{ "schemaVersion": 1, "model": "Freidel-Livine Eq. (38), four unit spinors, closed equal-area face-normal family", "areaLabelJ": 2, "areaDefinition": "A_FL / ell_p^2 = J for the fixed-area state", "normalization": "Project-normalized positive RS/AL expectations; physical prefactor remains open", "shapeScope": "Equal face-area ratios only; this is a controlled subfamily at fixed total J, not all Gr(2,4) labels or all area partitions. Face labels are ordered and samples are not quotiented by leg permutations.", "coordinates": { "xDiagonal": "x = |n_0+n_1|/2 in (0,1), with each |n_i|=1", "phiRadians": "Bending angle between the (0,1) and (2,3) face-normal planes", "crossRatio": "lambda = <0,2><1,3> / (<0,3><1,2>) for the four normalized spinor rays", "crossRatioInShapeCoordinates": "lambda = ((t^2 - exp(i*phi))/(t^2 + exp(i*phi)))^2, t^2=(1-x)/(1+x)", "thurstonRelation": "For four marked points, lambda is a complex coordinate on M_0,4. It labels the spinor-ray configuration here; the cone-metric K\u00e4hler metric and its curvature data are not assumed to equal the LQG flux geometry." }, "sampling": { "xValues": [ 0.03, 0.08222222222222222, 0.13444444444444442, 0.18666666666666665, 0.23888888888888887, 0.2911111111111111, 0.34333333333333327, 0.39555555555555555, 0.4477777777777777, 0.5, 0.5522222222222222, 0.5773502691896258, 0.6044444444444445, 0.6566666666666666, 0.7088888888888889, 0.7611111111111111, 0.8133333333333334, 0.8655555555555555, 0.9177777777777777, 0.97 ], "phiDegrees": [ 14.999999999999998, 29.999999999999996, 45.0, 59.99999999999999, 75.0, 90.0, 105.0, 119.99999999999999, 135.0, 150.0, 165.0, 195.0, 210.0, 224.99999999999997, 239.99999999999997, 255.00000000000003, 270.0, 285.0, 300.0, 315.0, 330.0, 344.99999999999994 ] }, "records": [ { "xDiagonal": 0.03, "phiRadians": 0.2617993877991494, "phiDegrees": 14.999999999999998, "crossRatioReal": -0.016369216526078197, "crossRatioImag": 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