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. The work establishes a formal mathematical mapping between operator classes and metaphysical structures through the introduction of the Lessard Identity (LCPI).

Mathematical Framework

The core of the paper presents the Lessard Identity (LCPI):

While the identity follows from completeness $\sum_i |e_i\rangle \langle e_i| = I$ and idempotency $\Pi^2 = \Pi$, the scaffold notation ($A_i$) introduced here is novel.

Key Contributions

• Lessard Coherence Limit (LCL): An analysis of the LCL ($\alpha \approx 0.8784$) as a fixed-point attractor for Autonomous Quantum Stabilization (AQS).

• Empirical Testing: Numerical verification within a 3-qubit Liouvillian family, establishing a metastable effective theory.

• Metaphysical Mapping: The mapping of 832 indexed units (including 796 SATI seeds and 36 Sanskrit operator keys) to operator classes on a 1728-state finite module $\mathbb{Z}_{12}^3$.

• Metalogical Grounding: Application of Stratified Axiomatics, categorizing results into tiers:

  • Tier $\Lambda_0$–$\Lambda_1$: LCPI and CPTP results.

  • Tier $\Lambda_2$: Metastability scaling.

  • Tier $\Lambda_4+$: Metaphysical mappings and philosophical integrations.

Technical Validation

Claims in this work are strictly categorized as [Derived], [Num. Verified – tested family], or [Axiomatic/Design].