Quantum-Metaphysical Architecture of Reality: Analysis of Self-Projected Unity

This research preprint formalizes a unified quantum-metaphysical framework bridging quantum mechanics, linear algebra, and the non-dual philosophy of Advaita Vedānta. We present the Lessard Identity (LCPI): Π = ∑ᵢ₌₁ᵈ Π |eᵢ ψ₀| · |ψ₀ eᵢ| Π The identity follows from the principles of completeness (∑ |eᵢ eᵢ| = I) and idempotency (Π² = Π). The work introduces the novel "scaffold notation" Aᵢ = Π |eᵢ ψ₀| to describe the mediation between basis states and the observer state. The paper further analyzes the Lessard Coherence Limit (LCL), identifying a stabilization fixed-point at α = 0.8783. This value defines a metastable window for Autonomous Quantum Stabilization (AQS). The framework maps the SATI-832 Codex onto a 1728-state finite module, utilizing Stratified Axiomatics to categorize derived technical results alongside interpretive metaphysical mappings.