The far side of the seam: the violent branch of the no-boundary beginning

A standalone note following the trilogy A smooth beginning for spacetime (Papers I–III). Papers I–III of the preceding series argued that the Feldbrugge–Lehners–Turok fluctuation catastrophe of the Lorentzian no-boundary path integral is erased thermally by the de Sitter horizon wherever the horizon's ledger can afford it, and computed the boundary of affordability: the seam σ ∼ 1, past which the quasi-static ledger defaults and the debt passes to backreaction. This paper crosses the seam. Coupling the biased fluctuation ensemble to the geometry it deforms, we find the far side has exact structure of its own: the seam parameter takes the closed form σ = 2ρ/(3H²), so that the default threshold is precisely bias–Λ equality; the quiet ledger's conserved charge becomes a monotone, with production rate 2Γσ²S_dS; Clausius bookkeeping bounds the far side's total erasure by the repository's own balance; and the fate of the cosmological constant is classified by the erasure throttle's large-bias exponent, with unthrottled absorption excluded on sign grounds and the physical class delivering an O(1) ratchet, Λ_f/Λ_i ∈ [0.40, 0.63], that brackets the near-side closed form. Carrying the biased occupations through the decelerating phase — dilution pays the energy debt, not the spectral one — we then confront the regulator dependence Paper III confessed. The sky partitions it: energy-per-mode regulators are excluded by the sign of the low quadrupole; occupation-type regulators are exactly invisible; amplitude-cap regulators are constrained and fingerprinted, with the quiet branch's own erasure confining the bias below the cut and forcing a spike at the cut scale whose absence bounds the regulated amplitude. The cut's position is proven irreducible without a model of the post-seam history; its shape is the predictive residue. The violent branch emerges neither as a free parameter nor as a prediction, but as a measured object: excluded in one direction, invisible in a second, and fingerprinted in the third. Gate scripts, dated logs and memos: doi:10.5281/zenodo.23015805.