Notes 28: mathematical corrections and scope Source snapshot: source/frequency_est.tex. Original: /home/sariel/rand_alg/notes/28_frequence_est/frequency_est.tex. Existing review consulted: source/review.md. The original notes were not edited. 1. Averaging uses at least one sample, finite variance, positive mean, and independent samples. Chebyshev is applied with a positive absolute threshold, including variance-zero cases. 2. The number of blocks is an odd positive integer; total samples are alpha times beta. Median failure implies a bad majority, not conversely. Logarithmic bounds use log(2/delta) for the whole range 0 < delta < 1. 3. Reservoir replacement resets the suffix counter even for the same key. All frequency sums use universe size n; stream length is m. 4. The general estimator's second moment is bounded above, not equal to km F_(2k-1). The variance proof uses F_(2k-1), not F_(2k-2). 5. Parameters use the proved upper bound k n^(1-1/k) on relative variance, not the unknown target mean/variance. Arithmetic/word bounds are stated for fixed integer k. Empty streams return zero. 6. The polynomial hash produces ternary values. Keep zeros and normalize T^2 by q=(p-1)/p. Never condition on all outputs being nonzero: such conditioning need not preserve independence. The repaired variance is 2 F_2^2 + (1/q-3) F_4 <= 2 F_2^2. An odd prime p>n of size O(max(n,2)) suffices, with independent degree-at-most-five coefficient vectors. 7. The ideal-sign calculation remains as the pedagogical first step; the finite-seed theorem uses the normalized ternary construction. 8. F_2 amplification uses an explicit exponential-moment bound and rounded, odd block counts. The stated update cost assumes unit-cost word arithmetic; prime selection is preprocessing. Content follows Chapter 28 and its imported probability/hash prerequisites. Diagrams instantiate the stated definitions; no additional streaming methods are introduced. Full-deck timing: 5 + 15 + 25 + 25 + 5 = 75 minutes.