Gravity-Mode Period Spacing as a Buoyancy Integral: Inverting Kepler Red-Giant Spacings for the Core Stratification

A red giant hides its core behind an enormous convective envelope, yet its oscillation spectrum reports on that core with surprising directness. This paper computes, from stated assumptions and published stellar values, a quantitative budget for the gravity-mode period spacing using published Kepler red-giant period spacings. The headline results are: I at 50 = 0.3948; I at 310 = 0.0637; ratio = 6.20; dp clump = 310. Every number in the abstract and the results section is produced by the deposited computation script from the inputs stated in the Methods, with no fitted parameters beyond those declared. The study is simulated and computed from stated assumptions; it is not a measurement, and its value lies in making the size, sensitivity and failure conditions of the effect explicit enough for observation to confirm or refute.