From bd529a52103100d877c97d8029de12e4e9d7370b Mon Sep 17 00:00:00 2001 From: l-proger Date: Tue, 13 May 2025 03:12:25 +0300 Subject: [PATCH] * --- Assets/BlackHoleRenderer.cs | 330 +++++++++ Assets/BlackHoleRenderer.cs.meta | 11 + Assets/DoubleMath.cs | 50 ++ Assets/DoubleMath.cs.meta | 11 + Assets/Editor.meta | 8 + Assets/Editor/BlackHoleRendererEditor.cs | 22 + Assets/Editor/BlackHoleRendererEditor.cs.meta | 11 + Assets/Integrator.cs | 168 +++++ Assets/Integrator.cs.meta | 11 + Assets/Scenes.meta | 8 + Assets/Scenes/SampleScene.unity | 365 ++++++++++ Assets/Scenes/SampleScene.unity.meta | 7 + Packages/manifest.json | 42 ++ ProjectSettings/AudioManager.asset | 19 + ProjectSettings/ClusterInputManager.asset | 6 + ProjectSettings/DynamicsManager.asset | 34 + ProjectSettings/EditorBuildSettings.asset | 8 + ProjectSettings/EditorSettings.asset | 35 + ProjectSettings/GraphicsSettings.asset | 63 ++ ProjectSettings/InputManager.asset | 295 ++++++++ ProjectSettings/NavMeshAreas.asset | 91 +++ ProjectSettings/Physics2DSettings.asset | 56 ++ ProjectSettings/PresetManager.asset | 7 + ProjectSettings/ProjectSettings.asset | 662 ++++++++++++++++++ ProjectSettings/ProjectVersion.txt | 2 + ProjectSettings/QualitySettings.asset | 232 ++++++ ProjectSettings/TagManager.asset | 43 ++ ProjectSettings/TimeManager.asset | 9 + ProjectSettings/UnityConnectSettings.asset | 34 + ProjectSettings/VFXManager.asset | 12 + ProjectSettings/XRSettings.asset | 10 + 31 files changed, 2662 insertions(+) create mode 100644 Assets/BlackHoleRenderer.cs create mode 100644 Assets/BlackHoleRenderer.cs.meta create mode 100644 Assets/DoubleMath.cs create mode 100644 Assets/DoubleMath.cs.meta create mode 100644 Assets/Editor.meta create mode 100644 Assets/Editor/BlackHoleRendererEditor.cs create mode 100644 Assets/Editor/BlackHoleRendererEditor.cs.meta create mode 100644 Assets/Integrator.cs create mode 100644 Assets/Integrator.cs.meta create mode 100644 Assets/Scenes.meta create mode 100644 Assets/Scenes/SampleScene.unity create mode 100644 Assets/Scenes/SampleScene.unity.meta create mode 100644 Packages/manifest.json create mode 100644 ProjectSettings/AudioManager.asset create mode 100644 ProjectSettings/ClusterInputManager.asset create mode 100644 ProjectSettings/DynamicsManager.asset create mode 100644 ProjectSettings/EditorBuildSettings.asset create mode 100644 ProjectSettings/EditorSettings.asset create mode 100644 ProjectSettings/GraphicsSettings.asset create mode 100644 ProjectSettings/InputManager.asset create mode 100644 ProjectSettings/NavMeshAreas.asset create mode 100644 ProjectSettings/Physics2DSettings.asset create mode 100644 ProjectSettings/PresetManager.asset create mode 100644 ProjectSettings/ProjectSettings.asset create mode 100644 ProjectSettings/ProjectVersion.txt create mode 100644 ProjectSettings/QualitySettings.asset create mode 100644 ProjectSettings/TagManager.asset create mode 100644 ProjectSettings/TimeManager.asset create mode 100644 ProjectSettings/UnityConnectSettings.asset create mode 100644 ProjectSettings/VFXManager.asset create mode 100644 ProjectSettings/XRSettings.asset diff --git a/Assets/BlackHoleRenderer.cs b/Assets/BlackHoleRenderer.cs new file mode 100644 index 0000000..0d208ff --- /dev/null +++ b/Assets/BlackHoleRenderer.cs @@ -0,0 +1,330 @@ +using System; +using System.Collections; +using System.Collections.Generic; +using System.Security.Cryptography; +using JetBrains.Annotations; +using TMPro; +using UnityEngine; +using UnityEngine.Rendering; + +public class BlackHoleRenderer : MonoBehaviour { + void Start() { + + } + + struct Ray + { + public SphericalDir Dir; + public SphericalCoord P; //Canonical momenta + public double b; + public double q; + + public Double3 DirectionOfMotionInCameraCortesianSpace(Double3 N, double beta) { //F + double betaSquare = beta * beta; + double nfy = (-N.Y + beta) / (1.0 - (beta * N.Y)); + double nfx = (-Math.Sqrt(1.0 - betaSquare) * N.X) / (1.0 - beta * N.Y); + double nfz = (-Math.Sqrt(1.0 - betaSquare) * N.Z) / (1.0 - beta * N.Y); + return new Double3 { X = nfx, Y = nfy, Z = nfz }; + } + + public SphericalCoord FSpherical(SphericalCoord B, Double3 nF) { + double kappa = Math.Sqrt(B.R * B.R + B.Dir.Phi * B.Dir.Phi); + + double nFr = ((B.Dir.Phi / kappa) * nF.X) + (B.R * nF.Y) + ((B.R * B.Dir.Theta) / kappa) * nF.Z; + double nFTheta = B.Dir.Theta * nF.Y - kappa * nF.Z; + double nFPhi = (-B.R / kappa) * nF.X + B.Dir.Phi * nF.Y + ((B.Dir.Phi * B.Dir.Theta) / kappa) * nF.Z; + + SphericalCoord result; + result.R = nFr; + result.Dir.Theta = nFTheta; + result.Dir.Phi = nFPhi; + return result; + } + + public void CanonicalMomenta(FidoCamera camera, KerrMetric metric) { //p + var N = Dir.ToCartesian(); + var Fdir = DirectionOfMotionInCameraCortesianSpace(N, camera.Beta); + var F = FSpherical(camera.Speed, Fdir); + + double Ef = 1.0 / (metric.Alpha + metric.Omega * metric.OmegaUpLine * F.Dir.Phi); + + double pr = Ef * (metric.Rho / Math.Sqrt(metric.Delta)) * F.R; + double pTheta = Ef * metric.Rho * F.Dir.Theta; + double pPhi = Ef * metric.OmegaUpLine * F.Dir.Phi; + + SphericalCoord result; + result.R = pr; + result.Dir.Phi = pPhi; + result.Dir.Theta = pTheta; + + P = result; + + } + + public void Update(FidoCamera camera, KerrMetric metric) + { + CanonicalMomenta(camera, metric); + + b = P.Dir.Phi; + double cosTheta = Math.Cos(Dir.Theta); + double sinTheta = Math.Sin(Dir.Theta); + q = P.Dir.Theta * P.Dir.Theta + + cosTheta * cosTheta * (((b * b) / (sinTheta * sinTheta)) - metric.A * metric.A); + } + } + + double betaZero(double r_zero, BlackHole hole) + { + double r_zero_square = r_zero * r_zero; + double r_zero_cube = r_zero_square * r_zero; + + double a_square = hole.A * hole.A; + return -((r_zero_cube - 3 * r_zero_square + a_square * r_zero + a_square) / (hole.A * (r_zero - 1.0))); + } + + double qZero(double r, BlackHole hole) { + double rSquare = r * r; + double rCube = rSquare * r; + double aSquare = hole.A * hole.A; + double rm1 = r - 1; + double rmSquare = rm1 * rm1; + return -(rCube * (rCube - 6 * rSquare + 9 * r - 4 * aSquare)) / (aSquare * rmSquare); + } + + double rZero_0(double b, double a) { //my + var aSquare = a * a; + var subExpr0 = 3 * aSquare + 3 * a * b - 9; + var subExpr2 = (54 - 54 * aSquare); + + var cubeRootOf2 = Math.Pow(2.0, 1.0 / 3.0); + var subExpr1 = Math.Pow(Math.Sqrt(Math.Abs(4 * subExpr0 * subExpr0 * subExpr0 + subExpr2 * subExpr2)) + subExpr2, 1.0 / 3.0); + + return -(cubeRootOf2 * subExpr0) / (3.0 * subExpr1) + (subExpr1 / (3.0 * cubeRootOf2)) + 1; + } + + double rZero_1(double b, double a) { //my + var aSquare = a * a; + var subExpr0 = 3 * aSquare + 3 * a * b - 9; + var subExpr2 = (54 - 54 * aSquare); + + var cubeRootOf2 = Math.Pow(2.0, 1.0 / 3.0); + + var subExpr1 = Math.Pow(Math.Sqrt(Math.Abs(4 * subExpr0 * subExpr0 * subExpr0 + subExpr2 * subExpr2)) + subExpr2, 1.0 / 3.0); + return ((1 + Math.Sqrt(3.0)) * subExpr0) / (3.0 * Math.Pow(2.0, 2.0/3.0) * subExpr1) - (( (1 - Math.Sqrt(3)) * subExpr1) / (6.0 * cubeRootOf2)) + 1; + } + + double rZero_2(double b, double a) { //my + var aSquare = a * a; + var subExpr0 = 3 * aSquare + 3 * a * b - 9; + var subExpr2 = (54 - 54 * aSquare); + + var cubeRootOf2 = Math.Pow(2.0, 1.0 / 3.0); + + var subExpr1 = Math.Pow(Math.Sqrt(Math.Abs(4 * subExpr0 * subExpr0 * subExpr0 + subExpr2 * subExpr2)) + subExpr2, 1.0 / 3.0); + return ((1 - Math.Sqrt(3.0)) * subExpr0) / (3.0 * Math.Pow(2.0, 2.0 / 3.0) * subExpr1) - (((1 + Math.Sqrt(3)) * subExpr1) / (6.0 * cubeRootOf2)) + 1; + } + + + [Serializable] + public class FidoCamera + { + public SphericalCoord Position; + public SphericalCoord Speed; + public double Beta; + + public void UpdateMetricAndSelf(KerrMetric metric, BlackHole hole) + { + metric.Update(hole.A, Position.R, Position.Dir.Theta); + double bigOmega = 1.0 / (metric.A + Math.Pow(Position.R, 3.0 / 2.0)); + Beta = (metric.OmegaUpLine / metric.Alpha) * (bigOmega - metric.Omega); + } + } + + [Serializable] + public class BlackHole + { + public double A; + public double r1() { + return 2 * (1 + Math.Cos((2.0 / 3.0) * Math.Acos(-A))); + } + + public double r2() { + return 2 * (1 + Math.Cos((2.0 / 3.0) * Math.Acos(A))); + } + } + + [Serializable] + public class KerrMetric { + public double Delta; + public double Rho; + public double OmegaUpLine; + public double Omega; + public double Sigma; + public double Alpha; + public double A; + + public void Update(double a, double r, double theta) { + double cosTheta = Math.Cos(theta); + double sinTheta = Math.Sin(theta); + + double cosThetaSquare = cosTheta * cosTheta; + double sinThetaSquare = sinTheta * sinTheta; + + double aSquare = a * a; + double rSquare = r * r; + + Rho = Math.Sqrt(rSquare + (aSquare * cosThetaSquare)); + Delta = rSquare - (2 * r) + aSquare; + Sigma = Math.Sqrt((rSquare + aSquare) * (rSquare + aSquare) - aSquare * Delta * sinThetaSquare); + Alpha = (Rho * Math.Sqrt(Delta)) / Sigma; + Omega = (2 * a * r) / (Sigma * Sigma); + OmegaUpLine = (Sigma * sinTheta) / Rho; + + A = a; + } + } + + public FidoCamera Camera = new FidoCamera(); + public KerrMetric Metric = new KerrMetric(); + public BlackHole Hole = new BlackHole(); + + public void RecalcState() + { + Camera.UpdateMetricAndSelf(Metric, Hole); + } + + double drdt(double delta, double rho, double Pr) + { + return delta / (rho * rho) * Pr; + } + + SphericalDir[] rays = new SphericalDir[256]; + + class BlackHoleRayIntegrator : Integrator + { + + } + + void DrawCameraGizmo() { + var pos = Camera.Position.ToCartesian().ToVector3(); + + UpdateRays(); + + foreach (var rayDir in rays) + { + Ray ray = new Ray(); + ray.Dir = rayDir; + ray.Update(Camera, Metric); + + + var v0 = rZero_0(0.666, 0.9); + var v1 = rZero_1(0.666, 0.9); + var v2 = rZero_2(0.666, 0.9); + // var b1 = betaZero(Hole.r2()); + // var b2 = betaZero(Hole.r1()); + + //-0.1184053483681316836 + 0.×10^-19 i + //0.7514421233051754296 + 0.×10^-19 i + //2.3669632250629562540 + 0.×10^-20 i + var N = ray.Dir.ToCartesian(); + var Fdir = ray.DirectionOfMotionInCameraCortesianSpace(N, Camera.Beta); + var F = ray.FSpherical(Camera.Speed, Fdir); + + Gizmos.DrawLine(pos, pos + ray.P.ToCartesian().ToVector3()); + + /* + var r0 = rZero2(b); + var r0_ = rZero(b); + //r0 = 2.1899962982234369; + var q0 = qZero2(r0, b); + + + Color rayColor = Color.white; + if (((b1 < b) && (b < b2)) && (q < q0)) + { + //there are no radial turning points for that {b, q} + if (rayCanonicalMomenta_.R > 0) + { + //horizon + rayColor = Color.black; + horizon++; + } + else + { + celestial++; + } + } + else + { + var a = a_spinAngularMomentumPerMass; + + double P = Math.Sqrt(Metric.Delta * ((b - a) * (b - a) + q)); + double rUp0 = P + a * b - a * a; + double rUp1 = -P + a * b - a * a; + + double rUp = rUp0 > rUp1 ? rUp0 : rUp1; + + if (cameraPosition.R > rUp) + { + celestial++; + } + else + { + horizon++; + //horizon + rayColor = Color.black; + } + }*/ + } + } + + public void OnDrawGizmos() { + + + // double accretionDiskInnerRadius = 9.26 * M_blackHoleMass; + // double accretionDiskOuterRadius = 18.7 * M_blackHoleMass; + + Gizmos.DrawLine(Vector3.zero, Camera.Position.ToCartesian().ToVector3()); + Gizmos.DrawWireSphere(Vector3.zero, 1); + + DrawCameraGizmo(); + // double OmegaBig = CameraGeodesicAngularVelocity(Rc); + //DrawCameraGizmo(cameraCoord, cameraDirectionOfMotion); + } + + void UpdateRays() + { + int imageHeight = 16; + int imageWidth = 16; + + int totalRays = imageHeight * imageWidth; + + if (rays == null || rays.Length != totalRays) + { + rays = new SphericalDir[totalRays]; + } + + + double verticalFov = Math.PI / 2; + double horizontalFov = ((double)imageWidth / imageHeight) * verticalFov; + + for (int y = 0; y < imageHeight; y++) + { + double rayTheta = (Math.PI / 2) - verticalFov / 2 + (verticalFov / (imageHeight - 1) * y); + for (int x = 0; x < imageWidth; x++) + { + double rayPhi = Math.PI + horizontalFov / 2 - (horizontalFov / (imageWidth - 1) * x); + + rays[y * imageWidth + x].Phi = rayPhi; + rays[y * imageWidth + x].Theta = rayTheta; + } + } + } + + public void Trace() + { + RecalcState(); + + + } +} \ No newline at end of file diff --git a/Assets/BlackHoleRenderer.cs.meta b/Assets/BlackHoleRenderer.cs.meta new file mode 100644 index 0000000..527a724 --- /dev/null +++ b/Assets/BlackHoleRenderer.cs.meta @@ -0,0 +1,11 @@ +fileFormatVersion: 2 +guid: fe74eaeeaa11b4d4aa23871a3a419cf2 +MonoImporter: + externalObjects: {} + serializedVersion: 2 + defaultReferences: [] + executionOrder: 0 + icon: {instanceID: 0} + userData: + assetBundleName: + assetBundleVariant: diff --git a/Assets/DoubleMath.cs b/Assets/DoubleMath.cs new file mode 100644 index 0000000..4f1f05e --- /dev/null +++ b/Assets/DoubleMath.cs @@ -0,0 +1,50 @@ +using System; +using System.Collections; +using System.Collections.Generic; +using UnityEngine; + +[Serializable] +public struct Double3 { + public double X; + public double Y; + public double Z; + + public static Double3 operator *(Double3 v, double r) { + return new Double3 { X = v.X * r, Y = v.Y * r, Z = v.Z * r }; + } + + public Vector3 ToVector3() { + return new Vector3((float)X, (float)Y, (float)Z); + } + + public double Length() { + return Math.Sqrt(X * X + Y * Y + Z * Z); + } + public void Normalize() { + var len = Length(); + X /= len; + Y /= len; + Z /= len; + } +} + +[Serializable] +public struct SphericalDir { + public double Theta; + public double Phi; + + public Double3 ToCartesian() { + return new Double3 { X = Math.Sin(Theta) * Math.Cos(Phi), Y = Math.Sin(Theta) * Math.Sin(Phi), Z = Math.Cos(Theta) }; + } +} + +[Serializable] +public struct SphericalCoord { + public double R; + public SphericalDir Dir; + + public Double3 ToCartesian() { + return Dir.ToCartesian() * R; + } +} + diff --git a/Assets/DoubleMath.cs.meta b/Assets/DoubleMath.cs.meta new file mode 100644 index 0000000..cb099d3 --- /dev/null +++ b/Assets/DoubleMath.cs.meta @@ -0,0 +1,11 @@ +fileFormatVersion: 2 +guid: a42185bdea1d2e6458565cbd8df52724 +MonoImporter: + externalObjects: {} + serializedVersion: 2 + defaultReferences: [] + executionOrder: 0 + icon: {instanceID: 0} + userData: + assetBundleName: + assetBundleVariant: diff --git a/Assets/Editor.meta b/Assets/Editor.meta new file mode 100644 index 0000000..06b5f60 --- /dev/null +++ b/Assets/Editor.meta @@ -0,0 +1,8 @@ +fileFormatVersion: 2 +guid: 20d786d69911c9d43bb7a8dbe8ab235f +folderAsset: yes +DefaultImporter: + externalObjects: {} + userData: + assetBundleName: + assetBundleVariant: diff --git a/Assets/Editor/BlackHoleRendererEditor.cs b/Assets/Editor/BlackHoleRendererEditor.cs new file mode 100644 index 0000000..2674867 --- /dev/null +++ b/Assets/Editor/BlackHoleRendererEditor.cs @@ -0,0 +1,22 @@ +using System.Collections; +using System.Collections.Generic; +using UnityEngine; +using UnityEditor; + +[CustomEditor(typeof(BlackHoleRenderer))] +public class BlackHoleRendererEditor : Editor +{ + public override void OnInspectorGUI() + { + base.OnInspectorGUI(); + + if (GUILayout.Button("Recalc")) + { + (target as BlackHoleRenderer).RecalcState(); + } + + if (GUILayout.Button("Trace")) { + (target as BlackHoleRenderer).Trace(); + } + } +} diff --git a/Assets/Editor/BlackHoleRendererEditor.cs.meta b/Assets/Editor/BlackHoleRendererEditor.cs.meta new file mode 100644 index 0000000..1c6d78f --- /dev/null +++ b/Assets/Editor/BlackHoleRendererEditor.cs.meta @@ -0,0 +1,11 @@ +fileFormatVersion: 2 +guid: beeda8413196da44c98a28d6f1c0921c +MonoImporter: + externalObjects: {} + serializedVersion: 2 + defaultReferences: [] + executionOrder: 0 + icon: {instanceID: 0} + userData: + assetBundleName: + assetBundleVariant: diff --git a/Assets/Integrator.cs b/Assets/Integrator.cs new file mode 100644 index 0000000..b75b9a2 --- /dev/null +++ b/Assets/Integrator.cs @@ -0,0 +1,168 @@ +// Integrator.cs +using System.Collections; +using System.Collections.Generic; +using UnityEngine; + +/// +/// Integrator is an abstract class for integrating a system of ODEs +/// +public abstract class Integrator { + + int nEquations; + double[] store; + double[] k1; + double[] k2; + double[] k3; + double[] k4; + double[] ym1; + double[] ym2; + double[] ym3; + double[] P; + double[] dm1; + double[] dm2; + double[] dm3; + double[] dp1; + int abmSteps = 0; + double abmRms2; + + public Integrator() { + Init(1); + } + + public double[] getK3() { + return k3; + } + + /// + /// Allocate memory for all storage arrays and set number of equations + /// + /// N equations. + public void Init(int nEquations) { + // set up temp arrays + this.nEquations = nEquations; + store = new double[nEquations]; + k1 = new double[nEquations]; + k2 = new double[nEquations]; + k3 = new double[nEquations]; + k4 = new double[nEquations]; + ym1 = new double[nEquations]; + ym2 = new double[nEquations]; + ym3 = new double[nEquations]; + P = new double[nEquations]; + dm1 = new double[nEquations]; + dm2 = new double[nEquations]; + dm3 = new double[nEquations]; + dp1 = new double[nEquations]; + abmSteps = 0; + } + + /// + /// Abstract void, override this method to set the ODEs to be + /// integrated. + /// + /// The values being integrated. + /// The derivatives being calculated. + public abstract void RatesOfChange(double[] x, double[] xdot, double t); + + /// + /// Step forward using Euler's method + /// + /// The values being integrated. + /// The time step. + public void EulerStep(double[] x, double t, double h) { + RatesOfChange(x, k1, t); + for (int i = 0; i < nEquations; i++) { + x[i] += k1[i] * h; + } + } + + /// + /// Step forward using 4th order Runge Kutta method + /// + /// The values being integrated. + /// The time step. + public double RK4Step(double[] x, double t, double h) { + RatesOfChange(x, k1, t); + for (int i = 0; i < nEquations; i++) { + store[i] = x[i] + k1[i] * h / 2.0; + } + RatesOfChange(store, k2, t); + for (int i = 0; i < nEquations; i++) { + store[i] = x[i] + k2[i] * h / 2.0; + } + RatesOfChange(store, k3, t); + for (int i = 0; i < nEquations; i++) { + store[i] = x[i] + k3[i] * h; + } + RatesOfChange(store, k4, t); + for (int i = 0; i < nEquations; i++) { + x[i] = x[i] + (k1[i] + 2.0 * k2[i] + 2.0 * k3[i] + k4[i]) * h / 6.0; + } + return t + h; + } + + + /** + * Calculates a single step using Adams Bashforth Moulton, + * + * @param x Array of values being integrated. + * @param t Time at which step begins + * @param h Duration of step + * @return Error prediction at end of step + */ + public double abmStep(double[] x, double t, double h) { + abmRms2 = 0.0; + if (abmSteps == 0) { + for (int i = 0; i < x.Length; i++) { + ym3[i] = x[i]; + ym2[i] = x[i]; + } + RatesOfChange(dm3, ym3, t); + t = RK4Step(ym2, t, h); + RatesOfChange(dm2, ym2, t); + for (int i = 0; i < x.Length; i++) { + x[i] = ym2[i]; + } + abmSteps += 1; + return 1.0; + } else if (abmSteps == 1) { + for (int i = 0; i < x.Length; i++) { + ym1[i] = ym2[i]; + } + t = RK4Step(ym1, t, h); + RatesOfChange(dm1, ym1, t); + for (int i = 0; i < x.Length; i++) { + x[i] = ym1[i]; + } + abmSteps += 1; + return 1.0; + } else { + RatesOfChange(k1, x, t); + for (int i = 0; i < x.Length; i++) { + P[i] = x[i] + (h / 24.0) * + (55.0 * k1[i] - 59.0 * dm1[i] + 37.0 * dm2[i] - 9.0 * dm3[i]); + } + RatesOfChange(dp1, P, t + h); + abmRms2 = 0.0; + for (int i = 0; i < x.Length; i++) { + store[i] = x[i]; + x[i] += (h / 24.0) * (9 * dp1[i] + 19.0 * k1[i] - 5.0 * dm1[i] + dm2[i]); + dm3[i] = dm2[i]; + dm2[i] = dm1[i]; + dm1[i] = k1[i]; + ym3[i] = ym2[i]; + ym2[i] = ym1[i]; + ym1[i] = store[i]; + abmRms2 += (x[i] - P[i]) * (x[i] - P[i]) / (x[i] + P[i]) / (x[i] + P[i]); + } + abmRms2 /= x.Length; + if (abmSteps < 5) abmSteps += 1; + return t + h; + } + } + + public double abmError() { + return abmRms2; + } + +} \ No newline at end of file diff --git a/Assets/Integrator.cs.meta b/Assets/Integrator.cs.meta new file mode 100644 index 0000000..2bcaf51 --- /dev/null +++ b/Assets/Integrator.cs.meta @@ -0,0 +1,11 @@ +fileFormatVersion: 2 +guid: 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