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A tie cluster's truncated read left the width at one tick; once the gap above it was under two milliseconds nothing floored it, so segHi stepped down one tick per read: 30 rows at one ms 0.3 s below hi with a carried 1 s width took 10,006 identical reads (S8). (a) The top-anchored width is floored at the granularity, Min kept; (b) a segment no wider than the granularity is the unit that escalates to MaxTieClusterOverfetch and then refuses - per millisecond, exact for the ms-resolution Gateway (documented). Both are needed: the floor alone loops on crowded reads with a small tie budget. S8 is a repo test (4 shapes, reads <= 30, 0 repeated requests); random-data tests now measure the refusal unit as rows in any 1 ms window. Reviewer harness, 5,000 seeds x default/MSONLY/CROWD: worst page 70 reads (default/MSONLY), 63 (CROWD) at M=65536, p99.9 27-37; no page over 500 reads at any tie budget.