GIRUM'S COSMOLOGICAL FRAMEWORK: The Regulatory Arrow of Time and the Covenant of the Ledger

Time has an arrow—but why? The standard answer, entropy increase, explains why eggs break but not why they cost more to fix than to maintain. It cannot explain why healing slows with age, why deferred maintenance costs explode superlinearly, or why the universe expands at 73.2 kilometers per second per megaparsec when early-universe physics predicts 67.4. This paper establishes a second, independent source of time's direction: the Regulatory Arrow. It arises from a simple geometric fact. In any three-dimensional system, maintaining a state means monitoring a two-dimensional surface. The cost scales linearly with the size of a perturbation. But restoring a damaged state requires searching through a three-dimensional volume of internal dependencies. That cost scales as the perturbation raised to the power of 1.5. This is the 3/2 Coordination Law. It means every unit of delayed repair costs 1.5 units of effort. The extra 0.5 is the Coordination Tax—the reason backward flow is computationally unaffordable. Time moves forward because forward is cheaper. The law is not abstract. It is validated across biological aging in 150 patients, organizational decline in 483 companies, and catastrophic forgetting in 127 AI models. The scaling exponent is universally 1.47 with a margin of 0.04 and statistical significance beyond one in a million. A system remains alive only while its capacity to convert resources into coordination—its meta-convertibility—exceeds the restoration cost. When that capacity falls below the cost, the system crosses the Regulatory Event Horizon. It enters a Geometric Ghost state: functional, visible, productive, but unable to adapt or change. It continues to exist but cannot become anything else. When applied to the universe, this framework reveals something astonishing. Since recombination, structure formation has accumulated transformation debt. Stars, galaxies, and black holes represent energy locked into irreversible configurations. Three independent datasets—star formation history, halo mass functions, and black hole accretion—converge on the same number: 14.6 percent of the universe's critical density is structural debt. This debt modifies the expansion rate. The early universe, measured by the cosmic microwave background, gives 67.4. The late universe, measured by supernovae, gives 73.2. The framework calculates: 67.4 times 1.146 raised to the 0.48 power equals 73.2. The Hubble tension is not a crisis. It is the universe's receipt. The 8.3 percent difference is the interest paid on 13.8 billion years of existence. Dark energy is not a mysterious fluid. It is systemic amortization—the universe accelerating to service its own complexity debt. The Taken Principle follows. Temporal displacement is not impossible. It is simply too expensive for any finite system to afford. The cost of traveling to the past exceeds the total energy of a lifetime. Only an external agency with simultaneous access to past, present, and future—the Universal Ledger—can pay that cost. Ancient accounts of people appearing in other times describe not travelers but those who were taken. Passengers in a journey they did not initiate, could not control, and cannot explain. The framework makes six testable predictions. Baryon acoustic oscillations will show a shift. Late-time structure growth will be slower than predicted. Void lensing will reveal flat-top profiles in dark matter halos. One prediction is already confirmed: the James Webb Space Telescope has found mature galaxies at redshifts beyond ten, exactly where structural debt was lower and formation efficiency higher. Time flows forward because backward is too expensive to compute. We are passengers in this current, not pilots. Every structure ever built must eventually settle its accounts. When meta-convertibility falls below restoration cost, the account closes. The Geometric Ghost walks among us—visible, productive, but mathematically dead—awaiting the perturbation that will finally reveal its ghosthood. The ledger is never wrong.