Notes 29: mathematical corrections and scope

Source snapshot: source/freq_est_2.tex.
Original: /home/sariel/rand_alg/notes/29_freq_est_2/freq_est_2.tex.
Existing review consulted: source/review.md. The original notes were not edited.

1. Uniform hash values at distinct keys are independent in the ideal model.
   The minimum's density is derived from its survival probability, with
   proper density notation instead of positive point probabilities.
2. Tail integration supplies both minimum moments. The reciprocal conversion
   uses Z=(1+theta)/(u+1), |theta|<=epsilon/4, and explicitly assumes u>=1.
3. The ideal minimum algorithm is labeled as an idealization: its storage
   bound assumes constant-word perfectly random real-valued hashes/values.
4. S is the distinct-value set. Indicator sums range over S, not occurrences.
   Pairwise independence suffices for the sample-size variance calculation.
5. Cap the sampling probability at one. Analyze the exact branch directly.
   Chebyshev uses Var(X)/(epsilon^2 (E X)^2), not its erroneous reciprocal
   epsilon factor. Interpret X as the final conceptual sample after overflow.
6. One unconditional good event proves both numerical and overflow outputs.
   Amplification bounds the number of bad copies below r/4; this ensures a
   majority of good numerical values after declaration outputs are discarded.
7. Finite seeds use affine hashing over a prime field: h(i)=a(i-1)+b mod Q.
   Threshold K=ceil(Q p_0) gives actual probability p'=K/Q. Use p' in both
   the capacity and returned estimate. This preserves concentration and space
   for dyadic scales N<2n. The seed/threshold use constantly many words.
8. The stopping proof uses the first scale N_i >= u, with u<=N_i<=2u.
   All levels through this witness satisfy u>N_j/4. A union bound with budget
   delta/L guarantees a numerical, accurate answer by the witness. No
   monotonicity of random outputs, and no guarantee beyond the witness,
   is assumed. If every output is a declaration, return zero (failure case).
9. Handle empty streams and n=1 exactly. Use log(2/delta) in bounds. State
   the general-delta result and derive O(epsilon^-2 log^2 n) for delta=n^-a.
   For requested epsilon>=1/4 use min(epsilon,1/8).

Content follows Chapter 29 and its imported probability/hash prerequisites;
the finite-seed details and repairs are documented in the supplied review.
Full-deck timing: 5 + 20 + 20 + 10 + 15 + 5 = 75 minutes.