FBT10A: The Spectral–Capacity Action of the Fracture–Berry–Tension Framework

The FBT spectral-capacity action is the heat trace of one specified geometric Dirac operator at fixed spectral resolution. This paper states its domain and trace hypotheses, exact first and second variations, stationarity tests, coupled relative-torus 4 + 2 expression, and complete finite-computation requirements. The current application uses the embeddingto-operator map already supplied by DCQ6 and FBT10D on the closed coherent product. No second source map is required. The degree-24 regular magnetic realization, its singular-end analysis and the separate torus numerical benchmark are removed from the main development. Their removal leaves the functional and the relative-torus geometry intact. The global line-extension obstruction is retained to explain this separation. The inherited twist, its closed domain and all metric, spin and connection variations are used together. Exact fibre integration preserves the full heat trace; the four-dimensional quadratic action and normal stability certificates are cited from FBT10D with their original scope. General spectral error bounds retain feedback through omitted modes and distinguish affine connection tests from nonlinear geometric families. A final ledger separates established results from resolution selection, balance-layer selection, full nonlinear control and real-time interpretation. This revision introduces no new numerical sign certificate or physical mass prediction.