Below is a summary of the principal discoveries of each investigation within the TCFQ programme, from Note R178 through R185, presented in the requested order: R178. Establishment of the symbolic involutivity of the projected Grassmannian jet tower associated with idempotent operators. It achieves the identification of the first universal non‑linear correction ($\Psi_{i,j}$) and the exact computation of the first diagonal defects ($D_{ij}, D_{ijk}$), demonstrating that symbolic involutivity is independent of effective local realizability. R179. Proof of universal Gram saturation for generic exponential models of any rank ($r \geq 2$), confirming the absence of linear or algebraic obstructions to quadratic closure. It also establishes by induction the universal formula for all diagonal defects ($D_\alpha$), thereby validating the structure of the jet tower. R180. Identification of the exact symmetry of the constitutive operator ($\hat{H}\nu = \hat{H}{-\nu}$) and its scale invariance, which places the infrared scale $m_*$ as an external parameter. It localises the symmetry breaking specifically within the spectral coefficient $D_0(\nu)$, an essential step for mass generation in the theory. R181. Localisation of the first carrier of asymmetry in the McMahon asymptotic shift ($c_\nu = \nu/2 - 1/4$), which arises from the phase of Bessel functions. It establishes the “even‑parity barrier”, proving mathematically that the odd structure required for $D_0(\nu)$ cannot originate directly from the operator. R182. Determination that the Friedrichs extension constitutively selects the regular branch ($J_\nu$) of the spectral problem by excluding the singular solution because it requires infinite energy. It further proves the uniqueness of the Dirichlet condition as the only local self‑adjoint extension compatible with the observed Bessel‑zero spectrum. R183. Exact numerical computation of the primary spectral object $D_0^{\text{exact}}(\nu)$ via a sum over Bessel zeros with rigorous error control. It discovers that this observable is strictly decreasing with respect to the parameter $\nu$, enabling precise evaluation of derived physical constants. R184. Constitutional first‑principles reconstruction of the relation $D_0(\nu) = \frac{1}{2}\sum j_{n,\nu}^{-3}$ via the Taylor expansion of the spectral generating function $\Psi_\nu$. It explains that the polygamma structure central to the programme emerges naturally from the McMahon linearisation of the spectrum. R185. Confirmation that the Spencer compatibility identities generate effective differential constraints (Scenario B), overcoming the possibility that they might be mere tautologies. It establishes the definitive structural bridge between the Grassmannian projector geometry and the spectral observable $D_0(\nu)$ as a closure condition of the system.