[sinnercode228]

What

• packages/core/src/hll-bias.ts holds the empirical data for precision 11 from the HyperLogLog++ paper (Heule, Nunkesser, Hall, EDBT 2013): rawEstimateData, biasData and the linear counting threshold 1,800, with the paper's 6-nearest-neighbour bias lookup.
• Hll.count() for dense sketches: linear counting up to 1,800, then the raw estimate minus its bias up to 5·m = 10,240, the plain raw estimate above.
• Unchanged: the sparse exact mode, merge and the toBytes/fromBytes format, so stored sketches keep working.
• README: the error table, limitation 2 and the test counts.

Why

The old count switched from linear counting to the uncorrected raw estimate at 5,120, where the raw estimate runs about 2.5% high. The 5,000 row was the worst in the README table:

distinct ids	rms before -> after	worst of 50
5,000	3.27% -> 1.82%	7.88% -> 5.80%

Other sizes are unchanged; every size from 1,800 to 6,000 improves.

How it is tested

• Accuracy over 100 seeded streams up to 200,000: rms under 3%, mean under 1%. Fails on main at 5,000.
• Continuity around 1,800, 5,120 and 10,240: on main one sketch jumps by 7.35% at the old switch; now the largest step is 3.16%.
• Sketches serialized by main decode to identical bytes and count the same; merge stays associative and commutative.
• The tables match three independent transcriptions of the appendix.
• 118 tests pass (core 63, server 34, web 21); lint, typecheck and build pass.