The Informational Substrate of Physical Law: Toward UV Completion — Bubble Nucleation, the Temporium Lagrangian, Phantom Element Field Theory, and the CIT/TIC Synthesis

We present the fifth and final paper of the Cosmic Information Theory (CIT/TIC) series, completing two results deferred across the preceding papers. First, we propose bubble nucleation at the first-order U(1)_sigma phase transition at T_QCD as the physically self-consistent dark matter production mechanism, resolving the 10^17-order discrepancy in the kinetic mixing freeze-in formula. Second — the central new result of this version — we derive the Temporium Lagrangian from first principles, completing the Phantom Periodic Table. Temporium (Z = -4) is re-identified as a T-odd scalar field Sigma defined as the localU(1)_sigma charge density of the substrate: Sigma = J^0_Phi / Lambda_Tm^2, where J^0_Phi = i g_sigma (Phi* d_0 Phi - Phi d_0 Phi*) is the temporal component of the Noether current of Phi. This identification is genuinely T-odd (under time reversal, J^0 → -J^0), resolving the T-symmetry error of v5 in which d_mu J^mu was incorrectly claimed to be T-odd. The Lagrangian is: L_Tm = (1/2)(d_mu Sigma)^2 - V(Sigma) - (1/6) R Sigma^2 + y_Tm Sigma rho_DM, where rho_DM is the local dark matter energy density and y_Tm is a portal coupling. The energy scale Lambda_Tm ~ 2.4×10⁻³ eV is set equal to the observed dark energy scale (an observational input, not a first-principles derivation). The Temporium field is T-odd, P-even, C-even, CPT-odd — consistent with a field that encodes the arrow of time. Temporium status is revised from 'established' (v5) to 'proposed with consistent theoretical basis, requiring further development'. Five predictions from the Temporium sector are retained with revised epistemic status. The complete series generates 39 falsifiable predictions, with 19 errors corrected across all versions.