Migrate or Stay: The Discount-Rate Verdict

At the fiducial destination gain (G = 10⁹, a power-ratio, no fuel stack assumed), transit survival probability (p_s = 0.5), and bare transit-plus-construction time (τ = 10⁵ yr, no braking), the closed-form threshold gives ρ* = 2.00×10⁻⁴ yr⁻¹, a half-life of 3.46×10³ yr. A lineage whose combined discount-plus-hazard rate sits below that clears the bar for migration over densification; the seed-and-stay hybrid band extends the same conclusion out to 1.69× that threshold. This value carries forward unchanged into Step 2, which asks whether ordinary discount-rate uncertainty alone can put a lineage under it.

A lineage uncertain between two possible discount rates values the far future by the expectation of the discount factor, not the expectation of the rate, and that certainty-equivalent rate declines toward the lower rate in the prior as the horizon lengthens. Under the patient profile (ρ₁=10⁻³, ρ₂=10⁻⁶, equal weight, t=10⁵ yr) the naive mean is 5.00×10⁻⁴ yr⁻¹ but ρ_eff falls to 7.93×10⁻⁶ yr⁻¹, well under the 2.00×10⁻⁴ yr⁻¹ threshold from Step 1: migration is favored under uncertainty alone. Under the impatient profile (ρ₁=10⁻², ρ₂=10⁻⁴, 70% weight on the higher rate, t=10⁴ yr) ρ_eff only falls to 2.20×10⁻⁴ yr⁻¹, still above the same threshold: this lineage has not bought its way to patience.

The workflow's own four-stage comparison (Drake prior, Sandberg aestivation gain, Landauer-limited IMBH ops, and the Bennett-corrected ratio) delivers the practical version of the same question. With the patient profile's large engine (30,000 M☉, a* = 0.9, B = 10⁶ T) the act strategy wins by 7.23×10¹⁰× (7.93×10¹²× under the Bennett critique): a lineage that has already cleared the patience threshold and holds a real IMBH platform should act now, not aestivate. With the impatient profile's small engine (1 M☉, a* = 0.01, B = 1 T) the same comparison flips: aestivation wins by 1.75×10¹⁴× (4.73×10¹⁴× under Bennett), since an engine too weak to outrun the CMB cooling toward the Landauer floor is not worth running at all, regardless of what Step 2 said about patience.