Thirty-Three Microseconds of Room: Earth's Rotation Record Prices a Rotation Coupling

Earth's rotation is the best-monitored rotation in science. The IERS length-of-day (LOD) series is public, continuous, and carries formal uncertainties at the level of microseconds to tens of microseconds in the modern era, and the published atmospheric and oceanic angular-momentum (AAM/OAM) budgets account for most of what it does. This paper asks the planetary-scale version of the question its sibling, Paper D (#759), asks at flyby scale: if a rotation coupling of the kind this house works with exists, what room is left for it in the planet's own rotation record — and what size of coupling does that room price? I do not assume Paper D's result, in either direction. I price three channels separately. (1) **The exchange channel** — a coupling that moves angular momentum between the solid Earth and anything else, coherently, at seasonal or sub-seasonal periods — is bounded by the published LOD residuals after the AAM/OAM budget is removed: residual phasors of **33.4 µs (annual), 44.4 µs (semiannual, 1980–2000 budget), 8.1 µs (terannual)**, with the semiannual residual falling to **17.1 µs** in the 1992–2000 budget that includes stratospheric winds. In fractional terms the room is a few ×10⁻¹⁰ of the day; as a fraction of the observed signal in each band, the treatment-proof caps are **0.12 (annual), 0.16 (semiannual), 0.16 (terannual)**, with best-treatment caps of 0.089 (annual, 1980–2000 budget) and 0.058 (semiannual). (2) **The back-reaction channel** — the momentum kick a flyby anomaly would return to the Earth — prices at **~10⁻²¹ s of LOD**, some sixteen orders of magnitude below the smallest room above; it is not a cross-check and I say so at full size. (3) **The trajectory channel** — a coupling that acts on a passing body as a function of geometry and exchanges nothing measurable with the planet — predicts no LOD signal at all, and this record therefore neither confirms nor refutes it. The compatibility statement is parametric and stands either way: whatever Paper D finds, the two prices conflict only if D's surviving coupling is *also* claimed to exchange angular momentum with the solid Earth above the caps in Table 2. The room is an upper bound, not a detection: the published literature already attributes these residuals to wind-field model error and unmodelled hydrology, and I spend them on nothing.