Paper E, Walked: Envelope to Adjudication

This sweep runs the impulsive-diffusion Monte Carlo across the full radius range at once: impact parameters from the gravitationally focused encounter rate, velocities from a Maxwellian at dispersion σ, masses from the perturber mass function, and survival defined as eccentricity walking to the orbit-crossing threshold. The mass function carries a mass-segregated heavy-remnant tail (31 M☉ black holes — the mean mass of holes inspiraling into the IMBH in the González Prieto et al. 2025 ω Cen models — at the fiducial 1% number fraction, the fbh deeplink here), and that tail sets the floor: the median survival time is ≈6×10⁷ yr impulsive (adiabatically corrected, it stays above ≈3×10⁸ yr at the envelope edge), roughly flat across the swept radius range, because the per-encounter kick variance and the encounter rate scale inversely with radius and their product cancels. This supersedes the stars-only ≈1.79×10⁹ yr floor Paper E first reported (recover it with fbh=0). The floor stays well above the 10⁶ yr passive-safety criterion, so flybys still never set the outer boundary; they are a trim budget, not a survival requirement.

Drilling into one radius from the swept envelope gives the encounter rate, mean wait time, penetrating fraction, orbital period, and influence radius that the sweep view compresses away. At the deep-swarm radius the structure sits inside the fueled boundary set by tidal stress and orbit stability (§2.2); at the outer-envelope radius it sits at the tidal-truncation edge (§2.3), the last radius the cluster’s own field does not eventually strip. Both radii return the same conservative diffusion floor family — the difference is in the encounter statistics, not the survival verdict.

Bondi accretion from an intracluster medium adopted by analogy with 47 Tucanae (n_e ≈ 0.23 cm⁻³, since ω Cen has no direct ionized-gas density measurement of its own) funds an extractable power roughly two orders of magnitude above the waste-heat ceiling: the entropy-transport floor of Appendix A.3, adopted here at 1−f_sink ≈ 10⁻⁴, caps the computation an installation can run without its own radiated heat exceeding the JWST mid-infrared point-source limit. The ordering is the paper’s central engineering result: for a fiducial 2×10⁴ M☉ hole, supply never binds and thermal concealment does. That ordering reverses for stellar-mass holes in the same environment, which is part of why the hypothesis family selects IMBHs.

Feeding the hierarchical Bayesian framework’s per-channel results into the same router used across the ChainGraph evidence chains gives the paper’s headline number directly: the mid-infrared waste-heat channel alone gives ln K_MIR = −0.474, and with the mass channel now also scored (ln K_mass = −0.027) the framework total across both live channels is ln K = −0.501 (2·ln K = −1.002) for the engineered hypothesis against the best astrophysical null, on the pre-registered Jeffreys/Kass–Raftery action bands. That routes to supports null hypothesis — the current data mildly favor the quiescent-IMBH null. Deeper mid-infrared photometry tightens the P_comp ceiling linearly (§3.1); the regulation-signature and relic-drainage channels are conditional and forecastable, not yet live (§3.2–3.4).