The main goal in this article is to justify that source-type and other global-in-time similarity solutions of the Cauchy problem for the fourth-order thin film equation $$ u_t=-\nabla \cdot (|u|^n \nabla \Delta u) \quad \text{in }\mathbb{R}^N \times \mathbb{R}_ + \text{where }n>0,\; N \ge 1 $$ can be obtained by a continuous deformation (a homotopy path) as $n \to 0^+$. This is done by reducing to similarity solutions (given by eigenfunctions of a rescaled linear operator $\mathbf{B}$) of the classic bi-harmonic equation $$ u_t = - \Delta^2 u \quad\text{in }\mathbb{R}^N \times \mathbb{R}_ +, \text{ where } \mathbf{B}=-\Delta^2 +\frac 14 y \cdot \nabla+ \frac N4 I. $$ This approach leads to a countable family of various global similarity patterns of the thin film equation, and describes their oscillatory sign-changing behav iour by using the known asymptotic properties of the fundamental solution of bi-harmonic equation. The branching from $n=0^+$ for thin film equation requires Hermitian spectral theory for a pair $\{\mathbf{B}, \mathbf{B}^*\}$ of non-self adjoint operators and leads to a number of difficult mathematical problems. These include, as a key part, the problem of multiplicity of solutions, which is under particular scrutiny.