DmcsRelaxed

Kanitschar's relaxed feasible set: what widening it costs and the length it feeds

9/9 passed in 134188ms

Test	What it does	Result
test_certificate_holds	Step 2 stays under step 1 and under ${\log }_2|Z|=2$ bits at one and ten steps, and one step certifies less than ten.	✅ pass
test_clip_exceeds_printed	The clipped operator norms are 2 and 3.84 times the constants Kanitschar Sec. V F prints, their own Appendix B stating the larger outright, and the printed pair certifies more than the engine's.	✅ pass
test_honest_is_feasible	The honest truncated state lies inside the relaxed set: every moment within its interval, the trace within the subnormalisation window, and half the trace distance to Alice's marginal under $\sqrt{w}$.	✅ pass
test_length_assembles	Theorem 6 assembles from the shipped pieces -- weight, clipped norms, acceptance half-widths, relaxed minimum and composed $ϵ$ -- into a positive key length dm_length accepts as source="relaxed".	✅ pass
test_operators_arbitrate	The displaced number operator and its square agree with numpy's $(a^{†}-{\beta }^{\ast })(a-\beta )$, and the honest state reads them back as $\eta \xi /2$ and $2{\overline{n}}^2+\overline{n}$, the displaced thermal moments.	✅ pass
test_printed_rows_empty	Kanitschar Eq. (21) as printed, at the paper's own block, testing share, soft limit, cutoff and weight, demands twice the acceptance half-width fit inside the dimension-reduction shift and misses by 319 on both observables, so the printed set is empty and Appendix E's slack form is what the engine assembles.	✅ pass
test_under_equality	At the acceptance a ten-billion-round block buys, the relaxed minimum sits 0.01 to 0.5 bit below dm_secure's equality minimum, the overclaim reading dm_secure into Theorem 6 Eq. (9) would make, measured rather than contained since the two sets' observables differ.	✅ pass
test_weight_is_deficit	dm_weight equals the trace the truncation drops to 1e-15 and falls by over two orders per two photons of cutoff.	✅ pass
test_widening_costs	Raising the weight outside the cutoff or widening the acceptance interval lowers both the step-1 objective and the certified entropy monotonically.	✅ pass