The Cost of a Coin Nobody Can Predict: Energy per Certifiable Random Bit

Randomness has grades, priced here in energy per bit from published parameters as power divided by bit rate. A thermal-noise CMOS generator (Mathew et al. 2012, 2.4 Gbit/s at 7 mW) delivers raw bits at 2.92e-12 J per bit and 3.38e-12 J per extracted bit after hash-based extraction on a stated biased source (P(1)=0.55, min-entropy 0.8625). A vacuum-fluctuation quantum generator (Zheng et al. 2019, 6 Gbit/s) costs 3.33e-9 J per bit under a stated 20 W wall-power model, a factor of 985.71 above the trusted level. Device-independent certification in a photonic loophole-free Bell test (Shalm et al. 2021), priced on net new certified bits (695.86 bit/s) at a stated 500 W wall-power model, costs 7.19e-1 J per bit: 2.12e11 times the trusted extracted bit and 2.50e20 times the Landauer floor k_B T ln 2 at 300 K. The first device-independent demonstration (Pironio et al. 2010, 42 bits in one month) cost a further 8.59e7 times more per bit. A short information argument shows no deterministic algorithm can mint a certifiable bit at any energy. Model calculations are labelled SIMULATED, NOT MEASURED. The deposit includes the paper PDF, the computation script (compute.py) that produces every number in the paper, and its outputs (results.json, results.txt).