SixStateThresholds

The 12.6% zero crossing, against BB84's 11.0% on the same arithmetic

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Test	What it does	Result
test_gap_positive	At every equal QBER below its own threshold the six-state fraction is the larger.	✅ pass
test_kato_printed	The computed crossing agrees to five figures with Kato and Tamaki's qubit threshold and sits 8e-5 above their threshold-detector figure.	✅ pass
test_leak_moves	Charging F_REC leakage rather than the Shannon limit moves the crossing to 10.7322%.	✅ pass
test_noiseless_limit	Both families give one full bit at Q = 0, where Eve's information is zero, and the six-state fraction falls monotonically in Q.	✅ pass
test_six_crossing	The six-state fraction crosses zero at 12.6193% and BB84's at 11.003%, a gap of 1.6 points and a ratio of 1.146919.	✅ pass