Degenerate Disformal Scalar-Tensor Gravity with Topological Interior Amplification: Ghost-Freedom, Interior Cosmological Constant, and a No-Go Theorem for Classical Completion

We present the action S_STKWC for a degenerate disformal Brans-Dicke scalar-tensor theory within the TKWC (Topological Knot-Web Cosmology) framework. The theory features non-minimal coupling f(φ)R, canonical scalar kinetics, and disformal matter coupling to the Jordan-frame metric g̃ = A g_μν + B ∂_μφ ∂_νφ. The paper establishes ghost-freedom via Dirac-Bergmann Hamiltonian analysis (N_dof: 3 → 2 at the degeneracy surface), spectral stability via Sturm-Liouville/Poincaré-Friedrichs analysis, GW170817 compliance (α_T = 0 from Bellini-Sawicki parametrization), and an Israel junction derivation of the interior de Sitter geometry with Λ = k̃²/3 in the classical thin-wall regime. The central result is a No-Go…