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Direction B results: Gerver sofa at T=100 produces χ=2 (bipartite), not reaching χ≥4. Confirms 'unit-distance events are measure-zero.' CRTSidonN: auto-generated, ~10 remaining structural issues. Design is correct (natural n-moduli extension of CRT Sidon theorem).
3766 lines
No EOL
84 KiB
JSON
3766 lines
No EOL
84 KiB
JSON
{
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"experiment": "direction_b_gerver_sidon",
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"direction": "B: Gerver Sofa as Sidon with CRT boundary + T=100 motion",
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"timestamp": "2026-07-04T16:02:16Z",
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"seed": 0,
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"quick": false,
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"config": {
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"n_values": [
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13,
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21
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],
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"chi_values": [
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1,
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2,
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3,
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5,
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7
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],
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"q_values": [
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"0.5",
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"0.75",
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"1.0",
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"1.333333",
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"2.0"
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|
],
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"q_count": 5,
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"n_motion_samples": 100,
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|
"corridor_width": 1,
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"eps_tolerance": 1e-05,
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"shapes": [
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"gerver_sofa",
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"half_disc",
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"hammersley",
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"rectangle"
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],
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"chromatic_method": "DSATUR + exact for <=16 + 50 greedy restarts",
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"gerver_arcs": 18,
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"motion_type": "gerver_optimal_cycloidal"
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},
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"data": [
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{
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"n": 13,
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"shape": "gerver_sofa",
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"q": "0.5",
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"q_value": 0.5,
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"chi_target": 1,
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"chi_actual": 2,
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"feasible": false,
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"area": 2.5161904257854686,
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"a_star": 0.0,
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"n_edges": 5,
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"max_degree": 1,
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"sidon_1d_valid": true,
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"sidon_2d_valid": true,
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"n_motion_samples": 100
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},
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{
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"n": 13,
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"shape": "gerver_sofa",
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"q": "0.5",
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"q_value": 0.5,
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"chi_target": 2,
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"chi_actual": 2,
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"feasible": true,
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"area": 2.5161904257854686,
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"a_star": 2.5161904257854686,
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"n_edges": 5,
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"max_degree": 1,
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"sidon_1d_valid": true,
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"sidon_2d_valid": true,
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"n_motion_samples": 100
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},
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{
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"n": 13,
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"shape": "gerver_sofa",
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"q": "0.5",
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"q_value": 0.5,
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"chi_target": 3,
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"chi_actual": 2,
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"feasible": true,
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"area": 2.5161904257854686,
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"a_star": 2.5161904257854686,
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"n_edges": 5,
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"max_degree": 1,
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"sidon_1d_valid": true,
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"sidon_2d_valid": true,
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"n_motion_samples": 100
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},
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{
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"n": 13,
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"shape": "gerver_sofa",
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"q": "0.5",
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"q_value": 0.5,
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"chi_target": 5,
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"chi_actual": 2,
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"feasible": true,
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"area": 2.5161904257854686,
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"a_star": 2.5161904257854686,
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"n_edges": 5,
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"max_degree": 1,
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"sidon_1d_valid": true,
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"sidon_2d_valid": true,
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"n_motion_samples": 100
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},
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{
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"n": 13,
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"shape": "gerver_sofa",
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"q": "0.5",
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"q_value": 0.5,
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"chi_target": 7,
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|
"chi_actual": 2,
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"feasible": true,
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"area": 2.5161904257854686,
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"a_star": 2.5161904257854686,
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"n_edges": 5,
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"max_degree": 1,
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"sidon_1d_valid": true,
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"sidon_2d_valid": true,
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"n_motion_samples": 100
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},
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{
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"n": 13,
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"shape": "gerver_sofa",
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"q": "0.75",
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"q_value": 0.75,
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"chi_target": 1,
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"chi_actual": 2,
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"feasible": false,
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"area": 2.5161904257854686,
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"a_star": 0.0,
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"n_edges": 5,
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"max_degree": 1,
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"sidon_1d_valid": true,
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"sidon_2d_valid": true,
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"n_motion_samples": 100
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},
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{
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"n": 13,
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"shape": "gerver_sofa",
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"q": "0.75",
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"q_value": 0.75,
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"chi_target": 2,
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"chi_actual": 2,
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"feasible": true,
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"area": 2.5161904257854686,
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"a_star": 2.5161904257854686,
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"n_edges": 5,
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"max_degree": 1,
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"sidon_1d_valid": true,
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"sidon_2d_valid": true,
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"n_motion_samples": 100
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},
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{
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"n": 13,
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"shape": "gerver_sofa",
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"q": "0.75",
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"q_value": 0.75,
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"chi_target": 3,
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"chi_actual": 2,
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"feasible": true,
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"n_edges": 5,
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"max_degree": 1,
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"sidon_1d_valid": true,
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"sidon_2d_valid": true,
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"n_motion_samples": 100
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},
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{
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"n": 13,
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"shape": "gerver_sofa",
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"q": "0.75",
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"q_value": 0.75,
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"chi_target": 5,
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"chi_actual": 2,
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"feasible": true,
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"n_edges": 5,
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"max_degree": 1,
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"sidon_1d_valid": true,
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"sidon_2d_valid": true,
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"n_motion_samples": 100
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},
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{
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"n": 13,
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"shape": "gerver_sofa",
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"q": "0.75",
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"q_value": 0.75,
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"chi_target": 7,
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"chi_actual": 2,
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"feasible": true,
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"area": 2.5161904257854686,
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"a_star": 2.5161904257854686,
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"n_edges": 5,
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"sidon_1d_valid": true,
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"sidon_2d_valid": true,
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"n_motion_samples": 100
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},
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{
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"n": 13,
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"shape": "gerver_sofa",
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"q": "1.0",
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"q_value": 1.0,
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"chi_target": 1,
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"chi_actual": 2,
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"feasible": false,
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"a_star": 0.0,
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"max_degree": 1,
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"sidon_1d_valid": true,
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"sidon_2d_valid": true,
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"n_motion_samples": 100
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},
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{
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"n": 13,
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"shape": "gerver_sofa",
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"q": "1.0",
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"q_value": 1.0,
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"chi_target": 2,
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"chi_actual": 2,
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"feasible": true,
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"n_motion_samples": 100
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},
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{
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"n": 13,
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"shape": "gerver_sofa",
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"q": "1.0",
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"q_value": 1.0,
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"chi_target": 3,
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"chi_actual": 2,
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"feasible": true,
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"area": 2.5161904257854686,
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"n_motion_samples": 100
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},
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{
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"n": 13,
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"shape": "gerver_sofa",
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"q": "1.0",
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"q_value": 1.0,
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"chi_target": 5,
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"chi_actual": 2,
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"feasible": true,
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"n_edges": 5,
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"sidon_1d_valid": true,
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"sidon_2d_valid": true,
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"n_motion_samples": 100
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},
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{
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"n": 13,
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"shape": "gerver_sofa",
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"q": "1.0",
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"q_value": 1.0,
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"chi_target": 7,
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"chi_actual": 2,
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"feasible": true,
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"area": 2.5161904257854686,
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"sidon_2d_valid": true,
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"n_motion_samples": 100
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},
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{
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"n": 13,
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"shape": "gerver_sofa",
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"q": "1.333333",
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"q_value": 1.333333,
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"chi_target": 1,
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"chi_actual": 2,
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"feasible": false,
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"area": 2.5161904257854686,
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"a_star": 0.0,
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"n_edges": 5,
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"max_degree": 1,
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"sidon_1d_valid": true,
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"sidon_2d_valid": true,
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"n_motion_samples": 100
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},
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{
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"n": 13,
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"shape": "gerver_sofa",
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"q": "1.333333",
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"q_value": 1.333333,
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"chi_target": 2,
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"chi_actual": 2,
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"feasible": true,
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"sidon_2d_valid": true,
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"n_motion_samples": 100
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},
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{
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"n": 13,
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"shape": "gerver_sofa",
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"q": "1.333333",
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"q_value": 1.333333,
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"chi_target": 3,
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"chi_actual": 2,
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"feasible": true,
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"n_motion_samples": 100
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},
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{
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"n": 13,
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"shape": "gerver_sofa",
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"q": "1.333333",
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"q_value": 1.333333,
|
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"chi_target": 5,
|
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"chi_actual": 2,
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|
"feasible": true,
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"area": 2.5161904257854686,
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"n_edges": 5,
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"sidon_1d_valid": true,
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"n_motion_samples": 100
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},
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{
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"n": 13,
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"shape": "gerver_sofa",
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"q": "1.333333",
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"chi_target": 7,
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"chi_actual": 2,
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"feasible": true,
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"n_motion_samples": 100
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},
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{
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"n": 13,
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"shape": "gerver_sofa",
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"q": "2.0",
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|
"q_value": 2.0,
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"chi_target": 1,
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"chi_actual": 2,
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"feasible": false,
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"a_star": 0.0,
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"n_motion_samples": 100
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},
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{
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"n": 13,
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"shape": "gerver_sofa",
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"q": "2.0",
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|
"q_value": 2.0,
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"chi_target": 2,
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|
"chi_actual": 2,
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"feasible": true,
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"sidon_1d_valid": true,
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"n_motion_samples": 100
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},
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{
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"n": 13,
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"shape": "gerver_sofa",
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"q": "2.0",
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"q_value": 2.0,
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"chi_target": 3,
|
|
"chi_actual": 2,
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"feasible": true,
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"max_degree": 1,
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"sidon_1d_valid": true,
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|
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"n_motion_samples": 100
|
|
},
|
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{
|
|
"n": 13,
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"shape": "gerver_sofa",
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"q": "2.0",
|
|
"q_value": 2.0,
|
|
"chi_target": 5,
|
|
"chi_actual": 2,
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"feasible": true,
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"sidon_1d_valid": true,
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"sidon_2d_valid": true,
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"n_motion_samples": 100
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|
},
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{
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"n": 13,
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"shape": "gerver_sofa",
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"q": "2.0",
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"q_value": 2.0,
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|
"chi_target": 7,
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|
"chi_actual": 2,
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|
"feasible": true,
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"n_edges": 5,
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"max_degree": 1,
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"sidon_1d_valid": true,
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"sidon_2d_valid": true,
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"n_motion_samples": 100
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|
},
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|
{
|
|
"n": 13,
|
|
"shape": "half_disc",
|
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"q": "0.5",
|
|
"q_value": 0.5,
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|
"chi_target": 1,
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|
"chi_actual": 2,
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|
"feasible": false,
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"area": 0.21837859517025,
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"a_star": 0.0,
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"n_edges": 6,
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|
"max_degree": 2,
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|
"sidon_1d_valid": true,
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"sidon_2d_valid": true,
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|
"n_motion_samples": 100
|
|
},
|
|
{
|
|
"n": 13,
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|
"shape": "half_disc",
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"q": "0.5",
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|
"q_value": 0.5,
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|
"chi_target": 2,
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|
"chi_actual": 2,
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"feasible": true,
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"area": 0.21837859517025,
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"n_edges": 6,
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|
"sidon_1d_valid": true,
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|
"sidon_2d_valid": true,
|
|
"n_motion_samples": 100
|
|
},
|
|
{
|
|
"n": 13,
|
|
"shape": "half_disc",
|
|
"q": "0.5",
|
|
"q_value": 0.5,
|
|
"chi_target": 3,
|
|
"chi_actual": 2,
|
|
"feasible": true,
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|
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"a_star": 0.21837859517025,
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"n_edges": 6,
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"max_degree": 2,
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|
"sidon_1d_valid": true,
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|
"sidon_2d_valid": true,
|
|
"n_motion_samples": 100
|
|
},
|
|
{
|
|
"n": 13,
|
|
"shape": "half_disc",
|
|
"q": "0.5",
|
|
"q_value": 0.5,
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|
"chi_target": 5,
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|
"chi_actual": 2,
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|
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|
|
"n_motion_samples": 100
|
|
},
|
|
{
|
|
"n": 13,
|
|
"shape": "half_disc",
|
|
"q": "0.5",
|
|
"q_value": 0.5,
|
|
"chi_target": 7,
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|
"chi_actual": 2,
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|
"feasible": true,
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