Picard-Lefschetz Lorentzian Dynamics: Quantum Reference Frames and Internal Information Capacity Boundaries

[VOLUME III OF THE PERSPECTIVAL RELATIONAL ALGEBRA WORKING MONOGRAPH SERIES]

CORE OBJECTIVE: This monograph resolves the "Problem of Time" and the frozen-universe paradox characteristic of background-independent quantum cosmology equations (such as the Wheeler-DeWitt equation).

THE ADVANCED CONTRIBUTION: Volume III abandons the unphysical practice of inserting an external, semi-classical clock system into cosmology. Instead, it models the observer (Omega) as a localized, internal matrix sub-block with a finite informational tracking capacity bound (K << N) embedded inside the global matrix network. By deforming a highly oscillatory Lorentzian path integral onto multi-dimensional geometric Lefschetz thimbles, the paper derives a localized four-dimensional pseudo-Riemannian metric tensor (g_mu_nu) directly from the internal spectral density variations of the sub-block channels. It mathematically defines the local speed of light as the maximum informational throughput velocity of the discrete network, proving that gravitational curvature is an operational measure of localized network congestion. Furthermore, it derives the experienced arrow of time as the sequential execution count of successive Borel-Écalle resummations as the observer's frame shifts across adjacent Stokes sectors.

WHAT THIS WORK IS NOT: This work does not introduce new physical particles or modify the Einstein field equations at macroscopic thresholds; it is an informational derivation of their origin.

EXPERT JOURNAL STANDARDS: This monograph plugs directly into the modern peer-reviewed literature on Quantum Reference Frames (QRFs) and Lorentzian path integral regularizations. It challenges standard paradigms by demonstrating that time and spatial geometry are not a fundamental background canvas, but are local, non-invertible computational records stabilized on-the-fly by the presence of an internal observer.

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