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/beta.go

@@ -0,0 +1,40 @@
+// 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 "gonum.org/v1/gonum/mathext/internal/gonum"
+
+// Beta returns the value of the complete beta function B(a, b). It is defined as
+//
+//	Γ(a)Γ(b) / Γ(a+b)
+//
+// Special cases are:
+//
+//	B(a,b) returns NaN if a or b is Inf
+//	B(a,b) returns NaN if a and b are 0
+//	B(a,b) returns NaN if a or b is NaN
+//	B(a,b) returns NaN if a or b is < 0
+//	B(a,b) returns +Inf if a xor b is 0.
+//
+// See http://mathworld.wolfram.com/BetaFunction.html for more detailed informations.
+func Beta(a, b float64) float64 {
+	return gonum.Beta(a, b)
+}
+
+// Lbeta returns the natural logarithm of the complete beta function B(a,b).
+// Lbeta is defined as:
+//
+//	Ln(Γ(a)Γ(b)/Γ(a+b))
+//
+// Special cases are:
+//
+//	Lbeta(a,b) returns NaN if a or b is Inf
+//	Lbeta(a,b) returns NaN if a and b are 0
+//	Lbeta(a,b) returns NaN if a or b is NaN
+//	Lbeta(a,b) returns NaN if a or b is < 0
+//	Lbeta(a,b) returns +Inf if a xor b is 0.
+func Lbeta(a, b float64) float64 {
+	return gonum.Lbeta(a, b)
+}