Integrate BACKBEAT SDK and resolve KACHING license validation

Major integrations and fixes:
- Added BACKBEAT SDK integration for P2P operation timing
- Implemented beat-aware status tracking for distributed operations
- Added Docker secrets support for secure license management
- Resolved KACHING license validation via HTTPS/TLS
- Updated docker-compose configuration for clean stack deployment
- Disabled rollback policies to prevent deployment failures
- Added license credential storage (CHORUS-DEV-MULTI-001)

Technical improvements:
- BACKBEAT P2P operation tracking with phase management
- Enhanced configuration system with file-based secrets
- Improved error handling for license validation
- Clean separation of KACHING and CHORUS deployment stacks

🤖 Generated with [Claude Code](https://claude.ai/code)

Co-Authored-By: Claude <noreply@anthropic.com>

vendor/github.com/blevesearch/geo/s2/matrix3x3.go

@@ -0,0 +1,128 @@
+// Copyright 2015 Google Inc. All rights reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package s2
+
+import (
+	"fmt"
+
+	"github.com/blevesearch/geo/r3"
+)
+
+// matrix3x3 represents a traditional 3x3 matrix of floating point values.
+// This is not a full fledged matrix. It only contains the pieces needed
+// to satisfy the computations done within the s2 package.
+type matrix3x3 [3][3]float64
+
+// col returns the given column as a Point.
+func (m *matrix3x3) col(col int) Point {
+	return Point{r3.Vector{X: m[0][col], Y: m[1][col], Z: m[2][col]}}
+}
+
+// row returns the given row as a Point.
+func (m *matrix3x3) row(row int) Point {
+	return Point{r3.Vector{X: m[row][0], Y: m[row][1], Z: m[row][2]}}
+}
+
+// setCol sets the specified column to the value in the given Point.
+func (m *matrix3x3) setCol(col int, p Point) *matrix3x3 {
+	m[0][col] = p.X
+	m[1][col] = p.Y
+	m[2][col] = p.Z
+
+	return m
+}
+
+// setRow sets the specified row to the value in the given Point.
+func (m *matrix3x3) setRow(row int, p Point) *matrix3x3 {
+	m[row][0] = p.X
+	m[row][1] = p.Y
+	m[row][2] = p.Z
+
+	return m
+}
+
+// scale multiplies the matrix by the given value.
+func (m *matrix3x3) scale(f float64) *matrix3x3 {
+	return &matrix3x3{
+		[3]float64{f * m[0][0], f * m[0][1], f * m[0][2]},
+		[3]float64{f * m[1][0], f * m[1][1], f * m[1][2]},
+		[3]float64{f * m[2][0], f * m[2][1], f * m[2][2]},
+	}
+}
+
+// mul returns the multiplication of m by the Point p and converts the
+// resulting 1x3 matrix into a Point.
+func (m *matrix3x3) mul(p Point) Point {
+	return Point{r3.Vector{
+		X: float64(m[0][0]*p.X) + float64(m[0][1]*p.Y) + float64(m[0][2]*p.Z),
+		Y: float64(m[1][0]*p.X) + float64(m[1][1]*p.Y) + float64(m[1][2]*p.Z),
+		Z: float64(m[2][0]*p.X) + float64(m[2][1]*p.Y) + float64(m[2][2]*p.Z),
+	}}
+}
+
+// det returns the determinant of this matrix.
+func (m *matrix3x3) det() float64 {
+	//      | a  b  c |
+	//  det | d  e  f | = aei + bfg + cdh - ceg - bdi - afh
+	//      | g  h  i |
+	return float64(m[0][0]*m[1][1]*m[2][2]) + float64(m[0][1]*m[1][2]*m[2][0]) +
+		float64(m[0][2]*m[1][0]*m[2][1]) - float64(m[0][2]*m[1][1]*m[2][0]) -
+		float64(m[0][1]*m[1][0]*m[2][2]) - float64(m[0][0]*m[1][2]*m[2][1])
+}
+
+// transpose reflects the matrix along its diagonal and returns the result.
+func (m *matrix3x3) transpose() *matrix3x3 {
+	m[0][1], m[1][0] = m[1][0], m[0][1]
+	m[0][2], m[2][0] = m[2][0], m[0][2]
+	m[1][2], m[2][1] = m[2][1], m[1][2]
+
+	return m
+}
+
+// String formats the matrix into an easier to read layout.
+func (m *matrix3x3) String() string {
+	return fmt.Sprintf("[ %0.4f %0.4f %0.4f ] [ %0.4f %0.4f %0.4f ] [ %0.4f %0.4f %0.4f ]",
+		m[0][0], m[0][1], m[0][2],
+		m[1][0], m[1][1], m[1][2],
+		m[2][0], m[2][1], m[2][2],
+	)
+}
+
+// getFrame returns the orthonormal frame for the given point on the unit sphere.
+func getFrame(p Point) matrix3x3 {
+	// Given the point p on the unit sphere, extend this into a right-handed
+	// coordinate frame of unit-length column vectors m = (x,y,z).  Note that
+	// the vectors (x,y) are an orthonormal frame for the tangent space at point p,
+	// while p itself is an orthonormal frame for the normal space at p.
+	m := matrix3x3{}
+	m.setCol(2, p)
+	m.setCol(1, Ortho(p))
+	m.setCol(0, Point{m.col(1).Cross(p.Vector)})
+	return m
+}
+
+// toFrame returns the coordinates of the given point with respect to its orthonormal basis m.
+// The resulting point q satisfies the identity (m * q == p).
+func toFrame(m matrix3x3, p Point) Point {
+	// The inverse of an orthonormal matrix is its transpose.
+	return m.transpose().mul(p)
+}
+
+// fromFrame returns the coordinates of the given point in standard axis-aligned basis
+// from its orthonormal basis m.
+// The resulting point p satisfies the identity (p == m * q).
+func fromFrame(m matrix3x3, q Point) Point {
+	return m.mul(q)
+}