Closure and Opening: A Unified Criterion for Cosmological Hypotheses

We propose a unified criterion for evaluating cosmological hypotheses: a closed, lossless system can only exchange its components reversibly, at 100%, and cannot sustain an arrow of time or growing structure; change happens only through an opening; 100% is a limit, bounded below by zero-point energy. The criterion has two measurable forms: the phase between two exchanging components together with the boundary reflection coefficient (standing versus travelling waves), and the determinant of a one-period map (equal to 1 for closure, less than 1 for an opening). Both forms have established instances in electromagnetism, gravitation and cosmology: anti-de Sitter space (AdS) is a cavity with a reflecting boundary; island computations reproduce the Page curve of an evaporating black hole only after coupling to an external bath; the sign of the heat capacity flips with the boundary; and an expanding universe has no global energy conservation, while comoving photon and baryon numbers are conserved.Applying the criterion to AdS/CFT, de Sitter holography, conformal cyclic cosmology, Tolman's oscillating universe, the no-boundary proposal, inflation, heat death and Poincaré recurrence yields three conclusions. First, our universe is not a closed loop but an open spiral, and the opening is expansion. Second, cosmic history reads as four layers, C→A→B→C′: the vacuum floor of inflation, the reversible (isentropic) opening of the radiation era, the irreversible opening after decoupling (entropy and structure production), and a higher floor in the dark-energy era; the switch between layers is a steep crossing of unity by the ratio of opening rate to internal exchange rate, and each crossing freezes a relic. Third, a de Sitter phase with finite entropy and unitary evolution recurs and is incompatible with a lasting arrow, so the criterion favours non-eternal dark energy. We give one falsifiable test (V6): the switch for structure growth and the switch for cosmic acceleration coincide only if w = −1.Each claim is labelled with one of three epistemic states — established, mapping, or conjecture — and every criterion is stated in dimensionless form. This is a structural paper in natural philosophy and claims no new physics; its unique predictions remain weak, as Section 6 states plainly.