Radiative Energy Balance Framework (REBF): A Scoped Consistency Structure Linking Classical Radiation Loss to Graviton-Mode Bookkeeping in Weak-Field Gravity

REBF is a scoped interpretive framework, not a new theory of gravity. It states precisely how gravitational-wave energy loss in classical general relativity can be read, at the same time, as far-zone flux, as source mass–energy decrease, and as weak-field graviton-mode occupation. The paper adds three things: an entropy vertex with an entropy-loading parameter η_gw that separates pure (coherent) from mixed (phase-randomized or thermal) radiative states at fixed energy; a quantum–classical boundary estimate near GHz for weak primordial backgrounds; a catalog residual Δ_REBF. We show that Δ_REBF is informative only when its two inputs are inferred independently; on current GWTC-4.0 catalog products it is zero by construction. As an application to public data, leading-order inspiral graviton counts are computed for 81 GWTC-4.0 events (10^77 to 5×10^78), confirming that every analysed signal is extremely classical. All code, input data (GWOSC, CC BY 4.0) and outputs are included for reproduction. AI assistants (Anthropic's Claude and OpenAI's Prism) carried out much of the derivation, coding and drafting under the author's direction; see the paper's "Author contributions and use of AI tools" section. Preprint; not peer reviewed.