sketch_mg_ss_bracket_bench.nx

sketch_mg_ss_bracket_bench.nx -- bracketing capability paired bench. CLAIM TO VALIDATE: Misra-Gries (1982) UNDERESTIMATES the count: mg_est <= truth. SpaceSaving (Metwally et al. 2005) OVERESTIMATES: ss_est >= truth. Together they BRACKET the true count. Apache DataSketches ships only the SpaceSaving-direction "frequent items" sketch. Substrate ships BOTH; bracket gives callers a guaranteed-correct interval (mg_est, ss_est) within which the true count lies. Capability EXCEED. WORKLOAD: k=10 for both. Heavy items 1..5 with counts 2000/1000/500/200/100. Noise: 500 singletons. Total N=4300. N/(k+1)=391 -- items 1..3 are guaranteed heavy (truth >= 391); items 4 and 5 are borderline. MEASUREMENT: For items 1..3 (guaranteed heavy): - mg_est <= truth (sealed underestimate property) - ss_est >= truth (sealed overestimate property) - bracket_width = ss_est - mg_est > 0 (non-degenerate interval) - truth INSIDE [mg_est, ss_est] Aggregate: signed bias over 3 items mg_signed <= 0 across all items (underestimate is sealed) ss_signed >= 0 across all items (overestimate is sealed)