Unified Loop Dynamics (ULD): A Topological Unification of Hadron Mass and Dark Energy via Dynamic Vacuum Tension

AbstractThis dissertation proposes a unified geometric framework, Unified Loop Dynamics (ULD), which posits that spacetime is not a passive background but an active, elastic spacetime fabric governed by a mechanism of Dynamic Vacuum Tension (DVT). We address two major crises in modern physics: the lack of a geometric derivation for hadronic masses and the cosmological tensions regarding Dark Matter. First, within the ULD framework, we identify a fundamental mass-length coupling constant Z ≈ 7.477. We derive a topological quantization condition for meson masses, demonstrating that the spectrum follows a harmonic series M ≈ μ0[(n2 + 1)Z^2 + kZ], where (n^2 + 1) represents topological area modes and k denotesgeometric charge loading. This formula predicts the masses of Pions and Kaons with < 0.1% accuracy. Second, we extend the DVT mechanism to the cosmological scale, proposing that vacuum tension relaxes over time via P(z) ∝ (1 + z)^3. We demonstrate that the high-tension vacuum of the early universe acts as a stiffening agent for gravitational potentials, successfully reproducing the third acoustic peak of the Cosmic Mi-crowave Background (CMB) power spectrum without invoking non-baryonic Dark Matter. Finally, we explore the implications of ULD for quantum gravity, deriving the Bekenstein-Hawking entropy from topological area counting and proposing that inertia is the reactive drag of vacuum tension against acceleration.Keywords: Unified Loop Dynamics (ULD), Dynamic Vacuum Tension (DVT), Topological Solitons, Skyrme Model, Hubble Tension, Proton Mass Decomposition, Lattice QCD, Baryonic Tully-Fisher Relation (BTFR), Quantum Gravity, Emergent Spacetime