48.0 }, "field_band_edge_cyc_per_nm": 0.044000000000000004, "grid": 128, "grid_nyquist_cyc_per_nm": 0.5, "mask": { "hi": 1.0, "lo": 0.0, "name": "chrome_or_absorber", "rationale": "amplitude in [0,1]; contains every binary mask" }, "na": 0.33, "pixel_nm": 1.0, "pw": { "defocus_half_nm": 60.0, "n_nodes": 5, "nodes_nm": [ -60.0, -30.0, 0.0, 30.0, 60.0 ] }, "rho_max": 0.28, "sigma_in": 0.4, "sigma_out": 0.8, "wavelength_nm": 13.5 }, "verdict": "FEASIBLE_DEMONSTRATED" }, { "best_any_rho": 0.3445730124653299, "best_random_rho": 0.5139014601455967, "n_random_masks": 300, "ratio": 1.000000000082091, "rho_floor": 0.3445730124370436, "spec": { "feature": { "duty": 0.5, "kind": "line_space", "pitch_nm": 32.0 }, "field_band_edge_cyc_per_nm": 0.044000000000000004, "grid": 128, "grid_nyquist_cyc_per_nm": 0.5, "mask": { "hi": 1.0, "lo": -0.2449489742783178, "name": "att_psm_6pct", "rationale": "6% transmission, 180 deg: amplitude in [-sqrt(0.06), 1]" }, "na": 0.33, "pixel_nm": 1.0, "pw": { "defocus_half_nm": 60.0, "n_nodes": 5, "nodes_nm": [ -60.0, -30.0, 0.0, 30.0, 60.0 ] }, "rho_max": 0.28, "sigma_in": 0.4, "sigma_out": 0.8, "wavelength_nm": 13.5 }, "verdict": "PROVABLY_UNPRINTABLE" }, { "best_any_rho": 0.6094008446366188, "best_random_rho": 0.750041815203676, "n_random_masks": 300, "ratio": 1.0000000241973233, "rho_floor": 0.60940082989075, "spec": { "feature": { "duty": 0.5, "kind": "contact_array", "pitch_nm": 32.0 }, "field_band_edge_cyc_per_nm": 0.044000000000000004, "grid": 128, "grid_nyquist_cyc_per_nm": 0.5, "mask": { "hi": 1.0, "lo": 0.0, "name": "chrome_or_absorber", "rationale": "amplitude in [0,1]; contains every binary mask" }, "na": 0.33, "pixel_nm": 1.0, "pw": { "defocus_half_nm": 60.0, "n_nodes": 5, "nodes_nm": [ -60.0, -30.0, 0.0, 30.0, 60.0 ] }, "rho_max": 0.28, "sigma_in": 0.4, "sigma_out": 0.8, "wavelength_nm": 13.5 }, "verdict": "PROVABLY_UNPRINTABLE" } ] }, "C": { "baseline": { "binding_mechanism": "dual_point_z2", "epe_floor_advisory_nm": 0.0, "margin": 0.3099203954, "mechanisms": { "bandlimit_oob": 0.09341066828196307, "dual_edges": 0.3666338450743034, "dual_edges_and_centre": 0.36668180028409936, "dual_point_z0": 0.3666338450743034, "dual_point_z1": 0.36670880095957925, "dual_point_z2": 0.36677771070369103, "dual_point_z3": 0.36670880095957925, "dual_point_z4": 0.3666338450743034, "dual_uniform": 0.3666926005542913 }, "refusal_reason": null, "rho_floor": 0.3667777107, "rho_max": 0.28, "scope": "rank-1 coherent field-matching residual under this repository's SOCS optics, lower-bounded over the box [lo,hi]^{g^2} (a superset of every binary mask in the class) and over the declared defocus nodes; NOT a bound on the full non-convex SOCS-intensity problem; EPE channel advisory and never verdict-driving; simulator-relative, not silicon", "spec": { "feature": { "duty": 0.5, "kind": "line_space", "pitch_nm": 32.0 }, "field_band_edge_cyc_per_nm": 0.044000000000000004, "grid": 128, "grid_nyquist_cyc_per_nm": 0.5, "mask": { "hi": 1.0, "lo": 0.0, "name": "chrome_or_absorber", "rationale": "amplitude in [0,1]; contains every binary mask" }, "na": 0.33, "oob_energy_frac": 0.09341066828196308, "pixel_nm": 1.0, "pw": { "defocus_half_nm": 60.0, "n_nodes": 5, "nodes_nm": [ -60.0, -30.0, 0.0, 30.0, 60.0 ] }, "rho_max": 0.28, "sigma_in": 0.4, "sigma_out": 0.8, "wavelength_nm": 13.5 }, "verdict": "PROVABLY_UNPRINTABLE", "witness_name": "target_as_mask", "witness_rho_pw": 0.3667777107, "witnesses": { "relaxed_edges": 0.36677771070369103, "relaxed_edges_and_centre": 0.36677771070369103, "relaxed_point_z0": 0.36677771070369103, "relaxed_point_z1": 0.36677771070369103, "relaxed_point_z2": 0.36677771070369103, "relaxed_point_z3": 0.36677771070369103, "relaxed_point_z4": 0.36677771070369103, "relaxed_uniform": 0.36677771070369103, "rounded_edges": 0.36677771070369103, "rounded_edges_and_centre": 0.36677771070369103, "rounded_point_z0": 0.36677771070369103, "rounded_point_z1": 0.36677771070369103, "rounded_point_z2": 0.36677771070369103, "rounded_point_z3": 0.36677771070369103, "rounded_point_z4": 0.36677771070369103, "rounded_uniform": 0.36677771070369103, "target_as_mask": 0.36677771070369103 }, "z_nodes_nm": [ -60.0, -30.0, 0.0, 30.0, 60.0 ] }, "bisection_vs_scan": [ { "agree": false, "axis": "na", "bisection_probes": [ { "k": 12, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 18, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 21, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 22, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 23, "verdict": "PROVABLY_UNPRINTABLE" } ], "bisection_steps": null, "headline_agree": true, "headline_bisection_steps": 6, "headline_scan_steps": 6, "probe_rho_max": 0.21560143663434292, "scan_steps": 19, "scan_trail": [ { "k": 1, "refusal": null, "rho_floor": 0.3197171067539253, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 2, "refusal": null, "rho_floor": 0.31578437921892977, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 3, "refusal": null, "rho_floor": 0.312346800343662, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 4, "refusal": null, "rho_floor": 0.30933405165257777, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 5, "refusal": null, "rho_floor": 0.29454462824044336, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 6, "refusal": null, "rho_floor": 0.2517795268853593, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 7, "refusal": null, "rho_floor": 0.2625312321066785, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 8, "refusal": null, "rho_floor": 0.26034374658605275, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 9, "refusal": null, "rho_floor": 0.2763479736587713, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 10, "refusal": null, "rho_floor": 0.2772461741748527, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 11, "refusal": null, "rho_floor": 0.2763779361143024, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 12, "refusal": null, "rho_floor": 0.25630194977825416, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 13, "refusal": null, "rho_floor": 0.25386916917797886, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 14, "refusal": null, "rho_floor": 0.25168604513552745, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 15, "refusal": null, "rho_floor": 0.22384459082302854, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 16, "refusal": null, "rho_floor": 0.22145707701282544, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 17, "refusal": null, "rho_floor": 0.2193031527402013, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 18, "refusal": null, "rho_floor": 0.21735892287509176, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 19, "refusal": null, "rho_floor": 0.21560043663434292, "verdict": "FEASIBLE_DEMONSTRATED" } ] }, { "agree": true, "axis": "sigma_out", "bisection_probes": [ { "k": 4, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 6, "verdict": "FEASIBLE_DEMONSTRATED" }, { "k": 5, "verdict": "PROVABLY_UNPRINTABLE" } ], "bisection_steps": 6, "headline_agree": true, "headline_bisection_steps": null, "headline_scan_steps": null, "probe_rho_max": 0.34204810466430874, "scan_steps": 6, "scan_trail": [ { "k": 1, "refusal": null, "rho_floor": 0.3667777107036908, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 2, "refusal": null, "rho_floor": 0.3667777107036908, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 3, "refusal": null, "rho_floor": 0.3667777107036908, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 4, "refusal": null, "rho_floor": 0.3667777107036908, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 5, "refusal": null, "rho_floor": 0.3667777107036908, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 6, "refusal": null, "rho_floor": 0.34204710466430877, "verdict": "FEASIBLE_DEMONSTRATED" } ] }, { "agree": true, "axis": "pw_defocus", "bisection_probes": [ { "k": 6, "verdict": "FEASIBLE_DEMONSTRATED" }, { "k": 3, "verdict": "FEASIBLE_DEMONSTRATED" }, { "k": 1, "verdict": "FEASIBLE_DEMONSTRATED" } ], "bisection_steps": 1, "headline_agree": true, "headline_bisection_steps": null, "headline_scan_steps": null, "probe_rho_max": 0.366778710703691, "scan_steps": 1, "scan_trail": [ { "k": 1, "refusal": null, "rho_floor": 0.36677771070369103, "verdict": "FEASIBLE_DEMONSTRATED" } ] } ], "monotonicity": [ { "axis": "na", "monotone": false, "n_points": 24, "points": [ { "k": 0, "rho_floor": 0.36677771070369103, "value": 0.33, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 1, "rho_floor": 0.3197171067539253, "value": 0.34, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 2, "rho_floor": 0.31578437921892977, "value": 0.35000000000000003, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 3, "rho_floor": 0.312346800343662, "value": 0.36, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 4, "rho_floor": 0.30933405165257777, "value": 0.37, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 5, "rho_floor": 0.29454462824044336, "value": 0.38, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 6, "rho_floor": 0.2517795268853593, "value": 0.39, "verdict": "FEASIBLE_DEMONSTRATED" }, { "k": 7, "rho_floor": 0.2625312321066785, "value": 0.4, "verdict": "FEASIBLE_DEMONSTRATED" }, { "k": 8, "rho_floor": 0.26034374658605275, "value": 0.41000000000000003, "verdict": "FEASIBLE_DEMONSTRATED" }, { "k": 9, "rho_floor": 0.2763479736587713, "value": 0.42000000000000004, "verdict": "FEASIBLE_DEMONSTRATED" }, { "k": 10, "rho_floor": 0.2772461741748527, "value": 0.43000000000000005, "verdict": "FEASIBLE_DEMONSTRATED" }, { "k": 11, "rho_floor": 0.2763779361143024, "value": 0.44, "verdict": "FEASIBLE_DEMONSTRATED" }, { "k": 12, "rho_floor": 0.25630194977825416, "value": 0.45, "verdict": "FEASIBLE_DEMONSTRATED" }, { "k": 13, "rho_floor": 0.25386916917797886, "value": 0.46, "verdict": "FEASIBLE_DEMONSTRATED" }, { "k": 14, "rho_floor": 0.25168604513552745, "value": 0.47000000000000003, "verdict": "FEASIBLE_DEMONSTRATED" }, { "k": 15, "rho_floor": 0.22384459082302854, "value": 0.48, "verdict": "FEASIBLE_DEMONSTRATED" }, { "k": 16, "rho_floor": 0.22145707701282544, "value": 0.49, "verdict": "FEASIBLE_DEMONSTRATED" }, { "k": 17, "rho_floor": 0.2193031527402013, "value": 0.5, "verdict": "FEASIBLE_DEMONSTRATED" }, { "k": 18, "rho_floor": 0.21735892287509176, "value": 0.51, "verdict": "FEASIBLE_DEMONSTRATED" }, { "k": 19, "rho_floor": 0.21560043663434292, "value": 0.52, "verdict": "FEASIBLE_DEMONSTRATED" }, { "k": 20, "rho_floor": 0.2201597873414043, "value": 0.53, "verdict": "FEASIBLE_DEMONSTRATED" }, { "k": 21, "rho_floor": 0.21858871801510288, "value": 0.54, "verdict": "FEASIBLE_DEMONSTRATED" }, { "k": 22, "rho_floor": 0.22338071745250598, "value": 0.55, "verdict": "FEASIBLE_DEMONSTRATED" }, { "k": 23, "rho_floor": 0.22056027471363765, "value": 0.56, "verdict": "FEASIBLE_DEMONSTRATED" } ], "reversals": [ { "from_k": 6, "rho": 0.2517795268853593, "rho_next": 0.2625312321066785, "to_k": 7 }, { "from_k": 8, "rho": 0.26034374658605275, "rho_next": 0.2763479736587713, "to_k": 9 }, { "from_k": 9, "rho": 0.2763479736587713, "rho_next": 0.2772461741748527, "to_k": 10 }, { "from_k": 19, "rho": 0.21560043663434292, "rho_next": 0.2201597873414043, "to_k": 20 }, { "from_k": 21, "rho": 0.21858871801510288, "rho_next": 0.22338071745250598, "to_k": 22 } ] }, { "axis": "sigma_out", "monotone": false, "n_points": 9, "points": [ { "k": 0, "rho_floor": 0.36677771070369103, "value": 0.8, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 1, "rho_floor": 0.3667777107036908, "value": 0.8200000000000001, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 2, "rho_floor": 0.3667777107036908, "value": 0.8400000000000001, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 3, "rho_floor": 0.3667777107036908, "value": 0.8600000000000001, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 4, "rho_floor": 0.3667777107036908, "value": 0.88, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 5, "rho_floor": 0.3667777107036908, "value": 0.9, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 6, "rho_floor": 0.34204710466430877, "value": 0.92, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 7, "rho_floor": 0.34204710466430877, "value": 0.9400000000000001, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 8, "rho_floor": 0.34317271243423036, "value": 0.9600000000000001, "verdict": "PROVABLY_UNPRINTABLE" } ], "reversals": [ { "from_k": 7, "rho": 0.34204710466430877, "rho_next": 0.34317271243423036, "to_k": 8 } ] }, { "axis": "pw_defocus", "monotone": true, "n_points": 13, "points": [ { "k": 0, "rho_floor": 0.36677771070369103, "value": 60.0, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 1, "rho_floor": 0.36677771070369103, "value": 55.0, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 2, "rho_floor": 0.36677771070369103, "value": 50.0, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 3, "rho_floor": 0.36677771070369103, "value": 45.0, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 4, "rho_floor": 0.36677771070369103, "value": 40.0, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 5, "rho_floor": 0.36677771070369103, "value": 35.0, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 6, "rho_floor": 0.36677771070369103, "value": 30.0, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 7, "rho_floor": 0.36677771070369103, "value": 25.0, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 8, "rho_floor": 0.36677771070369103, "value": 20.0, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 9, "rho_floor": 0.36677771070369103, "value": 15.0, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 10, "rho_floor": 0.36677771070369103, "value": 10.0, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 11, "rho_floor": 0.36677771070369103, "value": 5.0, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 12, "rho_floor": 0.36677771070369103, "value": 0.0, "verdict": "PROVABLY_UNPRINTABLE" } ], "reversals": [] } ], "report": { "baseline_rho_floor": 0.36677771070369103, "baseline_verdict": "PROVABLY_UNPRINTABLE", "cost_model": { "mask": 2.0, "na": 3.0, "pitch": 6.0, "pw_defocus": 4.0, "rho_max": 8.0, "sigma_in": 1.0, "sigma_out": 1.0, "wavelength_nm": 10.0 }, "note": "per-axis minimal steps are the measurement; the single winner is that table read through the DECLARED cost model in `cost_model`", "refusal_reason": null, "rows": [ { "axis": "na", "control_verdict": "PROVABLY_UNPRINTABLE", "cost": 18.0, "kind": "spec", "reachable": true, "steps": 6, "terminal_reason": null, "trail": [ { "k": 1, "refusal": null, "rho_floor": 0.3197171067539253, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 2, "refusal": null, "rho_floor": 0.31578437921892977, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 3, "refusal": null, "rho_floor": 0.312346800343662, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 4, "refusal": null, "rho_floor": 0.30933405165257777, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 5, "refusal": null, "rho_floor": 0.29454462824044336, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 6, "refusal": null, "rho_floor": 0.2517795268853593, "verdict": "FEASIBLE_DEMONSTRATED" } ], "value_at_step": 0.39 }, { "axis": "wavelength_nm", "control_verdict": "PROVABLY_UNPRINTABLE", "cost": 20.0, "kind": "spec", "reachable": true, "steps": 2, "terminal_reason": null, "trail": [ { "k": 1, "refusal": null, "rho_floor": 0.3135319633560042, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 2, "refusal": null, "rho_floor": 0.2525355325761163, "verdict": "FEASIBLE_DEMONSTRATED" } ], "value_at_step": 11.5 }, { "axis": "sigma_out", "control_verdict": null, "cost": null, "kind": "spec", "reachable": false, "steps": null, "terminal_reason": "lattice exhausted at k=8 with verdict PROVABLY_UNPRINTABLE", "trail": [ { "k": 1, "refusal": null, "rho_floor": 0.3667777107036908, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 2, "refusal": null, "rho_floor": 0.3667777107036908, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 3, "refusal": null, "rho_floor": 0.3667777107036908, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 4, "refusal": null, "rho_floor": 0.3667777107036908, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 5, "refusal": null, "rho_floor": 0.3667777107036908, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 6, "refusal": null, "rho_floor": 0.34204710466430877, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 7, "refusal": null, "rho_floor": 0.34204710466430877, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 8, "refusal": null, "rho_floor": 0.34317271243423036, "verdict": "PROVABLY_UNPRINTABLE" } ], "value_at_step": null }, { "axis": "sigma_in", "control_verdict": null, "cost": null, "kind": "spec", "reachable": false, "steps": null, "terminal_reason": "lattice exhausted at k=8 with verdict PROVABLY_UNPRINTABLE", "trail": [ { "k": 1, "refusal": null, "rho_floor": 0.36677771070369103, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 2, "refusal": null, "rho_floor": 0.37897393965685994, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 3, "refusal": null, "rho_floor": 0.37897393965685994, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 4, "refusal": null, "rho_floor": 0.37897393965685994, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 5, "refusal": null, "rho_floor": 0.37897393965685994, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 6, "refusal": null, "rho_floor": 0.37897393965685994, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 7, "refusal": null, "rho_floor": 0.37897393965685994, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 8, "refusal": null, "rho_floor": 0.3879768758548964, "verdict": "PROVABLY_UNPRINTABLE" } ], "value_at_step": null }, { "axis": "mask", "control_verdict": null, "cost": null, "kind": "spec", "reachable": false, "steps": null, "terminal_reason": "lattice exhausted at k=2 with verdict PROVABLY_UNPRINTABLE", "trail": [ { "k": 1, "refusal": null, "rho_floor": 0.3445730124370436, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 2, "refusal": null, "rho_floor": 0.31450638216296456, "verdict": "PROVABLY_UNPRINTABLE" } ], "value_at_step": null }, { "axis": "pw_defocus", "control_verdict": null, "cost": null, "kind": "spec", "reachable": false, "steps": null, "terminal_reason": "lattice exhausted at k=12 with verdict PROVABLY_UNPRINTABLE", "trail": [ { "k": 1, "refusal": null, "rho_floor": 0.36677771070369103, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 2, "refusal": null, "rho_floor": 0.36677771070369103, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 3, "refusal": null, "rho_floor": 0.36677771070369103, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 4, "refusal": null, "rho_floor": 0.36677771070369103, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 5, "refusal": null, "rho_floor": 0.36677771070369103, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 6, "refusal": null, "rho_floor": 0.36677771070369103, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 7, "refusal": null, "rho_floor": 0.36677771070369103, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 8, "refusal": null, "rho_floor": 0.36677771070369103, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 9, "refusal": null, "rho_floor": 0.36677771070369103, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 10, "refusal": null, "rho_floor": 0.36677771070369103, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 11, "refusal": null, "rho_floor": 0.36677771070369103, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 12, "refusal": null, "rho_floor": 0.36677771070369103, "verdict": "PROVABLY_UNPRINTABLE" } ], "value_at_step": null }, { "axis": "rho_max", "control_verdict": "PROVABLY_UNPRINTABLE", "cost": 40.0, "kind": "spec", "reachable": true, "steps": 5, "terminal_reason": null, "trail": [ { "k": 1, "refusal": null, "rho_floor": 0.36677771070369103, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 2, "refusal": null, "rho_floor": 0.36677771070369103, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 3, "refusal": null, "rho_floor": 0.36677771070369103, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 4, "refusal": null, "rho_floor": 0.36677771070369103, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 5, "refusal": null, "rho_floor": 0.36677771070369103, "verdict": "FEASIBLE_DEMONSTRATED" } ], "value_at_step": 0.38 }, { "axis": "pitch", "control_verdict": "PROVABLY_UNPRINTABLE", "cost": 24.0, "kind": "design", "reachable": true, "steps": 4, "terminal_reason": null, "trail": [ { "k": 1, "refusal": null, "rho_floor": 0.33285306034009615, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 2, "refusal": null, "rho_floor": 0.30712183146648747, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 3, "refusal": null, "rho_floor": 0.28292118500467206, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 4, "refusal": null, "rho_floor": 0.2618966998444968, "verdict": "FEASIBLE_DEMONSTRATED" } ], "value_at_step": 40.0 } ], "winner": "na", "winner_cost": 18.0, "winner_steps": 6 } }, "D": { "attribution": { "axis": "na", "axis_cost": 18.0, "axis_steps": 6, "mechanism": "dual_point_z2", "mechanism_rho": 0.36677771070369103, "mechanisms": { "bandlimit_oob": 0.09341066828196307, "dual_edges": 0.3666338450743034, "dual_edges_and_centre": 0.36668180028409936, "dual_point_z0": 0.3666338450743034, "dual_point_z1": 0.36670880095957925, "dual_point_z2": 0.36677771070369103, "dual_point_z3": 0.36670880095957925, "dual_point_z4": 0.3666338450743034, "dual_uniform": 0.3666926005542913 }, "physical_bottleneck": "in-band achievability at a single focus: the spectrum is inside the band but no mask in the class reproduces it well enough", "runners_up": [ { "axis": "wavelength_nm", "cost": 20.0, "steps": 2 }, { "axis": "rho_max", "cost": 40.0, "steps": 5 } ] }, "cost_budget_controls": [ { "affordable_steps": 1, "axis": "wavelength_nm", "rho_floor": 0.3135319633560042, "verdict": "PROVABLY_UNPRINTABLE" }, { "affordable_steps": 8, "axis": "sigma_out", "rho_floor": 0.34317271243423036, "verdict": "PROVABLY_UNPRINTABLE" }, { "affordable_steps": 8, "axis": "sigma_in", "rho_floor": 0.3879768758548964, "verdict": "PROVABLY_UNPRINTABLE" }, { "affordable_steps": 2, "axis": "mask", "rho_floor": 0.31450638216296456, "verdict": "PROVABLY_UNPRINTABLE" }, { "affordable_steps": 4, "axis": "pw_defocus", "rho_floor": 0.36677771070369103, "verdict": "PROVABLY_UNPRINTABLE" }, { "affordable_steps": 2, "axis": "rho_max", "rho_floor": 0.36677771070369103, "verdict": "PROVABLY_UNPRINTABLE" } ], "no_single_bottleneck": { "attribution": { "axis": null, "axis_reason": "no_single_axis_relaxation_within_the_declared_lattice", "interaction": { "budget": 24, "found": null, "pairs_tried": 21, "reading": "no pair reached feasibility in 21 evaluations; this is not a proof that none exists" }, "mechanism": "dual_edges_and_centre", "mechanism_rho": 0.5000159823407894, "mechanisms": { "bandlimit_oob": 0.5000000000000001, "dual_edges": 0.5000000000000001, "dual_edges_and_centre": 0.5000159823407894, "dual_point_z0": 0.5, "dual_point_z1": 0.5, "dual_point_z2": 0.49999999999999994, "dual_point_z3": 0.5, "dual_point_z4": 0.5, "dual_uniform": 0.5000128126201266 }, "physical_bottleneck": "the process window: the binding bound is a multi-node weighting, i.e. no one mask serves the whole defocus band" }, "report": { "baseline_rho_floor": 0.5000159823407894, "baseline_verdict": "PROVABLY_UNPRINTABLE", "cost_model": { "mask": 2.0, "na": 3.0, "pitch": 6.0, "pw_defocus": 4.0, "rho_max": 8.0, "sigma_in": 1.0, "sigma_out": 1.0, "wavelength_nm": 10.0 }, "note": "per-axis minimal steps are the measurement; the single winner is that table read through the DECLARED cost model in `cost_model`", "refusal_reason": "no_single_axis_relaxation_within_the_declared_lattice", "rows": [ { "axis": "na", "control_verdict": null, "cost": null, "kind": "spec", "reachable": false, "steps": null, "terminal_reason": "lattice exhausted at k=23 with verdict PROVABLY_UNPRINTABLE", "trail": [ { "k": 1, "refusal": null, "rho_floor": 0.5000489197017421, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 2, "refusal": null, "rho_floor": 0.5000388889448901, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 3, "refusal": null, "rho_floor": 0.5000311005390468, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 4, "refusal": null, "rho_floor": 0.5000250130452094, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 5, "refusal": null, "rho_floor": 0.5000343684915514, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 6, "refusal": null, "rho_floor": 0.5000270241864134, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 7, "refusal": null, "rho_floor": 0.5000712903467325, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 8, "refusal": null, "rho_floor": 0.5000584359517924, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 9, "refusal": null, "rho_floor": 0.5000543930813351, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 10, "refusal": null, "rho_floor": 0.5000889671243842, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 11, "refusal": null, "rho_floor": 0.500074059114275, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 12, "refusal": null, "rho_floor": 0.5000660705279546, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 13, "refusal": null, "rho_floor": 0.5000552544031537, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 14, "refusal": null, "rho_floor": 0.5000463935008904, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 15, "refusal": null, "rho_floor": 0.5001168369119559, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 16, "refusal": null, "rho_floor": 0.5000992771150793, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 17, "refusal": null, "rho_floor": 0.5000846205527784, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 18, "refusal": null, "rho_floor": 0.5000723461490587, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 19, "refusal": null, "rho_floor": 0.5000620331711363, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 20, "refusal": null, "rho_floor": 0.47133773156357683, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 21, "refusal": null, "rho_floor": 0.4488833672086994, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 22, "refusal": null, "rho_floor": 0.4227154744982906, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 23, "refusal": null, "rho_floor": 0.42543167162909473, "verdict": "PROVABLY_UNPRINTABLE" } ], "value_at_step": null }, { "axis": "wavelength_nm", "control_verdict": null, "cost": null, "kind": "spec", "reachable": false, "steps": null, "terminal_reason": "lattice exhausted at k=7 with verdict PROVABLY_UNPRINTABLE", "trail": [ { "k": 1, "refusal": null, "rho_floor": 0.5000336836145546, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 2, "refusal": null, "rho_floor": 0.5000285255641829, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 3, "refusal": null, "rho_floor": 0.5000993468940351, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 4, "refusal": null, "rho_floor": 0.5000472463753468, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 5, "refusal": null, "rho_floor": 0.5000582747566483, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 6, "refusal": null, "rho_floor": 0.3651817877818614, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 7, "refusal": null, "rho_floor": 0.31093240233418556, "verdict": "PROVABLY_UNPRINTABLE" } ], "value_at_step": null }, { "axis": "sigma_out", "control_verdict": null, "cost": null, "kind": "spec", "reachable": false, "steps": null, "terminal_reason": "lattice exhausted at k=8 with verdict PROVABLY_UNPRINTABLE", "trail": [ { "k": 1, "refusal": null, "rho_floor": 0.5000159823407894, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 2, "refusal": null, "rho_floor": 0.5000159823407894, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 3, "refusal": null, "rho_floor": 0.5000159823407894, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 4, "refusal": null, "rho_floor": 0.5000159823407894, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 5, "refusal": null, "rho_floor": 0.5000159823407894, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 6, "refusal": null, "rho_floor": 0.5003028501297285, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 7, "refusal": null, "rho_floor": 0.5003028501297285, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 8, "refusal": null, "rho_floor": 0.5006847355064523, "verdict": "PROVABLY_UNPRINTABLE" } ], "value_at_step": null }, { "axis": "sigma_in", "control_verdict": null, "cost": null, "kind": "spec", "reachable": false, "steps": null, "terminal_reason": "lattice exhausted at k=8 with verdict PROVABLY_UNPRINTABLE", "trail": [ { "k": 1, "refusal": null, "rho_floor": 0.5000159823407894, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 2, "refusal": null, "rho_floor": 0.5001970017590209, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 3, "refusal": null, "rho_floor": 0.5001970017590209, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 4, "refusal": null, "rho_floor": 0.5001970017590209, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 5, "refusal": null, "rho_floor": 0.5001970017590209, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 6, "refusal": null, "rho_floor": 0.5001970017590209, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 7, "refusal": null, "rho_floor": 0.5001970017590209, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 8, "refusal": null, "rho_floor": 0.5002588364761632, "verdict": "PROVABLY_UNPRINTABLE" } ], "value_at_step": null }, { "axis": "mask", "control_verdict": null, "cost": null, "kind": "spec", "reachable": false, "steps": null, "terminal_reason": "lattice exhausted at k=2 with verdict PROVABLY_UNPRINTABLE", "trail": [ { "k": 1, "refusal": null, "rho_floor": 0.5000159823407894, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 2, "refusal": null, "rho_floor": 0.5000159823407894, "verdict": "PROVABLY_UNPRINTABLE" } ], "value_at_step": null }, { "axis": "pw_defocus", "control_verdict": null, "cost": null, "kind": "spec", "reachable": false, "steps": null, "terminal_reason": "lattice exhausted at k=12 with verdict PROVABLY_UNPRINTABLE", "trail": [ { "k": 1, "refusal": null, "rho_floor": 0.5000111217352073, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 2, "refusal": null, "rho_floor": 0.5000074357889874, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 3, "refusal": null, "rho_floor": 0.5000047463979358, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 4, "refusal": null, "rho_floor": 0.5000028681429568, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 5, "refusal": null, "rho_floor": 0.5000016212640457, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 6, "refusal": null, "rho_floor": 0.5000008422075406, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 7, "refusal": null, "rho_floor": 0.5000003909161552, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 8, "refusal": null, "rho_floor": 0.5000001544817851, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 9, "refusal": null, "rho_floor": 0.5000000473843352, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 10, "refusal": null, "rho_floor": 0.5000000091374541, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 11, "refusal": null, "rho_floor": 0.5000000005624603, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 12, "refusal": null, "rho_floor": 0.5000000000000001, "verdict": "PROVABLY_UNPRINTABLE" } ], "value_at_step": null }, { "axis": "rho_max", "control_verdict": null, "cost": null, "kind": "spec", "reachable": false, "steps": null, "terminal_reason": "lattice exhausted at k=8 with verdict PROVABLY_UNPRINTABLE", "trail": [ { "k": 1, "refusal": null, "rho_floor": 0.5000159823407894, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 2, "refusal": null, "rho_floor": 0.5000159823407894, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 3, "refusal": null, "rho_floor": 0.5000159823407894, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 4, "refusal": null, "rho_floor": 0.5000159823407894, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 5, "refusal": null, "rho_floor": 0.5000159823407894, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 6, "refusal": null, "rho_floor": 0.5000159823407894, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 7, "refusal": null, "rho_floor": 0.5000159823407894, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 8, "refusal": null, "rho_floor": 0.5000159823407894, "verdict": "PROVABLY_UNPRINTABLE" } ], "value_at_step": null }, { "axis": "pitch", "control_verdict": null, "cost": null, "kind": "design", "reachable": false, "steps": null, "terminal_reason": "lattice exhausted at k=12 with verdict PROVABLY_UNPRINTABLE", "trail": [ { "k": 1, "refusal": null, "rho_floor": 0.5051452280637518, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 2, "refusal": null, "rho_floor": 0.5034097860655982, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 3, "refusal": null, "rho_floor": 0.4948611422242412, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 4, "refusal": null, "rho_floor": 0.4835990085210983, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 5, "refusal": null, "rho_floor": 0.4526243965768171, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 6, "refusal": null, "rho_floor": 0.4195836573654195, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 7, "refusal": null, "rho_floor": 0.3897370706860004, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 8, "refusal": null, "rho_floor": 0.36677771070369103, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 9, "refusal": null, "rho_floor": 0.33285306034009615, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 10, "refusal": null, "rho_floor": 0.30712183146648747, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 11, "refusal": null, "rho_floor": 0.28292118500467206, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 12, "refusal": null, "rho_floor": 0.2618966998444968, "verdict": "PROVABLY_UNPRINTABLE" } ], "value_at_step": null } ], "winner": null, "winner_cost": null, "winner_steps": null } } }, "E": { "negative_control": { "binding_mechanism": "dual_point_z0", "epe_floor_advisory_nm": 0.0, "margin": -0.5935641615, "mechanisms": { "bandlimit_oob": 0.05019002258646299, "dual_edges": 0.11380203478628981, "dual_edges_and_centre": 0.10862364924242011, "dual_point_z0": 0.11380203478628981, "dual_point_z1": 0.10148482363775667, "dual_point_z2": 0.09805943243817028, "dual_point_z3": 0.10148482363775668, "dual_point_z4": 0.1138020347862898, "dual_uniform": 0.10578130300940702 }, "refusal_reason": null, "rho_floor": 0.1138020348, "rho_max": 0.28, "scope": "rank-1 coherent field-matching residual under this repository's SOCS optics, lower-bounded over the box [lo,hi]^{g^2} (a superset of every binary mask in the class) and over the declared defocus nodes; NOT a bound on the full non-convex SOCS-intensity problem; EPE channel advisory and never verdict-driving; simulator-relative, not silicon", "spec": { "feature": { "duty": 0.5, "kind": "line_space", "pitch_nm": 96.0 }, "field_band_edge_cyc_per_nm": 0.044000000000000004, "grid": 128, "grid_nyquist_cyc_per_nm": 0.5, "mask": { "hi": 1.0, "lo": 0.0, "name": "chrome_or_absorber", "rationale": "amplitude in [0,1]; contains every binary mask" }, "na": 0.33, "oob_energy_frac": 0.050190022586463, "pixel_nm": 1.0, "pw": { "defocus_half_nm": 60.0, "n_nodes": 5, "nodes_nm": [ -60.0, -30.0, 0.0, 30.0, 60.0 ] }, "rho_max": 0.28, "sigma_in": 0.4, "sigma_out": 0.8, "wavelength_nm": 13.5 }, "verdict": "FEASIBLE_DEMONSTRATED", "witness_name": "relaxed_point_z4", "witness_rho_pw": 0.1138020352, "witnesses": { "relaxed_edges": 0.11380203523088206, "relaxed_edges_and_centre": 0.11384745002272896, "relaxed_point_z0": 0.11380203523088206, "relaxed_point_z1": 0.11395521228207128, "relaxed_point_z2": 0.11395521228207128, "relaxed_point_z3": 0.11395521228207128, "relaxed_point_z4": 0.11380203523088205, "relaxed_uniform": 0.1138995835429234, "rounded_edges": 0.11395521228207128, "rounded_edges_and_centre": 0.11395521228207128, "rounded_point_z0": 0.11395521228207128, "rounded_point_z1": 0.11395521228207128, "rounded_point_z2": 0.11395521228207128, "rounded_point_z3": 0.11395521228207128, "rounded_point_z4": 0.11395521228207128, "rounded_uniform": 0.11395521228207128, "target_as_mask": 0.11395521228207128 }, "z_nodes_nm": [ -60.0, -30.0, 0.0, 30.0, 60.0 ] }, "nyquist_underreport": { "rho_coarse": 0.0, "rho_fine": 0.09341066828196307 }, "refusals": { "band_edge_above_grid_nyquist": { "detail": "band edge 0.077407 cyc/nm exceeds the grid Nyquist 0.062500; the sampled spectrum has folded and the out-of-band floor would be UNDER-reported", "reason": "band_edge_above_grid_nyquist", "verdict": "REFUSED" }, "pitch_below_two_pixels": { "detail": "pitch 1.0 nm is 1.0000 px on a 1.0 nm raster; a line and a space need two", "reason": "pitch_below_two_pixels", "verdict": "REFUSED" }, "pitch_not_on_the_raster": { "detail": "pitch 33.5 nm is 16.750000 px; the rasteriser would answer about 17 px = 34.0 nm instead", "reason": "pitch_not_on_the_raster", "verdict": "REFUSED" }, "source_annulus_inverted": { "detail": "sigma_in 0.9 >= sigma_out 0.8", "reason": "source_annulus_inverted", "verdict": "REFUSED" }, "unknown_feature_kind": { "detail": "serpentine", "reason": "unknown_feature_kind", "verdict": "REFUSED" } }, "soundness_violation_path": "SOUNDNESS_VIOLATION" }, "F": { "relaxed_rule": { "min_periods": 2, "min_pitch_nm": 32.0, "n_periods_at_rule": 4, "rows": [ { "insufficient_periods": false, "n_periods": 8, "pitch_nm": 16.0, "refusal": null, "rho_floor": 0.5000660705279546, "rho_max": 0.28, "verdict": "PROVABLY_UNPRINTABLE", "witness_rho_pw": 0.5000751125208077 }, { "insufficient_periods": false, "n_periods": 6, "pitch_nm": 20.0, "refusal": null, "rho_floor": 0.40154659964420175, "rho_max": 0.28, "verdict": "PROVABLY_UNPRINTABLE", "witness_rho_pw": 0.40154660362057926 }, { "insufficient_periods": false, "n_periods": 5, "pitch_nm": 24.0, "refusal": null, "rho_floor": 0.33280046581709954, "rho_max": 0.28, "verdict": "PROVABLY_UNPRINTABLE", "witness_rho_pw": 0.33280046593820595 }, { "insufficient_periods": false, "n_periods": 4, "pitch_nm": 28.0, "refusal": null, "rho_floor": 0.2873517515851442, "rho_max": 0.28, "verdict": "PROVABLY_UNPRINTABLE", "witness_rho_pw": 0.28735175158514414 }, { "insufficient_periods": false, "n_periods": 4, "pitch_nm": 32.0, "refusal": null, "rho_floor": 0.25630194977825416, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.25630194977825416 }, { "insufficient_periods": false, "n_periods": 3, "pitch_nm": 36.0, "refusal": null, "rho_floor": 0.22929423427928497, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.2292942344114955 }, { "insufficient_periods": false, "n_periods": 3, "pitch_nm": 40.0, "refusal": null, "rho_floor": 0.21311210030837346, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.21311210045310552 }, { "insufficient_periods": false, "n_periods": 2, "pitch_nm": 44.0, "refusal": null, "rho_floor": 0.1867328765439142, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.1867328768954576 }, { "insufficient_periods": false, "n_periods": 2, "pitch_nm": 48.0, "refusal": null, "rho_floor": 0.16998395437641675, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.16998395474396913 }, { "insufficient_periods": false, "n_periods": 2, "pitch_nm": 52.0, "refusal": null, "rho_floor": 0.1538823668233848, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.15388236684477632 }, { "insufficient_periods": false, "n_periods": 2, "pitch_nm": 56.0, "refusal": null, "rho_floor": 0.1396501837041657, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.13965018371467558 }, { "insufficient_periods": false, "n_periods": 2, "pitch_nm": 60.0, "refusal": null, "rho_floor": 0.12760754433211122, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.12760754440329777 }, { "insufficient_periods": false, "n_periods": 2, "pitch_nm": 64.0, "refusal": null, "rho_floor": 0.11849099942207439, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.11849099942391428 }, { "insufficient_periods": true, "n_periods": 1, "pitch_nm": 68.0, "refusal": null, "rho_floor": 0.10734486715653843, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.10734488561209708 }, { "insufficient_periods": true, "n_periods": 1, "pitch_nm": 72.0, "refusal": null, "rho_floor": 0.10070783908756309, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.1007078443753315 }, { "insufficient_periods": true, "n_periods": 1, "pitch_nm": 76.0, "refusal": null, "rho_floor": 0.09503806277602095, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.09503806278404917 }, { "insufficient_periods": true, "n_periods": 1, "pitch_nm": 80.0, "refusal": null, "rho_floor": 0.09006021626359381, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.09006021709446584 }, { "insufficient_periods": true, "n_periods": 1, "pitch_nm": 84.0, "refusal": null, "rho_floor": 0.08557634501334606, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.08557634656453354 } ], "rule": "At NA 0.45, lambda 13.5 nm, sigma 0.4-0.8, chrome_or_absorber, +/-60.0 nm defocus and a relative-field-residual budget of 0.28, the minimum line_space pitch is 32 nm (28 nm is provably unprintable).", "scope": "a design rule under this repository's rank-1 field proxy at the stated spec; simulator-relative, not a foundry design rule", "step_below": { "insufficient_periods": false, "n_periods": 4, "pitch_nm": 28.0, "refusal": null, "rho_floor": 0.2873517515851442, "rho_max": 0.28, "verdict": "PROVABLY_UNPRINTABLE", "witness_rho_pw": 0.28735175158514414 }, "tight": true }, "rules": { "contact_array": { "min_periods": 2, "min_pitch_nm": null, "reason": "no pitch on the scanned lattice reaches FEASIBLE_DEMONSTRATED with at least 2 complete periods on the field; 3 pitch(es) [76.0, 80.0, 84.0] DO meet the spec but carry fewer than 2 periods, so they are a statement about an isolated feature and not about this array", "rows": [ { "insufficient_periods": false, "n_periods": 8, "pitch_nm": 16.0, "refusal": null, "rho_floor": 0.7500079911703947, "rho_max": 0.28, "verdict": "PROVABLY_UNPRINTABLE", "witness_rho_pw": 0.7500093051721696 }, { "insufficient_periods": false, "n_periods": 6, "pitch_nm": 20.0, "refusal": null, "rho_floor": 0.7525456705531778, "rho_max": 0.28, "verdict": "PROVABLY_UNPRINTABLE", "witness_rho_pw": 0.7525465023142421 }, { "insufficient_periods": false, "n_periods": 5, "pitch_nm": 24.0, "refusal": null, "rho_floor": 0.7319104130397396, "rho_max": 0.28, "verdict": "PROVABLY_UNPRINTABLE", "witness_rho_pw": 0.731910770054364 }, { "insufficient_periods": false, "n_periods": 4, "pitch_nm": 28.0, "refusal": null, "rho_floor": 0.6641711699056291, "rho_max": 0.28, "verdict": "PROVABLY_UNPRINTABLE", "witness_rho_pw": 0.6641712229520873 }, { "insufficient_periods": false, "n_periods": 4, "pitch_nm": 32.0, "refusal": null, "rho_floor": 0.60940082989075, "rho_max": 0.28, "verdict": "PROVABLY_UNPRINTABLE", "witness_rho_pw": 0.6094008446366188 }, { "insufficient_periods": false, "n_periods": 3, "pitch_nm": 36.0, "refusal": null, "rho_floor": 0.5186943497059047, "rho_max": 0.28, "verdict": "PROVABLY_UNPRINTABLE", "witness_rho_pw": 0.5186943898299085 }, { "insufficient_periods": false, "n_periods": 3, "pitch_nm": 40.0, "refusal": null, "rho_floor": 0.45624309252305906, "rho_max": 0.28, "verdict": "PROVABLY_UNPRINTABLE", "witness_rho_pw": 0.45624309263297785 }, { "insufficient_periods": false, "n_periods": 2, "pitch_nm": 44.0, "refusal": null, "rho_floor": 0.4149197666423693, "rho_max": 0.28, "verdict": "PROVABLY_UNPRINTABLE", "witness_rho_pw": 0.4149198416995726 }, { "insufficient_periods": false, "n_periods": 2, "pitch_nm": 48.0, "refusal": null, "rho_floor": 0.39046653369036544, "rho_max": 0.28, "verdict": "PROVABLY_UNPRINTABLE", "witness_rho_pw": 0.39046653642316553 }, { "insufficient_periods": false, "n_periods": 2, "pitch_nm": 52.0, "refusal": null, "rho_floor": 0.3743471523249761, "rho_max": 0.28, "verdict": "PROVABLY_UNPRINTABLE", "witness_rho_pw": 0.3743471523249761 }, { "insufficient_periods": false, "n_periods": 2, "pitch_nm": 56.0, "refusal": null, "rho_floor": 0.3626714152580883, "rho_max": 0.28, "verdict": "PROVABLY_UNPRINTABLE", "witness_rho_pw": 0.3626714286428802 }, { "insufficient_periods": false, "n_periods": 2, "pitch_nm": 60.0, "refusal": null, "rho_floor": 0.3504282661929705, "rho_max": 0.28, "verdict": "PROVABLY_UNPRINTABLE", "witness_rho_pw": 0.3504282764005571 }, { "insufficient_periods": false, "n_periods": 2, "pitch_nm": 64.0, "refusal": null, "rho_floor": 0.33521593950261214, "rho_max": 0.28, "verdict": "PROVABLY_UNPRINTABLE", "witness_rho_pw": 0.33521594640917096 }, { "insufficient_periods": true, "n_periods": 1, "pitch_nm": 68.0, "refusal": null, "rho_floor": 0.30031482562241896, "rho_max": 0.28, "verdict": "PROVABLY_UNPRINTABLE", "witness_rho_pw": 0.30031482562241896 }, { "insufficient_periods": true, "n_periods": 1, "pitch_nm": 72.0, "refusal": null, "rho_floor": 0.2866421344566009, "rho_max": 0.28, "verdict": "PROVABLY_UNPRINTABLE", "witness_rho_pw": 0.2866421471774629 }, { "insufficient_periods": true, "n_periods": 1, "pitch_nm": 76.0, "refusal": null, "rho_floor": 0.27319726560737273, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.2731973180452984 }, { "insufficient_periods": true, "n_periods": 1, "pitch_nm": 80.0, "refusal": null, "rho_floor": 0.2600193984440902, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.26001939844409017 }, { "insufficient_periods": true, "n_periods": 1, "pitch_nm": 84.0, "refusal": null, "rho_floor": 0.24739352465649106, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.2473935274474534 } ], "rule": null, "tight": false }, "line_space": { "min_periods": 2, "min_pitch_nm": 40.0, "n_periods_at_rule": 3, "rows": [ { "insufficient_periods": false, "n_periods": 8, "pitch_nm": 16.0, "refusal": null, "rho_floor": 0.5000159823407894, "rho_max": 0.28, "verdict": "PROVABLY_UNPRINTABLE", "witness_rho_pw": 0.5000186103443386 }, { "insufficient_periods": false, "n_periods": 6, "pitch_nm": 20.0, "refusal": null, "rho_floor": 0.5034097860655982, "rho_max": 0.28, "verdict": "PROVABLY_UNPRINTABLE", "witness_rho_pw": 0.5034115396500731 }, { "insufficient_periods": false, "n_periods": 5, "pitch_nm": 24.0, "refusal": null, "rho_floor": 0.4835990085210983, "rho_max": 0.28, "verdict": "PROVABLY_UNPRINTABLE", "witness_rho_pw": 0.4835999377131339 }, { "insufficient_periods": false, "n_periods": 4, "pitch_nm": 28.0, "refusal": null, "rho_floor": 0.4195836573654195, "rho_max": 0.28, "verdict": "PROVABLY_UNPRINTABLE", "witness_rho_pw": 0.41958366261801255 }, { "insufficient_periods": false, "n_periods": 4, "pitch_nm": 32.0, "refusal": null, "rho_floor": 0.36677771070369103, "rho_max": 0.28, "verdict": "PROVABLY_UNPRINTABLE", "witness_rho_pw": 0.36677771070369103 }, { "insufficient_periods": false, "n_periods": 3, "pitch_nm": 36.0, "refusal": null, "rho_floor": 0.30712183146648747, "rho_max": 0.28, "verdict": "PROVABLY_UNPRINTABLE", "witness_rho_pw": 0.3071218317856366 }, { "insufficient_periods": false, "n_periods": 3, "pitch_nm": 40.0, "refusal": null, "rho_floor": 0.2618966998444968, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.2618966999168345 }, { "insufficient_periods": false, "n_periods": 2, "pitch_nm": 44.0, "refusal": null, "rho_floor": 0.24395042399800596, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.24395042399800593 }, { "insufficient_periods": false, "n_periods": 2, "pitch_nm": 48.0, "refusal": null, "rho_floor": 0.23066271429374752, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.2306627142937475 }, { "insufficient_periods": false, "n_periods": 2, "pitch_nm": 52.0, "refusal": null, "rho_floor": 0.22215993438704612, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.2221599357544553 }, { "insufficient_periods": false, "n_periods": 2, "pitch_nm": 56.0, "refusal": null, "rho_floor": 0.21518420289239573, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.21518420510428213 }, { "insufficient_periods": false, "n_periods": 2, "pitch_nm": 60.0, "refusal": null, "rho_floor": 0.207032000603677, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.20703200078056022 }, { "insufficient_periods": false, "n_periods": 2, "pitch_nm": 64.0, "refusal": null, "rho_floor": 0.1960971123763083, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.19609711237630822 }, { "insufficient_periods": true, "n_periods": 1, "pitch_nm": 68.0, "refusal": null, "rho_floor": 0.1675914606043018, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.16759146073190567 }, { "insufficient_periods": true, "n_periods": 1, "pitch_nm": 72.0, "refusal": null, "rho_floor": 0.15855714900538503, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.15855715056895509 }, { "insufficient_periods": true, "n_periods": 1, "pitch_nm": 76.0, "refusal": null, "rho_floor": 0.14999105820277686, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.1499910605084738 }, { "insufficient_periods": true, "n_periods": 1, "pitch_nm": 80.0, "refusal": null, "rho_floor": 0.14185023843123418, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.14185023934711918 }, { "insufficient_periods": true, "n_periods": 1, "pitch_nm": 84.0, "refusal": null, "rho_floor": 0.13413808482021533, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.1341380851111234 } ], "rule": "At NA 0.33, lambda 13.5 nm, sigma 0.4-0.8, chrome_or_absorber, +/-60.0 nm defocus and a relative-field-residual budget of 0.28, the minimum line_space pitch is 40 nm (36 nm is provably unprintable).", "scope": "a design rule under this repository's rank-1 field proxy at the stated spec; simulator-relative, not a foundry design rule", "step_below": { "insufficient_periods": false, "n_periods": 3, "pitch_nm": 36.0, "refusal": null, "rho_floor": 0.30712183146648747, "rho_max": 0.28, "verdict": "PROVABLY_UNPRINTABLE", "witness_rho_pw": 0.3071218317856366 }, "tight": true } } }, "checks": [ { "called": [ "_fista_fw", "boxqp_lagrangian_lower_bound", "split_target_band" ], "detail": "all 3 primitives imported AND called; no function in litholab/unprintable/ both iterates and touches the FFT (the shape of a local solver)", "gate": true, "id": "A1 the floor consumes the committed dual, it does not re-implement one", "imported": [ "litholab.theory.certified_optimality._fista_fw", "litholab.theory.certified_optimality.boxqp_lagrangian_lower_bound", "litholab.theory.reachability_floor.split_target_band" ], "ok": true, "solver_shaped": [] }, { "detail": "max |stacked - certified_optimality_gap_tight| = 0.000e+00 over 5 defocus nodes", "gate": true, "id": "A2 a point-mass weighting reproduces the committed single-focus bound", "nodes": [ { "abs_diff": 0.0, "committed_rho": 0.3666338450743034, "kept_nodes": [ -60.0 ], "stacked_rho": 0.3666338450743034, "z_nm": -60.0 }, { "abs_diff": 0.0, "committed_rho": 0.36670880095957925, "kept_nodes": [ -30.0 ], "stacked_rho": 0.36670880095957925, "z_nm": -30.0 }, { "abs_diff": 0.0, "committed_rho": 0.36677771070369103, "kept_nodes": [ 0.0 ], "stacked_rho": 0.36677771070369103, "z_nm": 0.0 }, { "abs_diff": 0.0, "committed_rho": 0.36670880095957925, "kept_nodes": [ 30.0 ], "stacked_rho": 0.36670880095957925, "z_nm": 30.0 }, { "abs_diff": 0.0, "committed_rho": 0.3666338450743034, "kept_nodes": [ 60.0 ], "stacked_rho": 0.3666338450743034, "z_nm": 60.0 } ], "ok": true }, { "detail": "rho_floor 0.366778 >= max point-mass 0.366778; the weight family contains all 5 point masses by construction", "gate": true, "id": "A3 the composed floor is never weaker than the best single-focus floor", "ok": true, "point_masses": [ 0.3666338450743034, 0.36670880095957925, 0.36677771070369103, 0.36670880095957925, 0.3666338450743034 ], "rho_floor": 0.36677771070369103 }, { "detail": "rho_oob = 0.09341067 at every defocus (defocus is a pupil phase; it does not move the support)", "gate": true, "id": "A4 the band-limit floor is defocus-independent", "ok": true, "values": [ 0.09341066828196307, 0.09341066828196307, 0.09341066828196307 ] }, { "detail": "0 of 1800 random masks + every built-in witness, over 6 specs x 5 defocus nodes, beat the floor", "gate": true, "id": "B1 no mask in the class comes in under the certified floor", "n_masks": 1800, "ok": true, "violations": [] }, { "detail": "tightest achieved/floor ratio 1.000000; the ratio is 1.000000 at 5 of 6 specs", "gate": true, "id": "B2 the floor is attained, so it is not a bound nothing approaches", "ok": true, "ratios": [ 1.0000019214101337, 1.0, 1.000000000276207, 0.9999999999999999, 1.000000000082091, 1.0000000241973233 ] }, { "detail": "NO on every spec measured: 0 of 6 show a strictly larger multi-node bound (max gain +5.55e-17). Published as the null it is -- U1 is sound and, at this window and these features, the point masses already dominate it.", "gains": [ { "best_multi_node": 0.4835990085210983, "best_point_mass": 0.4835990085210983, "gain": 0.0, "kind": "line_space", "spec_pitch_nm": 24.0 }, { "best_multi_node": 0.3666926005542913, "best_point_mass": 0.36677771070369103, "gain": -8.511014939971417e-05, "kind": "line_space", "spec_pitch_nm": 32.0 }, { "best_multi_node": 0.2618966998444968, "best_point_mass": 0.2618966998444968, "gain": 0.0, "kind": "line_space", "spec_pitch_nm": 40.0 }, { "best_multi_node": 0.23066271429374752, "best_point_mass": 0.2306627142937475, "gain": 2.7755575615628914e-17, "kind": "line_space", "spec_pitch_nm": 48.0 }, { "best_multi_node": 0.3445730124370436, "best_point_mass": 0.3445730124370435, "gain": 5.551115123125783e-17, "kind": "line_space", "spec_pitch_nm": 32.0 }, { "best_multi_node": 0.6089219331807733, "best_point_mass": 0.60940082989075, "gain": -0.000478896709976695, "kind": "contact_array", "spec_pitch_nm": 32.0 } ], "gate": false, "id": "B3 does any multi-node weighting beat the best single focus?", "ok": true }, { "cert": { "binding_mechanism": "dual_point_z2", "epe_floor_advisory_nm": 0.0, "margin": 0.3099203954, "mechanisms": { "bandlimit_oob": 0.09341066828196307, "dual_edges": 0.3666338450743034, "dual_edges_and_centre": 0.36668180028409936, "dual_point_z0": 0.3666338450743034, "dual_point_z1": 0.36670880095957925, "dual_point_z2": 0.36677771070369103, "dual_point_z3": 0.36670880095957925, "dual_point_z4": 0.3666338450743034, "dual_uniform": 0.3666926005542913 }, "refusal_reason": null, "rho_floor": 0.3667777107, "rho_max": 0.28, "scope": "rank-1 coherent field-matching residual under this repository's SOCS optics, lower-bounded over the box [lo,hi]^{g^2} (a superset of every binary mask in the class) and over the declared defocus nodes; NOT a bound on the full non-convex SOCS-intensity problem; EPE channel advisory and never verdict-driving; simulator-relative, not silicon", "spec": { "feature": { "duty": 0.5, "kind": "line_space", "pitch_nm": 32.0 }, "field_band_edge_cyc_per_nm": 0.044000000000000004, "grid": 128, "grid_nyquist_cyc_per_nm": 0.5, "mask": { "hi": 1.0, "lo": 0.0, "name": "chrome_or_absorber", "rationale": "amplitude in [0,1]; contains every binary mask" }, "na": 0.33, "oob_energy_frac": 0.09341066828196308, "pixel_nm": 1.0, "pw": { "defocus_half_nm": 60.0, "n_nodes": 5, "nodes_nm": [ -60.0, -30.0, 0.0, 30.0, 60.0 ] }, "rho_max": 0.28, "sigma_in": 0.4, "sigma_out": 0.8, "wavelength_nm": 13.5 }, "verdict": "PROVABLY_UNPRINTABLE", "witness_name": "target_as_mask", "witness_rho_pw": 0.3667777107, "witnesses": { "relaxed_edges": 0.36677771070369103, "relaxed_edges_and_centre": 0.36677771070369103, "relaxed_point_z0": 0.36677771070369103, "relaxed_point_z1": 0.36677771070369103, "relaxed_point_z2": 0.36677771070369103, "relaxed_point_z3": 0.36677771070369103, "relaxed_point_z4": 0.36677771070369103, "relaxed_uniform": 0.36677771070369103, "rounded_edges": 0.36677771070369103, "rounded_edges_and_centre": 0.36677771070369103, "rounded_point_z0": 0.36677771070369103, "rounded_point_z1": 0.36677771070369103, "rounded_point_z2": 0.36677771070369103, "rounded_point_z3": 0.36677771070369103, "rounded_point_z4": 0.36677771070369103, "rounded_uniform": 0.36677771070369103, "target_as_mask": 0.36677771070369103 }, "z_nodes_nm": [ -60.0, -30.0, 0.0, 30.0, 60.0 ] }, "detail": "32 nm pitch: rho_floor 0.36678 > rho_max 0.28 (margin +0.310), binding dual_point_z2", "gate": true, "id": "C0 the headline feature is certified unprintable at the baseline spec", "ok": true }, { "detail": "na=6; wavelength_nm=2; sigma_out=unreachable; sigma_in=unreachable; mask=unreachable; pw_defocus=unreachable; rho_max=5; pitch=4 -> winner na at 6 step(s), declared cost 18.0", "gate": false, "id": "C1 the per-axis minimal-relaxation table", "ok": true, "report": { "baseline_rho_floor": 0.36677771070369103, "baseline_verdict": "PROVABLY_UNPRINTABLE", "cost_model": { "mask": 2.0, "na": 3.0, "pitch": 6.0, "pw_defocus": 4.0, "rho_max": 8.0, "sigma_in": 1.0, "sigma_out": 1.0, "wavelength_nm": 10.0 }, "note": "per-axis minimal steps are the measurement; the single winner is that table read through the DECLARED cost model in `cost_model`", "refusal_reason": null, "rows": [ { "axis": "na", "control_verdict": "PROVABLY_UNPRINTABLE", "cost": 18.0, "kind": "spec", "reachable": true, "steps": 6, "terminal_reason": null, "trail": [ { "k": 1, "refusal": null, "rho_floor": 0.3197171067539253, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 2, "refusal": null, "rho_floor": 0.31578437921892977, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 3, "refusal": null, "rho_floor": 0.312346800343662, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 4, "refusal": null, "rho_floor": 0.30933405165257777, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 5, "refusal": null, "rho_floor": 0.29454462824044336, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 6, "refusal": null, "rho_floor": 0.2517795268853593, "verdict": "FEASIBLE_DEMONSTRATED" } ], "value_at_step": 0.39 }, { "axis": "wavelength_nm", "control_verdict": "PROVABLY_UNPRINTABLE", "cost": 20.0, "kind": "spec", "reachable": true, "steps": 2, "terminal_reason": null, "trail": [ { "k": 1, "refusal": null, "rho_floor": 0.3135319633560042, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 2, "refusal": null, "rho_floor": 0.2525355325761163, "verdict": "FEASIBLE_DEMONSTRATED" } ], "value_at_step": 11.5 }, { "axis": "sigma_out", "control_verdict": null, "cost": null, "kind": "spec", "reachable": false, "steps": null, "terminal_reason": "lattice exhausted at k=8 with verdict PROVABLY_UNPRINTABLE", "trail": [ { "k": 1, "refusal": null, "rho_floor": 0.3667777107036908, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 2, "refusal": null, "rho_floor": 0.3667777107036908, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 3, "refusal": null, "rho_floor": 0.3667777107036908, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 4, "refusal": null, "rho_floor": 0.3667777107036908, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 5, "refusal": null, "rho_floor": 0.3667777107036908, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 6, "refusal": null, "rho_floor": 0.34204710466430877, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 7, "refusal": null, "rho_floor": 0.34204710466430877, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 8, "refusal": null, "rho_floor": 0.34317271243423036, "verdict": "PROVABLY_UNPRINTABLE" } ], "value_at_step": null }, { "axis": "sigma_in", "control_verdict": null, "cost": null, "kind": "spec", "reachable": false, "steps": null, "terminal_reason": "lattice exhausted at k=8 with verdict PROVABLY_UNPRINTABLE", "trail": [ { "k": 1, "refusal": null, "rho_floor": 0.36677771070369103, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 2, "refusal": null, "rho_floor": 0.37897393965685994, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 3, "refusal": null, "rho_floor": 0.37897393965685994, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 4, "refusal": null, "rho_floor": 0.37897393965685994, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 5, "refusal": null, "rho_floor": 0.37897393965685994, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 6, "refusal": null, "rho_floor": 0.37897393965685994, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 7, "refusal": null, "rho_floor": 0.37897393965685994, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 8, "refusal": null, "rho_floor": 0.3879768758548964, "verdict": "PROVABLY_UNPRINTABLE" } ], "value_at_step": null }, { "axis": "mask", "control_verdict": null, "cost": null, "kind": "spec", "reachable": false, "steps": null, "terminal_reason": "lattice exhausted at k=2 with verdict PROVABLY_UNPRINTABLE", "trail": [ { "k": 1, "refusal": null, "rho_floor": 0.3445730124370436, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 2, "refusal": null, "rho_floor": 0.31450638216296456, "verdict": "PROVABLY_UNPRINTABLE" } ], "value_at_step": null }, { "axis": "pw_defocus", "control_verdict": null, "cost": null, "kind": "spec", "reachable": false, "steps": null, "terminal_reason": "lattice exhausted at k=12 with verdict PROVABLY_UNPRINTABLE", "trail": [ { "k": 1, "refusal": null, "rho_floor": 0.36677771070369103, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 2, "refusal": null, "rho_floor": 0.36677771070369103, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 3, "refusal": null, "rho_floor": 0.36677771070369103, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 4, "refusal": null, "rho_floor": 0.36677771070369103, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 5, "refusal": null, "rho_floor": 0.36677771070369103, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 6, "refusal": null, "rho_floor": 0.36677771070369103, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 7, "refusal": null, "rho_floor": 0.36677771070369103, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 8, "refusal": null, "rho_floor": 0.36677771070369103, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 9, "refusal": null, "rho_floor": 0.36677771070369103, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 10, "refusal": null, "rho_floor": 0.36677771070369103, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 11, "refusal": null, "rho_floor": 0.36677771070369103, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 12, "refusal": null, "rho_floor": 0.36677771070369103, "verdict": "PROVABLY_UNPRINTABLE" } ], "value_at_step": null }, { "axis": "rho_max", "control_verdict": "PROVABLY_UNPRINTABLE", "cost": 40.0, "kind": "spec", "reachable": true, "steps": 5, "terminal_reason": null, "trail": [ { "k": 1, "refusal": null, "rho_floor": 0.36677771070369103, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 2, "refusal": null, "rho_floor": 0.36677771070369103, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 3, "refusal": null, "rho_floor": 0.36677771070369103, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 4, "refusal": null, "rho_floor": 0.36677771070369103, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 5, "refusal": null, "rho_floor": 0.36677771070369103, "verdict": "FEASIBLE_DEMONSTRATED" } ], "value_at_step": 0.38 }, { "axis": "pitch", "control_verdict": "PROVABLY_UNPRINTABLE", "cost": 24.0, "kind": "design", "reachable": true, "steps": 4, "terminal_reason": null, "trail": [ { "k": 1, "refusal": null, "rho_floor": 0.33285306034009615, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 2, "refusal": null, "rho_floor": 0.30712183146648747, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 3, "refusal": null, "rho_floor": 0.28292118500467206, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 4, "refusal": null, "rho_floor": 0.2618966998444968, "verdict": "FEASIBLE_DEMONSTRATED" } ], "value_at_step": 40.0 } ], "winner": "na", "winner_cost": 18.0, "winner_steps": 6 } }, { "counterexamples": [], "detail": "4 reachable axes; no feasible point sits below any reported minimum", "gate": true, "id": "C2 every reported minimum is minimal on its axis", "ok": true }, { "control_cert": { "binding_mechanism": "dual_point_z0", "epe_floor_advisory_nm": 0.0, "margin": 0.0519451009, "mechanisms": { "bandlimit_oob": 0.09341066828196307, "dual_edges": 0.29454462824044336, "dual_edges_and_centre": 0.29307667247407965, "dual_point_z0": 0.29454462824044336, "dual_point_z1": 0.29122957933253557, "dual_point_z2": 0.2901407609413523, "dual_point_z3": 0.29122957933253557, "dual_point_z4": 0.29454462824044336, "dual_uniform": 0.292337835217462 }, "refusal_reason": null, "rho_floor": 0.2945446282, "rho_max": 0.28, "scope": "rank-1 coherent field-matching residual under this repository's SOCS optics, lower-bounded over the box [lo,hi]^{g^2} (a superset of every binary mask in the class) and over the declared defocus nodes; NOT a bound on the full non-convex SOCS-intensity problem; EPE channel advisory and never verdict-driving; simulator-relative, not silicon", "spec": { "feature": { "duty": 0.5, "kind": "line_space", "pitch_nm": 32.0 }, "field_band_edge_cyc_per_nm": 0.05066666666666667, "grid": 128, "grid_nyquist_cyc_per_nm": 0.5, "mask": { "hi": 1.0, "lo": 0.0, "name": "chrome_or_absorber", "rationale": "amplitude in [0,1]; contains every binary mask" }, "na": 0.38, "oob_energy_frac": 0.09341066828196308, "pixel_nm": 1.0, "pw": { "defocus_half_nm": 60.0, "n_nodes": 5, "nodes_nm": [ -60.0, -30.0, 0.0, 30.0, 60.0 ] }, "rho_max": 0.28, "sigma_in": 0.4, "sigma_out": 0.8, "wavelength_nm": 13.5 }, "verdict": "PROVABLY_UNPRINTABLE", "witness_name": "target_as_mask", "witness_rho_pw": 0.2945446282, "witnesses": { "relaxed_edges": 0.29454462824044336, "relaxed_edges_and_centre": 0.29454462824044336, "relaxed_point_z0": 0.29454462824044336, "relaxed_point_z1": 0.29454462824044336, "relaxed_point_z2": 0.29454462824044336, "relaxed_point_z3": 0.29454462824044336, "relaxed_point_z4": 0.29454462824044336, "relaxed_uniform": 0.29454462824044336, "rounded_edges": 0.29454462824044336, "rounded_edges_and_centre": 0.29454462824044336, "rounded_point_z0": 0.29454462824044336, "rounded_point_z1": 0.29454462824044336, "rounded_point_z2": 0.29454462824044336, "rounded_point_z3": 0.29454462824044336, "rounded_point_z4": 0.29454462824044336, "rounded_uniform": 0.29454462824044336, "target_as_mask": 0.29454462824044336 }, "z_nodes_nm": [ -60.0, -30.0, 0.0, 30.0, 60.0 ] }, "detail": "na 0.38 -> 0.39: PROVABLY_UNPRINTABLE -> FEASIBLE_DEMONSTRATED (rho_floor 0.29454 -> 0.25178 against rho_max 0.28)", "gate": true, "id": "C3 the winning relaxation really flips the verdict, and one step less does not", "ok": true, "winner": { "feature": { "duty": 0.5, "kind": "line_space", "pitch_nm": 32.0 }, "field_band_edge_cyc_per_nm": 0.052000000000000005, "grid": 128, "grid_nyquist_cyc_per_nm": 0.5, "mask": { "hi": 1.0, "lo": 0.0, "name": "chrome_or_absorber", "rationale": "amplitude in [0,1]; contains every binary mask" }, "na": 0.39, "pixel_nm": 1.0, "pw": { "defocus_half_nm": 60.0, "n_nodes": 5, "nodes_nm": [ -60.0, -30.0, 0.0, 30.0, 60.0 ] }, "rho_max": 0.28, "sigma_in": 0.4, "sigma_out": 0.8, "wavelength_nm": 13.5 }, "winner_cert": { "binding_mechanism": "dual_point_z0", "epe_floor_advisory_nm": 0.0, "margin": -0.100787404, "mechanisms": { "bandlimit_oob": 0.09341066828196307, "dual_edges": 0.2517795268853593, "dual_edges_and_centre": 0.24236696894710824, "dual_point_z0": 0.2517795268853593, "dual_point_z1": 0.23066491902445999, "dual_point_z2": 0.2235418530706063, "dual_point_z3": 0.23066491902445996, "dual_point_z4": 0.2517795268853593, "dual_uniform": 0.237686148978049 }, "refusal_reason": null, "rho_floor": 0.2517795269, "rho_max": 0.28, "scope": "rank-1 coherent field-matching residual under this repository's SOCS optics, lower-bounded over the box [lo,hi]^{g^2} (a superset of every binary mask in the class) and over the declared defocus nodes; NOT a bound on the full non-convex SOCS-intensity problem; EPE channel advisory and never verdict-driving; simulator-relative, not silicon", "spec": { "feature": { "duty": 0.5, "kind": "line_space", "pitch_nm": 32.0 }, "field_band_edge_cyc_per_nm": 0.052000000000000005, "grid": 128, "grid_nyquist_cyc_per_nm": 0.5, "mask": { "hi": 1.0, "lo": 0.0, "name": "chrome_or_absorber", "rationale": "amplitude in [0,1]; contains every binary mask" }, "na": 0.39, "oob_energy_frac": 0.09341066828196308, "pixel_nm": 1.0, "pw": { "defocus_half_nm": 60.0, "n_nodes": 5, "nodes_nm": [ -60.0, -30.0, 0.0, 30.0, 60.0 ] }, "rho_max": 0.28, "sigma_in": 0.4, "sigma_out": 0.8, "wavelength_nm": 13.5 }, "verdict": "FEASIBLE_DEMONSTRATED", "witness_name": "target_as_mask", "witness_rho_pw": 0.2517795269, "witnesses": { "relaxed_edges": 0.2517795268853593, "relaxed_edges_and_centre": 0.2517795268853593, "relaxed_point_z0": 0.2517795268853593, "relaxed_point_z1": 0.2517795268853593, "relaxed_point_z2": 0.2517795268853593, "relaxed_point_z3": 0.2517795268853593, "relaxed_point_z4": 0.2517795268853593, "relaxed_uniform": 0.2517795268853593, "rounded_edges": 0.2517795268853593, "rounded_edges_and_centre": 0.2517795268853593, "rounded_point_z0": 0.2517795268853593, "rounded_point_z1": 0.2517795268853593, "rounded_point_z2": 0.2517795268853593, "rounded_point_z3": 0.2517795268853593, "rounded_point_z4": 0.2517795268853593, "rounded_uniform": 0.2517795268853593, "target_as_mask": 0.2517795268853593 }, "z_nodes_nm": [ -60.0, -30.0, 0.0, 30.0, 60.0 ] } }, { "audits": [ { "axis": "na", "monotone": false, "n_points": 24, "points": [ { "k": 0, "rho_floor": 0.36677771070369103, "value": 0.33, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 1, "rho_floor": 0.3197171067539253, "value": 0.34, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 2, "rho_floor": 0.31578437921892977, "value": 0.35000000000000003, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 3, "rho_floor": 0.312346800343662, "value": 0.36, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 4, "rho_floor": 0.30933405165257777, "value": 0.37, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 5, "rho_floor": 0.29454462824044336, "value": 0.38, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 6, "rho_floor": 0.2517795268853593, "value": 0.39, "verdict": "FEASIBLE_DEMONSTRATED" }, { "k": 7, "rho_floor": 0.2625312321066785, "value": 0.4, "verdict": "FEASIBLE_DEMONSTRATED" }, { "k": 8, "rho_floor": 0.26034374658605275, "value": 0.41000000000000003, "verdict": "FEASIBLE_DEMONSTRATED" }, { "k": 9, "rho_floor": 0.2763479736587713, "value": 0.42000000000000004, "verdict": "FEASIBLE_DEMONSTRATED" }, { "k": 10, "rho_floor": 0.2772461741748527, "value": 0.43000000000000005, "verdict": "FEASIBLE_DEMONSTRATED" }, { "k": 11, "rho_floor": 0.2763779361143024, "value": 0.44, "verdict": "FEASIBLE_DEMONSTRATED" }, { "k": 12, "rho_floor": 0.25630194977825416, "value": 0.45, "verdict": "FEASIBLE_DEMONSTRATED" }, { "k": 13, "rho_floor": 0.25386916917797886, "value": 0.46, "verdict": "FEASIBLE_DEMONSTRATED" }, { "k": 14, "rho_floor": 0.25168604513552745, "value": 0.47000000000000003, "verdict": "FEASIBLE_DEMONSTRATED" }, { "k": 15, "rho_floor": 0.22384459082302854, "value": 0.48, "verdict": "FEASIBLE_DEMONSTRATED" }, { "k": 16, "rho_floor": 0.22145707701282544, "value": 0.49, "verdict": "FEASIBLE_DEMONSTRATED" }, { "k": 17, "rho_floor": 0.2193031527402013, "value": 0.5, "verdict": "FEASIBLE_DEMONSTRATED" }, { "k": 18, "rho_floor": 0.21735892287509176, "value": 0.51, "verdict": "FEASIBLE_DEMONSTRATED" }, { "k": 19, "rho_floor": 0.21560043663434292, "value": 0.52, "verdict": "FEASIBLE_DEMONSTRATED" }, { "k": 20, "rho_floor": 0.2201597873414043, "value": 0.53, "verdict": "FEASIBLE_DEMONSTRATED" }, { "k": 21, "rho_floor": 0.21858871801510288, "value": 0.54, "verdict": "FEASIBLE_DEMONSTRATED" }, { "k": 22, "rho_floor": 0.22338071745250598, "value": 0.55, "verdict": "FEASIBLE_DEMONSTRATED" }, { "k": 23, "rho_floor": 0.22056027471363765, "value": 0.56, "verdict": "FEASIBLE_DEMONSTRATED" } ], "reversals": [ { "from_k": 6, "rho": 0.2517795268853593, "rho_next": 0.2625312321066785, "to_k": 7 }, { "from_k": 8, "rho": 0.26034374658605275, "rho_next": 0.2763479736587713, "to_k": 9 }, { "from_k": 9, "rho": 0.2763479736587713, "rho_next": 0.2772461741748527, "to_k": 10 }, { "from_k": 19, "rho": 0.21560043663434292, "rho_next": 0.2201597873414043, "to_k": 20 }, { "from_k": 21, "rho": 0.21858871801510288, "rho_next": 0.22338071745250598, "to_k": 22 } ] }, { "axis": "sigma_out", "monotone": false, "n_points": 9, "points": [ { "k": 0, "rho_floor": 0.36677771070369103, "value": 0.8, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 1, "rho_floor": 0.3667777107036908, "value": 0.8200000000000001, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 2, "rho_floor": 0.3667777107036908, "value": 0.8400000000000001, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 3, "rho_floor": 0.3667777107036908, "value": 0.8600000000000001, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 4, "rho_floor": 0.3667777107036908, "value": 0.88, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 5, "rho_floor": 0.3667777107036908, "value": 0.9, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 6, "rho_floor": 0.34204710466430877, "value": 0.92, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 7, "rho_floor": 0.34204710466430877, "value": 0.9400000000000001, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 8, "rho_floor": 0.34317271243423036, "value": 0.9600000000000001, "verdict": "PROVABLY_UNPRINTABLE" } ], "reversals": [ { "from_k": 7, "rho": 0.34204710466430877, "rho_next": 0.34317271243423036, "to_k": 8 } ] }, { "axis": "pw_defocus", "monotone": true, "n_points": 13, "points": [ { "k": 0, "rho_floor": 0.36677771070369103, "value": 60.0, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 1, "rho_floor": 0.36677771070369103, "value": 55.0, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 2, "rho_floor": 0.36677771070369103, "value": 50.0, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 3, "rho_floor": 0.36677771070369103, "value": 45.0, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 4, "rho_floor": 0.36677771070369103, "value": 40.0, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 5, "rho_floor": 0.36677771070369103, "value": 35.0, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 6, "rho_floor": 0.36677771070369103, "value": 30.0, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 7, "rho_floor": 0.36677771070369103, "value": 25.0, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 8, "rho_floor": 0.36677771070369103, "value": 20.0, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 9, "rho_floor": 0.36677771070369103, "value": 15.0, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 10, "rho_floor": 0.36677771070369103, "value": 10.0, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 11, "rho_floor": 0.36677771070369103, "value": 5.0, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 12, "rho_floor": 0.36677771070369103, "value": 0.0, "verdict": "PROVABLY_UNPRINTABLE" } ], "reversals": [] } ], "detail": "na: 5 reversal(s) over 24 points; sigma_out: 1 reversal(s) over 9 points; pw_defocus: 0 reversal(s) over 13 points -- so a search that assumes monotonicity is searching a shape that is not there", "gate": true, "id": "C5 the certified floor is measurably non-monotone in at least one axis", "ok": true }, { "detail": "na: scan 19 vs bisection None at rho_max 0.215601 (1 of 3 axes disagree at the probe budget; at the HEADLINE budget 0 of 3 disagree, published as the partial null it is)", "disagreements": [ { "agree": false, "axis": "na", "bisection_probes": [ { "k": 12, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 18, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 21, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 22, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 23, "verdict": "PROVABLY_UNPRINTABLE" } ], "bisection_steps": null, "headline_agree": true, "headline_bisection_steps": 6, "headline_scan_steps": 6, "probe_rho_max": 0.21560143663434292, "scan_steps": 19, "scan_trail": [ { "k": 1, "refusal": null, "rho_floor": 0.3197171067539253, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 2, "refusal": null, "rho_floor": 0.31578437921892977, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 3, "refusal": null, "rho_floor": 0.312346800343662, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 4, "refusal": null, "rho_floor": 0.30933405165257777, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 5, "refusal": null, "rho_floor": 0.29454462824044336, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 6, "refusal": null, "rho_floor": 0.2517795268853593, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 7, "refusal": null, "rho_floor": 0.2625312321066785, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 8, "refusal": null, "rho_floor": 0.26034374658605275, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 9, "refusal": null, "rho_floor": 0.2763479736587713, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 10, "refusal": null, "rho_floor": 0.2772461741748527, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 11, "refusal": null, "rho_floor": 0.2763779361143024, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 12, "refusal": null, "rho_floor": 0.25630194977825416, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 13, "refusal": null, "rho_floor": 0.25386916917797886, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 14, "refusal": null, "rho_floor": 0.25168604513552745, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 15, "refusal": null, "rho_floor": 0.22384459082302854, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 16, "refusal": null, "rho_floor": 0.22145707701282544, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 17, "refusal": null, "rho_floor": 0.2193031527402013, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 18, "refusal": null, "rho_floor": 0.21735892287509176, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 19, "refusal": null, "rho_floor": 0.21560043663434292, "verdict": "FEASIBLE_DEMONSTRATED" } ] }, { "agree": true, "axis": "sigma_out", "bisection_probes": [ { "k": 4, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 6, "verdict": "FEASIBLE_DEMONSTRATED" }, { "k": 5, "verdict": "PROVABLY_UNPRINTABLE" } ], "bisection_steps": 6, "headline_agree": true, "headline_bisection_steps": null, "headline_scan_steps": null, "probe_rho_max": 0.34204810466430874, "scan_steps": 6, "scan_trail": [ { "k": 1, "refusal": null, "rho_floor": 0.3667777107036908, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 2, "refusal": null, "rho_floor": 0.3667777107036908, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 3, "refusal": null, "rho_floor": 0.3667777107036908, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 4, "refusal": null, "rho_floor": 0.3667777107036908, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 5, "refusal": null, "rho_floor": 0.3667777107036908, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 6, "refusal": null, "rho_floor": 0.34204710466430877, "verdict": "FEASIBLE_DEMONSTRATED" } ] }, { "agree": true, "axis": "pw_defocus", "bisection_probes": [ { "k": 6, "verdict": "FEASIBLE_DEMONSTRATED" }, { "k": 3, "verdict": "FEASIBLE_DEMONSTRATED" }, { "k": 1, "verdict": "FEASIBLE_DEMONSTRATED" } ], "bisection_steps": 1, "headline_agree": true, "headline_bisection_steps": null, "headline_scan_steps": null, "probe_rho_max": 0.366778710703691, "scan_steps": 1, "scan_trail": [ { "k": 1, "refusal": null, "rho_floor": 0.36677771070369103, "verdict": "FEASIBLE_DEMONSTRATED" } ] } ], "gate": true, "id": "C4 the monotonicity-assuming bisection returns a NON-minimal 'minimum'", "ok": true }, { "attribution": { "axis": "na", "axis_cost": 18.0, "axis_steps": 6, "mechanism": "dual_point_z2", "mechanism_rho": 0.36677771070369103, "mechanisms": { "bandlimit_oob": 0.09341066828196307, "dual_edges": 0.3666338450743034, "dual_edges_and_centre": 0.36668180028409936, "dual_point_z0": 0.3666338450743034, "dual_point_z1": 0.36670880095957925, "dual_point_z2": 0.36677771070369103, "dual_point_z3": 0.36670880095957925, "dual_point_z4": 0.3666338450743034, "dual_uniform": 0.3666926005542913 }, "physical_bottleneck": "in-band achievability at a single focus: the spectrum is inside the band but no mask in the class reproduces it well enough", "runners_up": [ { "axis": "wavelength_nm", "cost": 20.0, "steps": 2 }, { "axis": "rho_max", "cost": 40.0, "steps": 5 } ] }, "detail": "binding mechanism dual_point_z2 (rho 0.36678) -> in-band achievability at a single focus: the spectrum is inside the band but no mask in the class reproduces it well enough", "gate": false, "id": "D1b what the mechanism attribution says", "ok": true }, { "budget": 18.0, "detail": "named na at cost 18.0; 6 other spec axes given the same budget: 6 do not reach feasibility, 0 do", "gate": true, "id": "D1 the named bottleneck axis is the only one that flips inside its own cost budget", "named": "na", "ok": true, "others": [ { "affordable_steps": 1, "axis": "wavelength_nm", "rho_floor": 0.3135319633560042, "verdict": "PROVABLY_UNPRINTABLE" }, { "affordable_steps": 8, "axis": "sigma_out", "rho_floor": 0.34317271243423036, "verdict": "PROVABLY_UNPRINTABLE" }, { "affordable_steps": 8, "axis": "sigma_in", "rho_floor": 0.3879768758548964, "verdict": "PROVABLY_UNPRINTABLE" }, { "affordable_steps": 2, "axis": "mask", "rho_floor": 0.31450638216296456, "verdict": "PROVABLY_UNPRINTABLE" }, { "affordable_steps": 4, "axis": "pw_defocus", "rho_floor": 0.36677771070369103, "verdict": "PROVABLY_UNPRINTABLE" }, { "affordable_steps": 2, "axis": "rho_max", "rho_floor": 0.36677771070369103, "verdict": "PROVABLY_UNPRINTABLE" } ] }, { "attribution": { "axis": null, "axis_reason": "no_single_axis_relaxation_within_the_declared_lattice", "interaction": { "budget": 24, "found": null, "pairs_tried": 21, "reading": "no pair reached feasibility in 21 evaluations; this is not a proof that none exists" }, "mechanism": "dual_edges_and_centre", "mechanism_rho": 0.5000159823407894, "mechanisms": { "bandlimit_oob": 0.5000000000000001, "dual_edges": 0.5000000000000001, "dual_edges_and_centre": 0.5000159823407894, "dual_point_z0": 0.5, "dual_point_z1": 0.5, "dual_point_z2": 0.49999999999999994, "dual_point_z3": 0.5, "dual_point_z4": 0.5, "dual_uniform": 0.5000128126201266 }, "physical_bottleneck": "the process window: the binding bound is a multi-node weighting, i.e. no one mask serves the whole defocus band" }, "detail": "16 nm pitch at rho_max 0.05 over 8 axes: winner=None, reason=no_single_axis_relaxation_within_the_declared_lattice; pair probe tried 21 pairs (budget 24), found=None", "gate": true, "id": "D2 a spec no single axis can fix is REFUSED, with what was tried named", "ok": true, "report": { "baseline_rho_floor": 0.5000159823407894, "baseline_verdict": "PROVABLY_UNPRINTABLE", "cost_model": { "mask": 2.0, "na": 3.0, "pitch": 6.0, "pw_defocus": 4.0, "rho_max": 8.0, "sigma_in": 1.0, "sigma_out": 1.0, "wavelength_nm": 10.0 }, "note": "per-axis minimal steps are the measurement; the single winner is that table read through the DECLARED cost model in `cost_model`", "refusal_reason": "no_single_axis_relaxation_within_the_declared_lattice", "rows": [ { "axis": "na", "control_verdict": null, "cost": null, "kind": "spec", "reachable": false, "steps": null, "terminal_reason": "lattice exhausted at k=23 with verdict PROVABLY_UNPRINTABLE", "trail": [ { "k": 1, "refusal": null, "rho_floor": 0.5000489197017421, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 2, "refusal": null, "rho_floor": 0.5000388889448901, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 3, "refusal": null, "rho_floor": 0.5000311005390468, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 4, "refusal": null, "rho_floor": 0.5000250130452094, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 5, "refusal": null, "rho_floor": 0.5000343684915514, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 6, "refusal": null, "rho_floor": 0.5000270241864134, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 7, "refusal": null, "rho_floor": 0.5000712903467325, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 8, "refusal": null, "rho_floor": 0.5000584359517924, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 9, "refusal": null, "rho_floor": 0.5000543930813351, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 10, "refusal": null, "rho_floor": 0.5000889671243842, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 11, "refusal": null, "rho_floor": 0.500074059114275, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 12, "refusal": null, "rho_floor": 0.5000660705279546, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 13, "refusal": null, "rho_floor": 0.5000552544031537, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 14, "refusal": null, "rho_floor": 0.5000463935008904, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 15, "refusal": null, "rho_floor": 0.5001168369119559, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 16, "refusal": null, "rho_floor": 0.5000992771150793, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 17, "refusal": null, "rho_floor": 0.5000846205527784, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 18, "refusal": null, "rho_floor": 0.5000723461490587, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 19, "refusal": null, "rho_floor": 0.5000620331711363, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 20, "refusal": null, "rho_floor": 0.47133773156357683, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 21, "refusal": null, "rho_floor": 0.4488833672086994, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 22, "refusal": null, "rho_floor": 0.4227154744982906, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 23, "refusal": null, "rho_floor": 0.42543167162909473, "verdict": "PROVABLY_UNPRINTABLE" } ], "value_at_step": null }, { "axis": "wavelength_nm", "control_verdict": null, "cost": null, "kind": "spec", "reachable": false, "steps": null, "terminal_reason": "lattice exhausted at k=7 with verdict PROVABLY_UNPRINTABLE", "trail": [ { "k": 1, "refusal": null, "rho_floor": 0.5000336836145546, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 2, "refusal": null, "rho_floor": 0.5000285255641829, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 3, "refusal": null, "rho_floor": 0.5000993468940351, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 4, "refusal": null, "rho_floor": 0.5000472463753468, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 5, "refusal": null, "rho_floor": 0.5000582747566483, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 6, "refusal": null, "rho_floor": 0.3651817877818614, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 7, "refusal": null, "rho_floor": 0.31093240233418556, "verdict": "PROVABLY_UNPRINTABLE" } ], "value_at_step": null }, { "axis": "sigma_out", "control_verdict": null, "cost": null, "kind": "spec", "reachable": false, "steps": null, "terminal_reason": "lattice exhausted at k=8 with verdict PROVABLY_UNPRINTABLE", "trail": [ { "k": 1, "refusal": null, "rho_floor": 0.5000159823407894, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 2, "refusal": null, "rho_floor": 0.5000159823407894, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 3, "refusal": null, "rho_floor": 0.5000159823407894, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 4, "refusal": null, "rho_floor": 0.5000159823407894, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 5, "refusal": null, "rho_floor": 0.5000159823407894, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 6, "refusal": null, "rho_floor": 0.5003028501297285, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 7, "refusal": null, "rho_floor": 0.5003028501297285, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 8, "refusal": null, "rho_floor": 0.5006847355064523, "verdict": "PROVABLY_UNPRINTABLE" } ], "value_at_step": null }, { "axis": "sigma_in", "control_verdict": null, "cost": null, "kind": "spec", "reachable": false, "steps": null, "terminal_reason": "lattice exhausted at k=8 with verdict PROVABLY_UNPRINTABLE", "trail": [ { "k": 1, "refusal": null, "rho_floor": 0.5000159823407894, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 2, "refusal": null, "rho_floor": 0.5001970017590209, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 3, "refusal": null, "rho_floor": 0.5001970017590209, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 4, "refusal": null, "rho_floor": 0.5001970017590209, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 5, "refusal": null, "rho_floor": 0.5001970017590209, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 6, "refusal": null, "rho_floor": 0.5001970017590209, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 7, "refusal": null, "rho_floor": 0.5001970017590209, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 8, "refusal": null, "rho_floor": 0.5002588364761632, "verdict": "PROVABLY_UNPRINTABLE" } ], "value_at_step": null }, { "axis": "mask", "control_verdict": null, "cost": null, "kind": "spec", "reachable": false, "steps": null, "terminal_reason": "lattice exhausted at k=2 with verdict PROVABLY_UNPRINTABLE", "trail": [ { "k": 1, "refusal": null, "rho_floor": 0.5000159823407894, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 2, "refusal": null, "rho_floor": 0.5000159823407894, "verdict": "PROVABLY_UNPRINTABLE" } ], "value_at_step": null }, { "axis": "pw_defocus", "control_verdict": null, "cost": null, "kind": "spec", "reachable": false, "steps": null, "terminal_reason": "lattice exhausted at k=12 with verdict PROVABLY_UNPRINTABLE", "trail": [ { "k": 1, "refusal": null, "rho_floor": 0.5000111217352073, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 2, "refusal": null, "rho_floor": 0.5000074357889874, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 3, "refusal": null, "rho_floor": 0.5000047463979358, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 4, "refusal": null, "rho_floor": 0.5000028681429568, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 5, "refusal": null, "rho_floor": 0.5000016212640457, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 6, "refusal": null, "rho_floor": 0.5000008422075406, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 7, "refusal": null, "rho_floor": 0.5000003909161552, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 8, "refusal": null, "rho_floor": 0.5000001544817851, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 9, "refusal": null, "rho_floor": 0.5000000473843352, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 10, "refusal": null, "rho_floor": 0.5000000091374541, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 11, "refusal": null, "rho_floor": 0.5000000005624603, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 12, "refusal": null, "rho_floor": 0.5000000000000001, "verdict": "PROVABLY_UNPRINTABLE" } ], "value_at_step": null }, { "axis": "rho_max", "control_verdict": null, "cost": null, "kind": "spec", "reachable": false, "steps": null, "terminal_reason": "lattice exhausted at k=8 with verdict PROVABLY_UNPRINTABLE", "trail": [ { "k": 1, "refusal": null, "rho_floor": 0.5000159823407894, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 2, "refusal": null, "rho_floor": 0.5000159823407894, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 3, "refusal": null, "rho_floor": 0.5000159823407894, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 4, "refusal": null, "rho_floor": 0.5000159823407894, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 5, "refusal": null, "rho_floor": 0.5000159823407894, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 6, "refusal": null, "rho_floor": 0.5000159823407894, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 7, "refusal": null, "rho_floor": 0.5000159823407894, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 8, "refusal": null, "rho_floor": 0.5000159823407894, "verdict": "PROVABLY_UNPRINTABLE" } ], "value_at_step": null }, { "axis": "pitch", "control_verdict": null, "cost": null, "kind": "design", "reachable": false, "steps": null, "terminal_reason": "lattice exhausted at k=12 with verdict PROVABLY_UNPRINTABLE", "trail": [ { "k": 1, "refusal": null, "rho_floor": 0.5051452280637518, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 2, "refusal": null, "rho_floor": 0.5034097860655982, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 3, "refusal": null, "rho_floor": 0.4948611422242412, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 4, "refusal": null, "rho_floor": 0.4835990085210983, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 5, "refusal": null, "rho_floor": 0.4526243965768171, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 6, "refusal": null, "rho_floor": 0.4195836573654195, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 7, "refusal": null, "rho_floor": 0.3897370706860004, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 8, "refusal": null, "rho_floor": 0.36677771070369103, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 9, "refusal": null, "rho_floor": 0.33285306034009615, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 10, "refusal": null, "rho_floor": 0.30712183146648747, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 11, "refusal": null, "rho_floor": 0.28292118500467206, "verdict": "PROVABLY_UNPRINTABLE" }, { "k": 12, "refusal": null, "rho_floor": 0.2618966998444968, "verdict": "PROVABLY_UNPRINTABLE" } ], "value_at_step": null } ], "winner": null, "winner_cost": null, "winner_steps": null } }, { "cert": { "binding_mechanism": "dual_point_z0", "epe_floor_advisory_nm": 0.0, "margin": -0.5935641615, "mechanisms": { "bandlimit_oob": 0.05019002258646299, "dual_edges": 0.11380203478628981, "dual_edges_and_centre": 0.10862364924242011, "dual_point_z0": 0.11380203478628981, "dual_point_z1": 0.10148482363775667, "dual_point_z2": 0.09805943243817028, "dual_point_z3": 0.10148482363775668, "dual_point_z4": 0.1138020347862898, "dual_uniform": 0.10578130300940702 }, "refusal_reason": null, "rho_floor": 0.1138020348, "rho_max": 0.28, "scope": "rank-1 coherent field-matching residual under this repository's SOCS optics, lower-bounded over the box [lo,hi]^{g^2} (a superset of every binary mask in the class) and over the declared defocus nodes; NOT a bound on the full non-convex SOCS-intensity problem; EPE channel advisory and never verdict-driving; simulator-relative, not silicon", "spec": { "feature": { "duty": 0.5, "kind": "line_space", "pitch_nm": 96.0 }, "field_band_edge_cyc_per_nm": 0.044000000000000004, "grid": 128, "grid_nyquist_cyc_per_nm": 0.5, "mask": { "hi": 1.0, "lo": 0.0, "name": "chrome_or_absorber", "rationale": "amplitude in [0,1]; contains every binary mask" }, "na": 0.33, "oob_energy_frac": 0.050190022586463, "pixel_nm": 1.0, "pw": { "defocus_half_nm": 60.0, "n_nodes": 5, "nodes_nm": [ -60.0, -30.0, 0.0, 30.0, 60.0 ] }, "rho_max": 0.28, "sigma_in": 0.4, "sigma_out": 0.8, "wavelength_nm": 13.5 }, "verdict": "FEASIBLE_DEMONSTRATED", "witness_name": "relaxed_point_z4", "witness_rho_pw": 0.1138020352, "witnesses": { "relaxed_edges": 0.11380203523088206, "relaxed_edges_and_centre": 0.11384745002272896, "relaxed_point_z0": 0.11380203523088206, "relaxed_point_z1": 0.11395521228207128, "relaxed_point_z2": 0.11395521228207128, "relaxed_point_z3": 0.11395521228207128, "relaxed_point_z4": 0.11380203523088205, "relaxed_uniform": 0.1138995835429234, "rounded_edges": 0.11395521228207128, "rounded_edges_and_centre": 0.11395521228207128, "rounded_point_z0": 0.11395521228207128, "rounded_point_z1": 0.11395521228207128, "rounded_point_z2": 0.11395521228207128, "rounded_point_z3": 0.11395521228207128, "rounded_point_z4": 0.11395521228207128, "rounded_uniform": 0.11395521228207128, "target_as_mask": 0.11395521228207128 }, "z_nodes_nm": [ -60.0, -30.0, 0.0, 30.0, 60.0 ] }, "detail": "96 nm pitch: FEASIBLE_DEMONSTRATED, rho_floor 0.11380 <= rho_max 0.28, witness relaxed_point_z4 at 0.11380", "gate": true, "id": "E1 a comfortably printable feature is NOT certified unprintable", "ok": true }, { "cases": { "band_edge_above_grid_nyquist": { "detail": "band edge 0.077407 cyc/nm exceeds the grid Nyquist 0.062500; the sampled spectrum has folded and the out-of-band floor would be UNDER-reported", "reason": "band_edge_above_grid_nyquist", "verdict": "REFUSED" }, "pitch_below_two_pixels": { "detail": "pitch 1.0 nm is 1.0000 px on a 1.0 nm raster; a line and a space need two", "reason": "pitch_below_two_pixels", "verdict": "REFUSED" }, "pitch_not_on_the_raster": { "detail": "pitch 33.5 nm is 16.750000 px; the rasteriser would answer about 17 px = 34.0 nm instead", "reason": "pitch_not_on_the_raster", "verdict": "REFUSED" }, "source_annulus_inverted": { "detail": "sigma_in 0.9 >= sigma_out 0.8", "reason": "source_annulus_inverted", "verdict": "REFUSED" }, "unknown_feature_kind": { "detail": "serpentine", "reason": "unknown_feature_kind", "verdict": "REFUSED" } }, "detail": "5/5 reasons reached: pitch_below_two_pixels->pitch_below_two_pixels, pitch_not_on_the_raster->pitch_not_on_the_raster, band_edge_above_grid_nyquist->band_edge_above_grid_nyquist, source_annulus_inverted->source_annulus_inverted, unknown_feature_kind->unknown_feature_kind", "gate": true, "id": "E2a every refusal reason is reachable and returns REFUSED, not an answer", "ok": true }, { "detail": "same 32 nm pitch at NA 0.55 / sigma_out 0.9: band edge 0.0774 cyc/nm against a coarse-raster Nyquist 0.0625. Out-of-band rho on the properly sampled raster 0.09341; on the aliased one 0.00000 (0.000x). Serving it would call an unprintable feature printable.", "gate": true, "id": "E2b the refused spec would have UNDER-reported the floor -- the unsound direction", "ok": true, "rho_coarse": 0.0, "rho_fine": 0.09341066828196307 }, { "advisory_nm": 0.0, "detail": "advisory driven to 1e9 nm: verdict stays PROVABLY_UNPRINTABLE; `_verdict`'s AST names ['FEASIBLE_DEMONSTRATED', 'GRAY_ZONE', 'PROVABLY_UNPRINTABLE', 'SOUNDNESS_VIOLATION', 'float', 'rho_floor', 'rho_max', 'str', 'witness_rho_pw'] -- no EPE symbol is in scope there", "gate": true, "id": "E3 the advisory EPE floor is programmatically incapable of setting the verdict", "ok": true, "verdict_symbols": [ "FEASIBLE_DEMONSTRATED", "GRAY_ZONE", "PROVABLY_UNPRINTABLE", "SOUNDNESS_VIOLATION", "float", "rho_floor", "rho_max", "str", "witness_rho_pw" ] }, { "detail": "_verdict(floor=0.30, spec=0.28, witness=0.10) = SOUNDNESS_VIOLATION; the run's gates fail on it rather than reporting a quiet FEASIBLE", "gate": true, "id": "E4 a mask that beats the certified floor is surfaced, not absorbed", "ok": true, "verdict": "SOUNDNESS_VIOLATION" }, { "detail": "At NA 0.33, lambda 13.5 nm, sigma 0.4-0.8, chrome_or_absorber, +/-60.0 nm defocus and a relative-field-residual budget of 0.28, the minimum line_space pitch is 40 nm (36 nm is provably unprintable). [tight=True, min_periods=2, periods at the rule=3]", "gate": true, "id": "F1 line_space: no untight rule is quoted", "ok": true, "rule": { "min_periods": 2, "min_pitch_nm": 40.0, "n_periods_at_rule": 3, "rows": [ { "insufficient_periods": false, "n_periods": 8, "pitch_nm": 16.0, "refusal": null, "rho_floor": 0.5000159823407894, "rho_max": 0.28, "verdict": "PROVABLY_UNPRINTABLE", "witness_rho_pw": 0.5000186103443386 }, { "insufficient_periods": false, "n_periods": 6, "pitch_nm": 20.0, "refusal": null, "rho_floor": 0.5034097860655982, "rho_max": 0.28, "verdict": "PROVABLY_UNPRINTABLE", "witness_rho_pw": 0.5034115396500731 }, { "insufficient_periods": false, "n_periods": 5, "pitch_nm": 24.0, "refusal": null, "rho_floor": 0.4835990085210983, "rho_max": 0.28, "verdict": "PROVABLY_UNPRINTABLE", "witness_rho_pw": 0.4835999377131339 }, { "insufficient_periods": false, "n_periods": 4, "pitch_nm": 28.0, "refusal": null, "rho_floor": 0.4195836573654195, "rho_max": 0.28, "verdict": "PROVABLY_UNPRINTABLE", "witness_rho_pw": 0.41958366261801255 }, { "insufficient_periods": false, "n_periods": 4, "pitch_nm": 32.0, "refusal": null, "rho_floor": 0.36677771070369103, "rho_max": 0.28, "verdict": "PROVABLY_UNPRINTABLE", "witness_rho_pw": 0.36677771070369103 }, { "insufficient_periods": false, "n_periods": 3, "pitch_nm": 36.0, "refusal": null, "rho_floor": 0.30712183146648747, "rho_max": 0.28, "verdict": "PROVABLY_UNPRINTABLE", "witness_rho_pw": 0.3071218317856366 }, { "insufficient_periods": false, "n_periods": 3, "pitch_nm": 40.0, "refusal": null, "rho_floor": 0.2618966998444968, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.2618966999168345 }, { "insufficient_periods": false, "n_periods": 2, "pitch_nm": 44.0, "refusal": null, "rho_floor": 0.24395042399800596, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.24395042399800593 }, { "insufficient_periods": false, "n_periods": 2, "pitch_nm": 48.0, "refusal": null, "rho_floor": 0.23066271429374752, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.2306627142937475 }, { "insufficient_periods": false, "n_periods": 2, "pitch_nm": 52.0, "refusal": null, "rho_floor": 0.22215993438704612, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.2221599357544553 }, { "insufficient_periods": false, "n_periods": 2, "pitch_nm": 56.0, "refusal": null, "rho_floor": 0.21518420289239573, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.21518420510428213 }, { "insufficient_periods": false, "n_periods": 2, "pitch_nm": 60.0, "refusal": null, "rho_floor": 0.207032000603677, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.20703200078056022 }, { "insufficient_periods": false, "n_periods": 2, "pitch_nm": 64.0, "refusal": null, "rho_floor": 0.1960971123763083, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.19609711237630822 }, { "insufficient_periods": true, "n_periods": 1, "pitch_nm": 68.0, "refusal": null, "rho_floor": 0.1675914606043018, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.16759146073190567 }, { "insufficient_periods": true, "n_periods": 1, "pitch_nm": 72.0, "refusal": null, "rho_floor": 0.15855714900538503, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.15855715056895509 }, { "insufficient_periods": true, "n_periods": 1, "pitch_nm": 76.0, "refusal": null, "rho_floor": 0.14999105820277686, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.1499910605084738 }, { "insufficient_periods": true, "n_periods": 1, "pitch_nm": 80.0, "refusal": null, "rho_floor": 0.14185023843123418, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.14185023934711918 }, { "insufficient_periods": true, "n_periods": 1, "pitch_nm": 84.0, "refusal": null, "rho_floor": 0.13413808482021533, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.1341380851111234 } ], "rule": "At NA 0.33, lambda 13.5 nm, sigma 0.4-0.8, chrome_or_absorber, +/-60.0 nm defocus and a relative-field-residual budget of 0.28, the minimum line_space pitch is 40 nm (36 nm is provably unprintable).", "scope": "a design rule under this repository's rank-1 field proxy at the stated spec; simulator-relative, not a foundry design rule", "step_below": { "insufficient_periods": false, "n_periods": 3, "pitch_nm": 36.0, "refusal": null, "rho_floor": 0.30712183146648747, "rho_max": 0.28, "verdict": "PROVABLY_UNPRINTABLE", "witness_rho_pw": 0.3071218317856366 }, "tight": true } }, { "detail": "NO RULE \u2014 no pitch on the scanned lattice reaches FEASIBLE_DEMONSTRATED with at least 2 complete periods on the field; 3 pitch(es) [76.0, 80.0, 84.0] DO meet the spec but carry fewer than 2 periods, so they are a statement about an isolated feature and not about this array [tight=False, min_periods=2]", "gate": true, "id": "F1 contact_array: no untight rule is quoted", "ok": true, "rule": { "min_periods": 2, "min_pitch_nm": null, "reason": "no pitch on the scanned lattice reaches FEASIBLE_DEMONSTRATED with at least 2 complete periods on the field; 3 pitch(es) [76.0, 80.0, 84.0] DO meet the spec but carry fewer than 2 periods, so they are a statement about an isolated feature and not about this array", "rows": [ { "insufficient_periods": false, "n_periods": 8, "pitch_nm": 16.0, "refusal": null, "rho_floor": 0.7500079911703947, "rho_max": 0.28, "verdict": "PROVABLY_UNPRINTABLE", "witness_rho_pw": 0.7500093051721696 }, { "insufficient_periods": false, "n_periods": 6, "pitch_nm": 20.0, "refusal": null, "rho_floor": 0.7525456705531778, "rho_max": 0.28, "verdict": "PROVABLY_UNPRINTABLE", "witness_rho_pw": 0.7525465023142421 }, { "insufficient_periods": false, "n_periods": 5, "pitch_nm": 24.0, "refusal": null, "rho_floor": 0.7319104130397396, "rho_max": 0.28, "verdict": "PROVABLY_UNPRINTABLE", "witness_rho_pw": 0.731910770054364 }, { "insufficient_periods": false, "n_periods": 4, "pitch_nm": 28.0, "refusal": null, "rho_floor": 0.6641711699056291, "rho_max": 0.28, "verdict": "PROVABLY_UNPRINTABLE", "witness_rho_pw": 0.6641712229520873 }, { "insufficient_periods": false, "n_periods": 4, "pitch_nm": 32.0, "refusal": null, "rho_floor": 0.60940082989075, "rho_max": 0.28, "verdict": "PROVABLY_UNPRINTABLE", "witness_rho_pw": 0.6094008446366188 }, { "insufficient_periods": false, "n_periods": 3, "pitch_nm": 36.0, "refusal": null, "rho_floor": 0.5186943497059047, "rho_max": 0.28, "verdict": "PROVABLY_UNPRINTABLE", "witness_rho_pw": 0.5186943898299085 }, { "insufficient_periods": false, "n_periods": 3, "pitch_nm": 40.0, "refusal": null, "rho_floor": 0.45624309252305906, "rho_max": 0.28, "verdict": "PROVABLY_UNPRINTABLE", "witness_rho_pw": 0.45624309263297785 }, { "insufficient_periods": false, "n_periods": 2, "pitch_nm": 44.0, "refusal": null, "rho_floor": 0.4149197666423693, "rho_max": 0.28, "verdict": "PROVABLY_UNPRINTABLE", "witness_rho_pw": 0.4149198416995726 }, { "insufficient_periods": false, "n_periods": 2, "pitch_nm": 48.0, "refusal": null, "rho_floor": 0.39046653369036544, "rho_max": 0.28, "verdict": "PROVABLY_UNPRINTABLE", "witness_rho_pw": 0.39046653642316553 }, { "insufficient_periods": false, "n_periods": 2, "pitch_nm": 52.0, "refusal": null, "rho_floor": 0.3743471523249761, "rho_max": 0.28, "verdict": "PROVABLY_UNPRINTABLE", "witness_rho_pw": 0.3743471523249761 }, { "insufficient_periods": false, "n_periods": 2, "pitch_nm": 56.0, "refusal": null, "rho_floor": 0.3626714152580883, "rho_max": 0.28, "verdict": "PROVABLY_UNPRINTABLE", "witness_rho_pw": 0.3626714286428802 }, { "insufficient_periods": false, "n_periods": 2, "pitch_nm": 60.0, "refusal": null, "rho_floor": 0.3504282661929705, "rho_max": 0.28, "verdict": "PROVABLY_UNPRINTABLE", "witness_rho_pw": 0.3504282764005571 }, { "insufficient_periods": false, "n_periods": 2, "pitch_nm": 64.0, "refusal": null, "rho_floor": 0.33521593950261214, "rho_max": 0.28, "verdict": "PROVABLY_UNPRINTABLE", "witness_rho_pw": 0.33521594640917096 }, { "insufficient_periods": true, "n_periods": 1, "pitch_nm": 68.0, "refusal": null, "rho_floor": 0.30031482562241896, "rho_max": 0.28, "verdict": "PROVABLY_UNPRINTABLE", "witness_rho_pw": 0.30031482562241896 }, { "insufficient_periods": true, "n_periods": 1, "pitch_nm": 72.0, "refusal": null, "rho_floor": 0.2866421344566009, "rho_max": 0.28, "verdict": "PROVABLY_UNPRINTABLE", "witness_rho_pw": 0.2866421471774629 }, { "insufficient_periods": true, "n_periods": 1, "pitch_nm": 76.0, "refusal": null, "rho_floor": 0.27319726560737273, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.2731973180452984 }, { "insufficient_periods": true, "n_periods": 1, "pitch_nm": 80.0, "refusal": null, "rho_floor": 0.2600193984440902, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.26001939844409017 }, { "insufficient_periods": true, "n_periods": 1, "pitch_nm": 84.0, "refusal": null, "rho_floor": 0.24739352465649106, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.2473935274474534 } ], "rule": null, "tight": false } }, { "detail": "tight rules for ['line_space']; no rule for ['contact_array']", "gate": true, "id": "F1a at least one feature kind yields a tight rule, so F1 is not satisfied by finding nothing", "ok": true }, { "detail": "NA 0.33 -> min pitch 40 nm; NA 0.45 -> 32.0 nm (tight=True)", "gate": false, "id": "F3 the design rule moves when the process does", "ok": true, "relaxed_rule": { "min_periods": 2, "min_pitch_nm": 32.0, "n_periods_at_rule": 4, "rows": [ { "insufficient_periods": false, "n_periods": 8, "pitch_nm": 16.0, "refusal": null, "rho_floor": 0.5000660705279546, "rho_max": 0.28, "verdict": "PROVABLY_UNPRINTABLE", "witness_rho_pw": 0.5000751125208077 }, { "insufficient_periods": false, "n_periods": 6, "pitch_nm": 20.0, "refusal": null, "rho_floor": 0.40154659964420175, "rho_max": 0.28, "verdict": "PROVABLY_UNPRINTABLE", "witness_rho_pw": 0.40154660362057926 }, { "insufficient_periods": false, "n_periods": 5, "pitch_nm": 24.0, "refusal": null, "rho_floor": 0.33280046581709954, "rho_max": 0.28, "verdict": "PROVABLY_UNPRINTABLE", "witness_rho_pw": 0.33280046593820595 }, { "insufficient_periods": false, "n_periods": 4, "pitch_nm": 28.0, "refusal": null, "rho_floor": 0.2873517515851442, "rho_max": 0.28, "verdict": "PROVABLY_UNPRINTABLE", "witness_rho_pw": 0.28735175158514414 }, { "insufficient_periods": false, "n_periods": 4, "pitch_nm": 32.0, "refusal": null, "rho_floor": 0.25630194977825416, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.25630194977825416 }, { "insufficient_periods": false, "n_periods": 3, "pitch_nm": 36.0, "refusal": null, "rho_floor": 0.22929423427928497, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.2292942344114955 }, { "insufficient_periods": false, "n_periods": 3, "pitch_nm": 40.0, "refusal": null, "rho_floor": 0.21311210030837346, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.21311210045310552 }, { "insufficient_periods": false, "n_periods": 2, "pitch_nm": 44.0, "refusal": null, "rho_floor": 0.1867328765439142, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.1867328768954576 }, { "insufficient_periods": false, "n_periods": 2, "pitch_nm": 48.0, "refusal": null, "rho_floor": 0.16998395437641675, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.16998395474396913 }, { "insufficient_periods": false, "n_periods": 2, "pitch_nm": 52.0, "refusal": null, "rho_floor": 0.1538823668233848, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.15388236684477632 }, { "insufficient_periods": false, "n_periods": 2, "pitch_nm": 56.0, "refusal": null, "rho_floor": 0.1396501837041657, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.13965018371467558 }, { "insufficient_periods": false, "n_periods": 2, "pitch_nm": 60.0, "refusal": null, "rho_floor": 0.12760754433211122, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.12760754440329777 }, { "insufficient_periods": false, "n_periods": 2, "pitch_nm": 64.0, "refusal": null, "rho_floor": 0.11849099942207439, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.11849099942391428 }, { "insufficient_periods": true, "n_periods": 1, "pitch_nm": 68.0, "refusal": null, "rho_floor": 0.10734486715653843, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.10734488561209708 }, { "insufficient_periods": true, "n_periods": 1, "pitch_nm": 72.0, "refusal": null, "rho_floor": 0.10070783908756309, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.1007078443753315 }, { "insufficient_periods": true, "n_periods": 1, "pitch_nm": 76.0, "refusal": null, "rho_floor": 0.09503806277602095, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.09503806278404917 }, { "insufficient_periods": true, "n_periods": 1, "pitch_nm": 80.0, "refusal": null, "rho_floor": 0.09006021626359381, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.09006021709446584 }, { "insufficient_periods": true, "n_periods": 1, "pitch_nm": 84.0, "refusal": null, "rho_floor": 0.08557634501334606, "rho_max": 0.28, "verdict": "FEASIBLE_DEMONSTRATED", "witness_rho_pw": 0.08557634656453354 } ], "rule": "At NA 0.45, lambda 13.5 nm, sigma 0.4-0.8, chrome_or_absorber, +/-60.0 nm defocus and a relative-field-residual budget of 0.28, the minimum line_space pitch is 32 nm (28 nm is provably unprintable).", "scope": "a design rule under this repository's rank-1 field proxy at the stated spec; simulator-relative, not a foundry design rule", "step_below": { "insufficient_periods": false, "n_periods": 4, "pitch_nm": 28.0, "refusal": null, "rho_floor": 0.2873517515851442, "rho_max": 0.28, "verdict": "PROVABLY_UNPRINTABLE", "witness_rho_pw": 0.28735175158514414 }, "tight": true } }, { "detail": "every key declared in RECORDINGS matches a check this run emitted", "gate": true, "id": "G1 the recordings map has no stale entries", "ok": true } ], "elapsed_s": 1139.485535625019, "honest": [ "**Model-relative, not silicon.** The certified object is the rank-1 coherent field-matching residual `1/2||G1(z) m - t||^2` under this repository's SOCS optics. It is a genuine lower bound over a box containing every binary mask of the declared class, and it is NOT a bound on the full non-convex SOCS-intensity problem, which is NP-hard and which no mechanism here touches. Every 'no mask can' in this report carries that qualifier.", "**`rho` is not EPE.** The spec is a relative field residual because that is the quantity the bound is on. Floor-to-EPE is not sound in general (residual energy can live off-contour), which is why the EPE channel is advisory and cannot set a verdict. A designer who wants nanometres does not get them from this certificate.", "**`rho_max = 0.28` is a declared budget.** It was chosen so that both verdicts are reachable inside the lattice -- 32 nm unprintable, 40 nm printable -- not measured from any process. Every design rule in part F is a rule *at that budget*, and the sentence says so.", "**The cost model is declared, not derived.** Ranking '+0.02 NA' against '-1.5 nm wavelength' needs a preference no physics supplies. `COST_PER_STEP` states one in the open. The per-axis minimal-step table is the measurement; the single winner is that table read through the preference, and both are in the artifact.", "**The process-window mechanism is sound and, here, worth nothing.** U1 is maximised over a declared weight family that contains the point masses, so it can never be weaker than the best single-defocus floor -- and on every spec measured no multi-node weighting was strictly stronger either (B3). The window still enters the answer through the *witness* side, which is scored worst-over-nodes. Reported as the null it is.", "**Dose latitude is out of scope and is named, not approximated.** Dose scales the aerial intensity; the certified object is a field residual and there is no dimensionally honest way to write a dose perturbation into it. `ProcessWindow` carries defocus only.", "**The lattice is finite, so 'unreachable' means unreachable on it.** An axis that does not reach feasibility within its declared steps is reported as `unreachable` with its terminal verdict, and the pair probe in D2 reports its own budget. 'No pair found in N evaluations' is not 'no pair exists'.", "**One spec, one raster.** The non-monotonicity in C4/C5 is measured at `grid=128, pixel_nm=1.0` on this feature family. It is enough to refute the monotonicity assumption a bisection needs -- one counterexample is all that takes -- and it is not a characterisation of how non-monotone the objective is in general.", "**The eigen-phase fix this item needed was a defect in committed code, and its blast radius is wider than F6-05.** `socs_linear_operator` handed out a field operator whose global phase came straight from a Hermitian eigendecomposition, i.e. arbitrary. Measured over 15 `(na, sigma_out)` points, 5 came back with a negative DC gain, and at those points the 'certified floor' for a 32 nm grating read 1.0 -- 'no mask can do anything' -- purely from the sign. Every consumer of the rank-1 *field* proxy was exposed; every intensity consumer was not, because `|A_k m|^2` is phase-invariant. Fixed at the class location with the convention documented there." ], "item": "F6-05", "n_calls": 349, "n_solves": 249, "operating_point": "grid 128 / pixel 1.0 nm / baseline EUV NA 0.33 annular 0.4-0.8 / +/-60.0 nm defocus over 5 nodes / rho_max 0.28", "scope": "Certified unprintability under the rank-1 coherent field-matching proxy of this repository's SOCS optics, over a box containing every binary mask of the declared class and over a declared defocus window. Simulator-relative, NOT silicon. EPE channel advisory and never verdict-driving.", "tier": "full" }