PairingAnchors

Square-root scaling, the intensity optimum and the repeaterless crossing

8/8 passed in 44ms

Test	What it does	Result
test_beats_repeaterless	The rate crosses the repeaterless capacity at 282.7181 km, 46.6485 dB, and falls back under it at 673.3811 km. Capacity as -log1p(-T)/ln2: -log2(1 - T) is 11% wrong by 160 dB and exactly zero by 176 dB.	✅ pass
test_linear_scaling	Neighbour-only pairing gives a slope of 0.996627.	✅ pass
test_needs_a_window	The peak rate-to-capacity ratio over 200 to 600 km is 0.00476746 at l = 1 and 0.45254514 at l = 100, both under one, and 4.06498441 at l = 1000 and 30.38392590 at $l={10}^4$, both over.	✅ pass
test_optimal_intensity	The sweep selects mu = 0.5 at a wide interval and mu = 1 at a narrow one over 200 to 350 km, Zeng's two closed-form optima.	✅ pass
test_root_scaling	The log-log slope against end-to-end transmittance is 0.501848 at a wide interval and has saturated by $l={10}^6$.	✅ pass
test_slope_between	The slope rises monotonically as the interval narrows, 0.762288 at l = 100.	✅ pass
test_three_hundred	The rate at 300 km is 2.245794808e-05 bits per round, at the mu = 0.5 the sweep selects.	✅ pass
test_window_buys_rate	The zero-key distance is 676.0949 km at both intervals while the wide one buys 291x more rate at 300 km.	✅ pass