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| **Table D.2 — the fitted per-step rates, where the fit holds.** The secondary reading of `RATE_READINGS.json`: turnover(t, D) = c(t) + A(t)(1 - exp(-r(t) D)), with `c(t)` fixed at the measured twin turnover and fitted on the original scale by nonlinear least squares. A rate is reported **only where R² > 0.8**; a dash is a start point whose fit did not clear the floor, and its R² is shown so the reader can see how far it fell short. The primary reading of the paper is fit-free (Figure 2); this table exists so the fitted form can be checked rather than trusted. | |
| | start (B tokens) | iteration | 5% set: r per 1,000 steps | 5% set: R² | cosine: r per 1,000 steps | cosine: R² | | |
| |---|---|---|---|---|---| | |
| | 4 | 1,000 | — | 0.668 | — | 0.752 | | |
| | 8 | 2,000 | — | 0.656 | — | 0.786 | | |
| | 13 | 3,000 | — | 0.698 | 0.1180 | 0.856 | | |
| | 17 | 4,000 | — | 0.733 | 0.0856 | 0.892 | | |
| | 21 | 5,000 | — | 0.769 | 0.0686 | 0.912 | | |
| | 25 | 6,000 | — | 0.793 | 0.0582 | 0.921 | | |
| | 29 | 7,000 | 0.1022 | 0.812 | 0.0505 | 0.926 | | |
| | 34 | 8,000 | 0.0935 | 0.822 | 0.0442 | 0.929 | | |
| | 38 | 9,000 | 0.0895 | 0.823 | 0.0404 | 0.930 | | |
| | 42 | 10,000 | 0.0873 | 0.828 | 0.0353 | 0.933 | | |
| | 46 | 11,000 | 0.0821 | 0.834 | 0.0310 | 0.937 | | |
| | 50 | 12,000 | 0.0807 | 0.830 | 0.0283 | 0.936 | | |
| | 55 | 13,000 | 0.0757 | 0.835 | 0.0250 | 0.940 | | |
| | 59 | 14,000 | 0.0750 | 0.821 | 0.0226 | 0.942 | | |
| | 63 | 15,000 | 0.0701 | 0.814 | 0.0206 | 0.943 | | |
| | 67 | 16,000 | — | 0.799 | 0.0194 | 0.946 | | |
| | 71 | 17,000 | 0.0498 | 0.801 | 0.0179 | 0.950 | | |
| | 75 | 18,000 | — | 0.798 | 0.0168 | 0.952 | | |
| | 80 | 19,000 | 0.0379 | 0.808 | 0.0161 | 0.950 | | |
| | 84 | 20,000 | 0.0352 | 0.813 | 0.0156 | 0.945 | | |
| | 105 | 25,000 | 0.0301 | 0.813 | 0.0132 | 0.951 | | |
| | 130 | 31,000 | 0.0255 | 0.823 | 0.0116 | 0.958 | | |
| | 164 | 39,000 | 0.0220 | 0.821 | 0.0101 | 0.960 | | |
| | 206 | 49,000 | 0.0201 | 0.822 | 0.0091 | 0.960 | | |
| | 256 | 61,000 | 0.0177 | 0.824 | 0.0082 | 0.959 | | |
| | 319 | 76,000 | 0.0153 | 0.829 | 0.0073 | 0.962 | | |
| | 398 | 95,000 | 0.0136 | 0.842 | 0.0068 | 0.964 | | |
| | 499 | 119,000 | 0.0121 | 0.856 | 0.0062 | 0.966 | | |
| | 625 | 149,000 | 0.0117 | 0.859 | 0.0058 | 0.960 | | |
| **Rates reported: 21 start points for the 5% set and 27 for the cosine, of 29 fitted. Median R²: 0.821 and 0.943.** | |