How fast can a preserved mind subjectively run? Not as fast as the datacenter — the brain brings its own rate limits. Pick how much of the biological substrate is replaced and see the ceiling, the floor that sets it, the thermal cost, and the subjective time it buys.
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A datacenter can run a physics simulation arbitrarily fast, but a biological brain fed by that simulation cannot consume it arbitrarily fast. The ceiling is set by the slowest of several floors: action-potential rates (~1 kHz peak, 10–100 Hz sustained), chemical synaptic delay (0.5–5 ms per relay), the ~10 Hz alpha-band perceptual-sampling rhythm that gates awareness, the visual Nyquist limit (~60 Hz), the thermal wall (the brain dissipates ~20 W, rising with speed), and neurotransmitter recycling.
Replacing more of the substrate raises the ceiling but changes what kind of brain it is. Past ~×10 you are replacing synapses, and whether the self survives that is a question of identity, not physics — which is why the top of the ladder is dashed. Thermal load here is a first-order estimate, ~20 W × ceiling, before any active heat extraction.
Grounded in the Feasibility Audit, §4.5. Pairs with the Time Dilation Instrument (what the acceleration does to families) and the Interface Bandwidth Gap (the write-side problem behind sensory augmentation).
Further reading: VanRullen, R. (2016). "Perceptual cycles." Trends in Cognitive Sciences 20(10), 723–735. Attwell, D. & Laughlin, S.B. (2001). "An energy budget for signaling in the grey matter of the brain." J. Cereb. Blood Flow Metab. 21(10), 1133–1145.