The Cheapest Possible Hello: A Transmitter Energy Floor for Interstellar Beacons

An interstellar beacon is a one-way signal built to be found, so its design question is a floor: the least transmitter EIRP a stated receiver can detect at a stated distance. For a reference receiver of Square Kilometre Array scale at 1.42 GHz (effective area 32,000 m2, system temperature 20 K, sensitivity 1,600 m2/K), under incoherent radiometer detection in a 1 Hz channel with 1,000 s integration and required SNR 10, the minimum received power is 8.7320e-23 W and the floor law is EIRP_min = 3.0692e6 (d/1 ly)^2 W: 3.0692e10 W at 100 light-years and 3.0692e12 W at 1,000 light-years. A pulsed beacon with duty cycle 0.01 and 1 ms pulses requires 3.16 times more average EIRP and 316.23 times more peak EIRP than the carrier. At a stated rate of 1 bit per second, the radiated energy per delivered bit for a stated 300 m transmitting antenna is 3.0802e3 J at 100 light-years and 3.0802e5 J at 1,000 light-years, scaling as distance squared. The published Arecibo planetary radar EIRP of 2.2e13 W exceeds the 1,000 light-year floor by a factor of 7.17 and would be detectable to 2,677 light-years under the stated conditions, while an isotropic 1 MW transmitter would be detectable only to 0.571 light-years. Receiver improvements are priced explicitly: ten times the area, a hundred times the integration, and halving the system temperature together lower the floor by a factor of 200. 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).