Infogravity 4.3: Spacetime as Fisher Information Geometry and the Co-Emergence of Time and Entropy

Infogravity 4.3 develops a principle-level framework in which spacetime geometry is interpreted as the pull-back of an underlying information-geometric structure. The starting point is a globally entangled quantum state, from which physical descriptions arise as coarse-grainings implemented by completely positive trace-preserving maps. The resulting manifold of effective states carries the Fisher information metric, uniquely characterised by monotonicity under coarse-graining. In this setting, spacetime geometry is identified with the Fisher metric induced on a four-dimensional manifold, so that gravitational curvature reflects the stability properties of relational structure rather than a fundamental force. We formulate an action principle in which the Einstein–Hilbert term is supplemented by an entanglement–entropy functional. Variation yields an Einstein-type field equation containing an additional informational stress tensor, which encodes the response of the entangled substrate to metric deformation. General relativity is recovered in suitable limits, while departures from equilibrium may lead to effective dark-sector contributions. A further conceptual element is the Co-Emergence Hypothesis, according to which temporal ordering and entropy production arise simultaneously when a consistent informational hierarchy becomes possible. In this view, the low entropy associated with the early universe is interpreted as a structural feature of the onset of temporality, rather than a finely tuned boundary condition. Infogravity 4.3 is presented as a unifying information-geometric framework rather than a completed microscopic theory. It provides a coherent organisational perspective linking gravity, entropy, and entanglement, while identifying observational and theoretical avenues through which the framework may be further constrained.