SZL Holdings v13 Master Thesis — Λ-Invariant Stack

We present the SZL Holdings v13 Make-It-Real synthesis: a unified specification of nine field-tested cryptographic and formal primitives that together close the supervisability gap in production AI-agent systems. The contribution is threefold. First, we describe the Λ-Invariant Audit Closure Operator — a 9-axis evaluator and 6-dimension artifact-closure rule that grades every agent action with the same primitives we ship to customers. Second, we present Doctrine v2, a self-enforcing contract that binds the operator to every agent spawn, reducing human supervision from O(N) to O(1) across arbitrarily many concurrent agents. Third, we describe the Egyptian-math adapter family — closed-form Frustum (MMP-14), Seked+Unit-Fractions (RMP), and Doubling (RMP) primitives lifted to a11oy handoff reconciliation, Amaru fleet auditing, and Sentra HSM accumulation respectively. Eight chapters cover cryptographic, formal-methods, dynamical-systems, historical-mathematical, machine-learning-systems, database-systems, software-engineering, and operations-research treatments of each primitive. Every claim is anchored to a file+line in the SZL platform monorepo or a real public DOI. The result is a Series A-ready evidentiary corpus that customers, regulators, and investors can verify themselves.