Pick an allowed IMBH mass. Extract BZ power. Apply the Bekenstein-Landauer-Lloyd limits. Factor in time dilation. The complete quantitative argument for why an ergosphere civilization outcomputes anything built from matter and light — in one browser session.
The IMBH mass is the single most important free parameter in the MTH argument. It sets both the BZ power (Stage 2) and the Schwarzschild radius for time dilation (Stage 4). The current observational window spans roughly 8,200 M☉ (Häberle 2024 kinematic lower bound) to ~70,000 M☉ (older kinematic upper region). The JWST non-detection (Chen et al. 2025) pushes the mass above ~20,000 M☉.
The Blandford-Znajek process couples a spinning black hole's angular momentum to magnetic field lines threading the horizon, pumping electromagnetic Poynting flux outward as a relativistic jet. The power scales as P_BZ ∝ B² M² a², making mass and spin the dominant handles. The magnetic field B is the engineering variable — it must be sustained by an accreting magnetised plasma or engineered magnetosphere. Mass M is fixed by Stage 1 and cannot be changed here.
Two independent physics bounds cap the ops/sec extractable from the BZ power. Landauer: every irreversible bit erasure costs at least k_B T ln 2 joules, so ops/sec ≤ P / (k_B T ln 2) — this depends on the operating temperature. Lloyd: the quantum-speed (Margolus-Levitin) theorem bounds ops/sec ≤ 2E / (π ħ) from the total available energy — temperature-independent. The binding limit (whichever is smaller) is the actual ceiling.
A clock at radius r near a Schwarzschild black hole ticks at rate √(1 − r_s/r) relative to a clock at infinity. An observer sitting at 1.5 r_s computes at the same physical ops/sec as computed in Stage 3 — but from the perspective of the outside universe, their computation runs faster by a factor of 1/√(1 − r_s/r). The MTH argument: the ergosphere civilisation exploits this dilation to perform an astronomically larger number of computations per external year.
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