Solvency Field Theory (Version 5.0): Dynamic Dark Energy from Baryonic Entropy Depletion and Black Hole Horizon Growth

We present Solvency Field Theory (SFT), a first-principles cosmological framework that derives the Hubble expansion rate and the dark energy equation of state $w(z)$ as necessary thermodynamic responses to the accumulation of cosmic information. In this framework, spatial expansion is not driven by a static vacuum energy (Λ), but by the physical requirement to maintain the holographic information bound of the universe as new entropy is continuously generated. We formalize the master equation H = Ṡₜₒₜₐₗ/I, where H is the fractional expansion rate, Ṡₜₒₜₐₗ is the active entropy production rate, and I is the accessible information ledger. Utilizing 150 gigabytes of high-resolution cosmological telemetry from the IllustrisTNG (TNG300) simulation, we compute the true thermodynamic history of the universe. We demonstrate that the Bekenstein-Hawking entropy production of supermassive black holes (ṠBH ∝ M × Ṁ) dominates the cosmic entropy budget. Crucially, as the universe depletes its accessible baryonic gas reservoirs, both the stellar and black hole entropy engines crash in perfect lockstep, losing approximately 70% of their power between $z = 1.5$ and $z = 0.2$. This baryonic fuel crisis starves the universe of its active thermodynamic exhaust. To satisfy the continued observation debt of the cosmological ledger (I ≈ 10⁸⁹ kB), the universe must transition to a geometric overdraft, generating entropy via the expansion of the de Sitter horizon. This purely geometric mechanism naturally accelerates expansion, forcing a phantom crossing ($w < -1$) at exactly the epoch observed by DESI DR2 (z ≈ 0.465). Repository Contents: SFT_V5_Master_Academic.pdf: The foundational framework, theoretical derivations, and primary TNG300 data mapping. SFT_arXiv_Spearhead_V4.pdf: A condensed mathematical letter detailing the Hazard Exit ODE and 2D Gaussian KDE scoring against DESI DR2/Y3 Cobaya chains. SFT_Telemetry_and_Scripts.zip: The open-source Python extraction pipelines, KDE statistical models, and raw TNG300 CSV telemetry used to map the macroscopic entropy crash.