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 (10 M☉ stellar BHs at the fiducial 1% number fraction, the fbh deeplink here), and that tail sets the floor: the median survival time is ≈3×10⁶ yr, roughly flat from 10⁻³ to 4×10³ AU, because the per-encounter kick variance and the encounter rate scale inversely with radius and their product cancels. This supersedes the stars-only ≈3×10⁹ 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 ω Cen’s measured intracluster medium (n_e ≈ 0.23 cm⁻³) 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 itself part of why the hypothesis family selects IMBHs.

Feeding the hierarchical Bayesian framework’s per-channel result into the same router used across the ChainGraph evidence chains gives the paper’s headline number directly: ln K = −0.29 (2·ln K = −0.58) for the engineered hypothesis against the best astrophysical null, on the pre-registered Jeffreys/Kass–Raftery action bands. That routes to supports null hypothesis — waste heat is presently the only live evidence channel, and the current silence mildly favors 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).