Coherence and growth, October 11, 2026: N = 4,000 per group, K = 1.90 (the threshold), eps = 0.1
Six fresh starts (starts 7 to 12) of the long run at the threshold: the same model, settling, gap (rms 1e-07 radians, put back every 5 time units) and length (6,000 time units), run by nudge_test.py's own code.
Set before the run: measured start by start over t = 2,000 to 6,000. 1. Same time: the correlation between coherence and growth rate in windows of 200 time units. 2. Later: the correlation between coherence and the growth rate 200 to 500 time units later. A link if the average over the starts is more than 3 error bars from 0. Error bars: from the starts.
Check: start 1, run by this script for 50 time units, repeats the long run exactly.

1. Same time (windows of 200): +0.2763 (0.1044); starts +0.43, -0.25, +0.50, +0.50, +0.22, +0.26; below 0 in 1 of 6: no clear link
2. Later (200 to 500 later): -0.2061 (0.0186); starts -0.22, -0.23, -0.13, -0.16, -0.27, -0.23; below 0 in 6 of 6: more coherence now, slower growth later
Beside Test 16: the fresh starts' long-run rate, t = 3,000 to 6,000: +0.0145 (0.0007); Test 16: +0.0147 (0.0006); difference -0.0001 (0.0009): agree

Shown, not read as tests: the fresh starts, then the earlier run (where the patterns were noticed)
Same time, correlation by window length (time units)
                            25                50               100               200               500        1,000 (+0)      1,000 (+250)      1,000 (+500)      1,000 (+750)
  fresh       +0.2835 (0.0558)  +0.3061 (0.0676)  +0.3011 (0.0775)  +0.2763 (0.1044)  +0.1742 (0.1258)  +0.3160 (0.1392)  -0.0702 (0.2750)  +0.2975 (0.1639)  +0.3788 (0.1687)
  earlier     +0.2992 (0.0560)  +0.3128 (0.0623)  +0.3156 (0.0678)  +0.3162 (0.0722)  +0.2439 (0.0950)  -0.4207 (0.2357)  +0.0696 (0.2879)  +0.4934 (0.2661)  +0.3355 (0.2938)
Coherence against the growth rate L time units later (negative L: the growth comes first)
                 -500     -300     -200     -100      -50       +0      +50     +100     +200     +300     +500
  fresh        +0.105   +0.156   +0.229   +0.182   +0.169   +0.265   +0.112   -0.037   -0.195   -0.198   -0.214
  earlier      +0.146   +0.190   +0.259   +0.221   +0.193   +0.271   +0.115   -0.007   -0.179   -0.224   -0.308
Coherence |z| over t = 2,000 to 6,000 (average of A and B over the starts): fresh 0.0251, earlier 0.0270
The two measures for the earlier run: same time +0.3162 (0.0722); later -0.2476 (0.0353)