Scale-Dependent Einstein Obstruction Dynamics

SCQG Paper 14 of 28 This paper studies corrections and fluctuations around Einstein gravity in Semantic Commitment Quantum Gravity. An obstruction is the correction that remains in the Einstein equation after the physical sources have been specified. The paper calculates how this correction and its fluctuations depend on the resolution at which the system is described. The construction begins with a causal set: a discrete ordering of events by causal relations. It uses this ordering to estimate curvature, then derives the retained corrections, causal response and fluctuations from a common physical action. Each microscopic contribution is counted once. Conservation laws include energy and momentum exchanged between the physical sectors. The paper gives conditions under which corrections decrease at large distances and low energies. It also bounds response with memory, where a disturbance continues to affect later evolution. Changes of resolution are treated separately from evolution in physical time. The fluctuation calculation retains correlations between sources and between the initial state and later forcing. For realized holographic screens, the capacity law is C = A/(4ℓₚ²), where A is the screen area and ℓₚ is the Planck length. The paper connects screen fluctuations to stress and metric fluctuations through a specified physical response. It also relates horizon area change to heat flow and shows how detector response and finite resolution enter an observable spectrum. The cosmological construction describes one completed universe with two temporal orientations. Physical dynamics occur within each orientation, subject to the reciprocal endpoint conditions. This is Paper 14 of the Semantic Commitment / Quantum Gravity series.