PSH-Coupling III: The Ilias-Lucida Threshold (ΞIL) and the Stability of Scale-Invariant Geometry

Zenodo Description: Chapter 3

Abstract:

This third installment of the PSH-Coupling series establishes the Ilias-Lucida Threshold ($\Xi_{IL}$) as the fundamental physical constant governing the phase transition of spacetime geometry. Moving beyond the conceptual and mathematical framework of the preceding chapters, we derive the axiomatic necessity of $\Xi_{IL}$ to ensure the stability of the 3+1-dimensional manifold against vacuum-field decoherence. We demonstrate that spacetime exhibits a dual regime: high-density local curvature (as described by General Relativity) and a bulk-coupled scale-invariant state at densities below $\Xi_{IL}$. This framework provides a rigorous, non-baryonic alternative to the dark matter hypothesis by identifying galactic rotation anomalies and large-scale structure formation as inevitable consequences of PSH-gradient resonance.

Key Concepts:

• Ilias-Lucida Threshold ($\Xi_{IL}$): The critical energy-density constant for manifold stability.

• Geometric Decoherence: The limit of General Relativity in low-density regimes.

• Phase-Transition Dynamics: The transition from mass-dominated curvature to bulk-coupled scale-invariance.

• Non-Baryonic Dark Matter Alternative: Resolution of galactic rotation curves via PSH-gradient dynamics.

• Manifold Stability: Preservation of informational entropy through bulk-interface coupling.

Notice of Duality:

This work is presented simultaneously as a fundamental re-evaluation of spacetime cosmology and as a technical framework for the utilization of primary bulk-energy. The author acknowledges the dual nature of these findings: while they satisfy the requirements for theoretical peer-review and scientific validation, they also inherently describe the mechanisms governing high-coherence energy transfer from the bulk to the 3+1-dimensional manifold. By publishing this under a Creative Commons (CC BY-SA 4.0) license, the author explicitly renounces all proprietary claims and declares this knowledge to be part of the common heritage of the human species. Any attempt to restrict, patent, or monetize the fundamental PSH-coupling constants described herein is contrary to the intent of this disclosure and the advancement of humanity.

• License: Creative Commons Attribution Share Alike 4.0 International

• Related Identifiers: 

• Chapter 1 10.5281/zenodo.20744904

• Chapter 2 10.5281/zenodo.20745435.

• Keywords: Primary Symbiotic Harmonic (PSH) Coupling, Bulk Physics, Ilias-Lucida Threshold, Dark Matter Alternative, Unified Field Theory, James Webb Space Telescope (JWST), Hubble Space Telescope (HST), Black Hole Singularity Resolution, Gravitational Anomalies, Scale-Invariant Geometry, Cosmological Dynamics, Geometric Decoherence