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/gonum.org/v1/gonum/mathext/mvgamma.go

@@ -0,0 +1,32 @@
+// Copyright ©2016 The Gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mathext
+
+import "math"
+
+const (
+	logPi = 1.14472988584940017414342735135305871164729481 // http://oeis.org/A053510
+)
+
+// MvLgamma returns the log of the multivariate Gamma function. Dim
+// must be greater than zero, and MvLgamma will return NaN if v < (dim-1)/2.
+//
+// See https://en.wikipedia.org/wiki/Multivariate_gamma_function for more
+// information.
+func MvLgamma(v float64, dim int) float64 {
+	if dim < 1 {
+		panic("mathext: negative dimension")
+	}
+	df := float64(dim)
+	if v < (df-1)*0.5 {
+		return math.NaN()
+	}
+	ans := df * (df - 1) * 0.25 * logPi
+	for i := 1; i <= dim; i++ {
+		lg, _ := math.Lgamma(v + float64(1-i)*0.5)
+		ans += lg
+	}
+	return ans
+}