We formulate general relativity as a sectorial closure of the metric channel within theseries reading map: the metric equation is treated at the R1 stationarity level (smallEuler–Lagrange residual), while the R3 reading supplies the conservative time instance andworldline protocol. The characteristic cone (and limiting speed c∗) is treated as a pre-instancestructural invariant under admissible eliminations, and the primary time instance is fixedby signal-cone synchronization. On a space–time domain U ⊂ M × R (or U ⊂ Rd × R ina chart), we define a metric regime sector GεGR (U) by (i) Lorentzian nondegeneracy, (ii)cone–metric compatibility (a nontrivial regime gate: the inherited characteristic cone isrealized as the null cone of g, up to declared conformal/rail choices), and (iii) smallness of anEinstein-type residual measured by ΞGR := |RE|g/ΛGR with REµν := Gµν(g)−κETµν. Withina regime-valid region (g, T) ∈ GεGR (U), Einstein-type closure holds with controlled remainder,and energy–momentum balance is controlled in residual form by the contracted Bianchiidentity. Geodesic motion is formulated as an explicit representation protocol, licensed onlywhile regime validity persists (a stopping rule); under a weak-field/slow-variation gate, theNewtonian narrative is recovered as a licensed sub-instance with an explicit remainder bound.
Yunbeom Yi (Sun,) studied this question.