validation/paper2/TABLE_D2_rates.md

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.