v2.0 Abstract

We propose a phenomenological framework in which spacetime carries two scalar fields of entropic character that modify gravitational dynamics across cosmic scales. ST (temporal entropy) is postulated to increase monotonically throughout the uni- verse, providing a dynamical mechanism for time’s arrow through an explicitly time- asymmetric potential. SS (spatial entropy) serves as an order parameter for the quantum-to-classical transition of spacetime itself: taking small values in regions where quantum coherence persists and large values where decoherence has created classical behavior. Within the DHOST (Degenerate Higher-Order Scalar-Tensor) formalism, we in- troduce three phenomenological functions: h (SS ) modifies the gravitational coupling in regions of quantum spacetime while recovering Einstein gravity in classical re- gions; V (ST , SS ) contains a linear term α ST that breaks time-reversal symmetry; and f (SS ) modulates matter-gravity coupling based on the local quantum state of spacetime. This framework offers a unified phenomenological description of several cosmo- logical puzzles: dark matter effects emerge from regions where partial decoherence creates intermediate SS values, dark energy arises from the time-asymmetric po- tential V , and the Hubble tension could result from different ST values probed by early versus late universe measurements. The framework requires several conjectures about how quantum coherence patterns persist across cosmic scales—mechanisms that would need justification from a future theory of quantum gravity. We identify observable predictions including: (i) environmental dependence of galaxy dynamics based on local SS values, (ii) correlations between regions of modi- fied gravity and time flow anomalies, (iii) deviations in black hole photon ring radii, and (iv) quantum interference experiments coupling to gravitational fields. While the mathematical consistency of this two-field DHOST theory requires further anal- ysis, the framework provides a concrete phenomenological target for testing whether quantum properties of spacetime itself might explain cosmic structure.

v2.1 Abstract We propose a framework for the emergence of physical reality from a single irreducible principle: the binary singularity, a primordial act of distinction giving rise to a propagating duality. From this minimal substrate, we construct the mathematical and physical structure of the universe, including Peano arithmetic, real analysis, and differential geometry. The core of the framework is an entropic resonance, Sresonance, a coupling between spatial and temporal entropy gradients hypothesized to seed the differentiation of geometry and fields. We define two scalar fields—SS(x) representing spatial organization and ST (x) representing directional entropy flow—whose interaction gives rise to a generalized entropic action. We argue that the variation of this action has the potential to reproduce key astrophysical and cosmological phenomena without invoking dark matter or inflation. As a proof-of-concept, our preliminary simulations show qualitative agreement with the flat rotation curves of galaxies and the primary features of the anisotropic polarization spectra of the cosmic microwave background (CMB). The framework is presented as a potential route toward a parsimonious explanation for gravitation, field dynamics, and the arrow of time as emergent consequences of information flow.