OCS / Tools / Workflow — MTH Compute Budget
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). Two current bounds are in genuine tension: Häberle et al. 2024 (stellar kinematics) places a lower limit of ≥8,200 M☉, while Bañares-Hernández et al. 2025 (pulsar timing) places an upper limit of ≤6,000 M☉ — the ranges do not overlap. The Chen et al. 2025 JWST non-detection constrains the product M × accretion efficiency from above, not mass alone; it is not a lower bound on mass.
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 dτ/dt = √(1 − r_s/r) relative to a clock at infinity, so hardware sitting at 1.5 r_s completes fewer operations per external year than an identical rig farther out, dwindling toward zero as r → r_s. Per subjective (proper) year the rate is unchanged: binding ops/sec × 3.16e7 s/yr, frame-invariant. What the dilation actually buys is the wait: one subjective year at 1.5 r_s corresponds to 1.73 exterior years, so a civilisation parked deep in the potential well reaches the far future of the universe while aging slowly. The MTH computation claim therefore rests on the time-skip benefit, not on any increase in compute rate.
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