The Story of Gravity in the Euler Universe: Un-thermalized gravity, the near-miss residual, and the arrow of time

A synthesis paper in the Euler Cosmos series. The series has built, in separate papers, an exact zero-energy balance, a low-entropy gravitational dawn, an inhomogeneous crunch, and a reading of the dark sector as the response of a de Sitter horizon to a ledger residual. This paper shows they are one account. The energy books of a flat universe close to exactly zero, but only through a near-perfect cancellation whose residual -- one part in 10^122, the cosmological constant -- reads three ways at once: as energy it is dark energy, as entropy it is the universe's distance from its equilibrium, and as a force it is gravity, since only the imbalance of the ledger gravitates. That distance from equilibrium is gravitational and gravitational alone, because gravity is the one field whose entropy runs backward -- smooth is low, clumped is high -- so it holds the entire low-entropy deficit while matter and radiation thermalize. Un-thermalized gravity is that deficit before it is spent; the arrow of time is its spending, from the smooth, Weyl-free dawn to the black-hole-dominated crunch. The synthesis adds no new falsifiable claim and carries each testable statement at its deposited strength; its work is coherence -- binding the forced w = -1 crossing, the zero-parameter growth fit, and the rotation-curve acceleration scale to a single residual, so that the model is falsified together or not at all. Claude (Anthropic) was used as an analytical, computational, and writing tool, and is not credited as an author.