The Ignition Transition: From the No-Boundary Saddle to Radiation Domination

The pre-geometric tessellation framework draws the primordial spectrum from a no-boundary path integral as described in the companion papers. The passage from Euclidean S⁴ saddle to a radiation-dominated Lorentzian universe is the ignition treated here. The transition is largely fixed by structure: the instanton's scale is a modulus, irrelevant to the dimensionless observables (n_s = 1 − ln2/(2π²), r = 0.034); a round S⁴ is a Euclidean initial condition, not an inflationary phase; and the radiation state is automatic, thermal at the Gibbons–Hawking temperature. The one dynamical step -- converting the saddle's vacuum energy into radiation -- is carried by the conformal trace anomaly, Starobinsky's de Sitter with the tuning removed: the converting energy is the anomaly-induced stress (∝ H⁴), not a fundamental cosmological constant, which would not decay; the zero-parameter action forces a heavy scalaron, so the de Sitter decays in under an e-fold, no inflation occurs, and the energy ledger closes at zero. The adiabatic-mode selection is re-derived for the de Sitter→radiation background in Appendix A -- an explicit stability eigenvalue confirming that the coherent, cosine-mode structure of the spectrum survives the conversion. What the conversion preserves at leading order is the combinatorial tilt: the forward transfer is P_obs = P_comb × T_early² × T_standard², and its one construction-specific factor, T_early -- the transfer through the conversion -- is the program's central open computation, diagonal at linear order so the tilt passes through with any departure confined to the lowest multipoles, its full form (backreaction and mode coupling at the trans-Planckian conversion scale) the remaining work. r = 0.034, at the BICEP/Keck bound, is the near-term test.