Add LinearLeiosTuner.html

docs/targeted-design-investigations/LinearLeiosTuner/LinearLeiosTuner-README.md

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+LeiosTuner.html is a interactive Dynamic HTML calculator with two inputs.
+
+Its title is Linear Leios Tuner. Its introduction is:
+
+> An interactive calculator for ballparking best-possible EB success rate and overall Leios capacity for various values of L and MaxSize, where L=3×L_hdr + L_vote + L_diff.
+
+The first section is titled Arrival rate of inter-RB gaps ≥ L (at 5% active slot coefficient).
+Its input is a simple integer 2≤L≤200, default of 14 (it's both a number input and a coupled slider).
+Its output is a step plot portraying the probability mass holding times in a renewal process defined by L (truncating x-axis after 95% cumulative).
+Repeatedly toss a coin that's biased 19:1 towards heads.
+The renewal process jumps when a run of L or more heads ends.
+The plot begins at x=0 and stops at the least value of x whose cumulative probability exceeds 95%.
+
+For example, suppose L=3; then
+
+```
+0         1         2         3
+0123456789012345678901234567890123456789
+HTHTHTHHHTTHHHTTTHTHHTTHTHHHHHHTHHHHT...
+      ---  ---           ------ ----
+```
+
+has four jumps, at 9, 14, 31, and 36.
+There're thus three holding times: 14-9=5, 31-14=17, 36-31=5.
+
+(The PMF can be computed efficiently via the linear recurrence
+
+```
+f(g) = f(g-1) − α · f(g-L-1)        with α := q · p^L
+f(g) = 0  for g ≤ L,    f(L+1) = α
+```
+
+— derivable from the renewal-cycle PGF φ_G(z) = α · z^(L+1) / (1 − z + α · z^(L+1)), itself a one-line consequence of decomposing the post-jump toss stream into i.i.d. cycles (each = one geometric H-run length R ≥ 0 followed by a T; a cycle "fires" iff R ≥ L, with probability p^L). The recurrence runs in O(1) per step, fast enough for values up to L=200, and its plot can be downsampled by uniform stride to merely several thousand points---together these prevent the user from noticing laggy response.)
+
+The plot includes rug stems that highlight 19 quantiles 5%, 10%, 15%... 85%, 90%, and 95%.
+(Recall that the x-axis is already truncated at the 95% quantile.)
+The stems for 25%, 50%, and 75% are taller than the others, and 50% taller still.
+
+The second section is titled Theoretical average capacity (with 100% stake participating, max EBs, succeed if L gap).
+Its input is a positive integer MaxSize, defaulting to 1000 (just a number input---no slider).
+Its output is another step plot, showing MaxSize divided by the mean holding time for all run lengths from 2 to ⌈L×4÷3⌉, with the value for L highlighted.