SargSplitting

Photon-number splitting: t^1.5 against BB84's t^2, and where they cross

4/4 passed in 1380ms

Test	What it does	Result
test_ceiling_root	sarg_ceiling vanishes at $\mu =2\sqrt{3t}$ and clamps to zero past it.	✅ pass
test_crossover_exists	The two ceilings cross once, at 7.702 km of 0.25 dB/km fibre, BB84 above before it and SARG04 after.	✅ pass
test_optimal_intensity	The ceiling peaks at $\mu =2\sqrt{t}$, Branciard Eq. (107), where BB84's peaks at $\mu =t$, Niederberger Eq. (29), equalling Branciard's $(\eta /3)h_2(p_1)t^{3/2}$ with $h_2(p_1)=0.60088$.	✅ pass
test_scaling_exponents	The optimised ceilings scale as $t^{3/2}$ for SARG04 and $t^2$ for BB84, the advantage widening as the square root of the loss: 2.5335 at t = 0.1, 25.335 at t = 0.001.	✅ pass