Cause test, design numbers: October 12, 2026. N = 4,000 per group, K = 1.90, eps = 0.1 Read-only, from the 18 saved starts (1 to 6: Test 16's long run; 7 to 12: the coherence-growth test; 13 to 18: the replication). The model is not run; the chances of each decision are simulated sampling. Moments T = 2,000, 2,005, ..., 5,500 in every start (701 per start). W: the growth rate of the gap over (T + 200, T + 500]. C: the coherence |z| at T, average of A and B. The benchmark: least squares start by start, then averaged over the 18 starts W = a + beta C(T) + c1 g1 + ... + c5 g5 (beta) -0.1602 (SD 0.0934, SD/sqrt(18) 0.0220); 1 to 6 -0.2251, 7 to 12 -0.1420, 13 to 18 -0.1134 W = a + beta C(T) (no earlier growth held fixed) -0.2132 (SD 0.0730, SD/sqrt(18) 0.0172); 1 to 6 -0.2384, 7 to 12 -0.1932, 13 to 18 -0.2079 with C averaged over (T - 5, T], as Test 17 -0.2374 (SD 0.1294, SD/sqrt(18) 0.0305); 1 to 6 -0.3245, 7 to 12 -0.2121, 13 to 18 -0.1756 below 0 in 18 of 18 starts (held fixed), 18 of 18 (plain) Spread later growth W: average 0.0140, SD within a start 0.00649 (root mean square over the starts) W left over once C(T) and g1 to g5 are known: 0.00552 (root mean square over the starts; per start 0.00364 to 0.00707) C at T: average 0.0260, SD within a start 0.0107 Natural persistence: the slope of the mean coherence over a later stretch on C(T) (T, T + 100] +0.423 (SD 0.065, SD/sqrt(18) 0.015); 1 to 6 +0.471, 7 to 12 +0.401, 13 to 18 +0.396 (T, T + 200] +0.363 (SD 0.062, SD/sqrt(18) 0.015); 1 to 6 +0.409, 7 to 12 +0.338, 13 to 18 +0.340 (T + 200, T + 500] +0.106 (SD 0.080, SD/sqrt(18) 0.019); 1 to 6 +0.136, 7 to 12 +0.087, 13 to 18 +0.096 autocorrelation of C, t = 2,000 to 5,500 (average over the starts): lag 1: 0.72, lag 5: 0.58, lag 25: 0.42, lag 100: 0.35, lag 200: 0.25, lag 500: -0.03 Each group's coherence, t = 2,000 to 5,500, all starts: centiles 1%: 0.003, 5%: 0.007, 25%: 0.016, 50%: 0.025, 75%: 0.034, 95%: 0.049, 99%: 0.060 Pulled oscillators per group: 3,872 of 4,000 (natural rates within +/-20); the sparse method moves 387 of them Planned largest phase change, radians, to move a group's coherence by 50% (first order: a = 0.5 R / ((1/N) sum of sin^2), about 1.03 R dense and 10.3 R sparse): at the 1% centile (R = 0.003): dense 0.003, sparse 0.032 at the 5% centile (R = 0.007): dense 0.007, sparse 0.073 at the 25% centile (R = 0.016): dense 0.017, sparse 0.168 at the 50% centile (R = 0.025): dense 0.026, sparse 0.256 at the 75% centile (R = 0.034): dense 0.035, sparse 0.354 at the 95% centile (R = 0.049): dense 0.051, sparse 0.508 at the 99% centile (R = 0.060): dense 0.062, sparse 0.624 Numbers the plan is set from benchmark slope |beta| = 0.1602; expected |change in C| = 0.5 x 0.0260 = 0.0130 if the whole link were cause: D_up = -0.00208, D_down = +0.00208, S = 0.00208 (15% of the average later growth; 0.32 SD of W) threshold delta = 0.5 x |beta| x |change in C| = 0.00104 persistence floor for a null result = 0.5 x 0.363 = 0.181 How much the ten moments of one start go together: the correlation between moments 350, 700, ..., 3,150 time units apart (average over the 18 starts; removing each start's own mean pulls these slightly below 0) W left over 350: -0.04, 700: -0.03, 1,050: -0.24, 1,400: -0.19, 1,750: +0.01, 2,100: +0.01, 2,450: +0.04, 2,800: +0.06, 3,150: -0.14; average over all 45 pairs of ten moments -0.068 W 350: +0.05, 700: -0.21, 1,050: -0.29, 1,400: -0.20, 1,750: +0.00, 2,100: +0.12, 2,450: +0.12, 2,800: -0.12, 3,150: -0.24; average over all 45 pairs of ten moments -0.091 C 350: +0.11, 700: -0.11, 1,050: -0.16, 1,400: -0.08, 1,750: +0.10, 2,100: +0.14, 2,450: +0.06, 2,800: -0.01, 3,150: -0.04; average over all 45 pairs of ten moments -0.010 W left over, each start's own average over the 45 pairs: -0.177 to +0.034 so: expected noise, moments independent; most cautious, 0.1 of the noise shared by a start's moments (above every start's own value) Chance of each decision, made by the plan's own rule (cause_rule.py): 4,000 simulated repeats of the whole test per row (20,000 for no effect); 42 starts, 10 moments, 2 methods, 3 arms; manipulation checks taken as passed; sampling only, not the model the benchmark's size: D_up = -0.00208, D_down = +0.00208 in both methods; threshold 0.00104 noise, expected: the spread left over once C and the earlier growth are known (0.00552), every branch and every moment independent overall decision PASS SMALL PARTIAL REVERSED FAIL INCONCLUSIVE error bar of S no effect 0.0000 0.0000 0.0020 0.0019 0.9961 0.0000 0.00013 a quarter of the benchmark 0.0000 0.1440 0.6593 0.0000 0.1968 0.0000 0.00013 half the benchmark 0.4930 0.4348 0.0722 0.0000 0.0000 0.0000 0.00013 the benchmark 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00013 the benchmark, starts differ by half of it 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00021 the benchmark, plus a kick speeding growth as much 0.0232 0.0000 0.9768 0.0000 0.0000 0.0000 0.00013 only lowering matters, the benchmark's size 0.0248 0.0037 0.9715 0.0000 0.0000 0.0000 0.00013 the benchmark in the dense method only 0.0275 0.0005 0.9720 0.0000 0.0000 0.0000 0.00013 the benchmark in the sparse method only 0.0227 0.0000 0.9772 0.0000 0.0000 0.0000 0.00013 reversed, the benchmark's size 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000 0.00013 each method's own reading, the same rule: dense | sparse (PASS, then PASS, SMALL or PARTIAL) no effect 0.000, 0.002 | 0.000, 0.003 a quarter of the benchmark 0.002, 0.405 | 0.002, 0.404 half the benchmark 0.379, 0.991 | 0.379, 0.992 the benchmark 0.999, 1.000 | 1.000, 1.000 the benchmark, starts differ by half of it 0.997, 1.000 | 0.998, 1.000 the benchmark, plus a kick speeding growth as much 0.025, 1.000 | 0.025, 1.000 only lowering matters, the benchmark's size 0.022, 0.988 | 0.023, 0.992 the benchmark in the dense method only 1.000, 1.000 | 0.000, 0.001 the benchmark in the sparse method only 0.000, 0.002 | 0.998, 1.000 reversed, the benchmark's size 0.000, 0.000 | 0.000, 0.000 noise, most cautious: all of later growth's spread (0.00649), the two methods' noise identical, and 0.1 of its variance shared by the ten moments of a start overall decision PASS SMALL PARTIAL REVERSED FAIL INCONCLUSIVE error bar of S no effect 0.0000 0.0000 0.0023 0.0019 0.9077 0.0880 0.00031 a quarter of the benchmark 0.0018 0.0000 0.1008 0.0000 0.3790 0.5185 0.00031 half the benchmark 0.0762 0.0000 0.5633 0.0000 0.0333 0.3272 0.00031 the benchmark 0.8035 0.0000 0.1965 0.0000 0.0000 0.0000 0.00031 the benchmark, starts differ by half of it 0.7812 0.0000 0.2162 0.0000 0.0000 0.0025 0.00035 the benchmark, plus a kick speeding growth as much 0.0323 0.0000 0.9675 0.0000 0.0000 0.0003 0.00031 only lowering matters, the benchmark's size 0.0143 0.0000 0.6300 0.0000 0.0235 0.3322 0.00031 the benchmark in the dense method only 0.0205 0.0000 0.6228 0.0000 0.0245 0.3322 0.00031 the benchmark in the sparse method only 0.0192 0.0000 0.6215 0.0000 0.0257 0.3335 0.00031 reversed, the benchmark's size 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000 0.00031 each method's own reading, the same rule: dense | sparse (PASS, then PASS, SMALL or PARTIAL) no effect 0.000, 0.002 | 0.000, 0.002 a quarter of the benchmark 0.002, 0.103 | 0.002, 0.103 half the benchmark 0.076, 0.640 | 0.076, 0.640 the benchmark 0.803, 1.000 | 0.803, 1.000 the benchmark, starts differ by half of it 0.781, 0.998 | 0.781, 0.998 the benchmark, plus a kick speeding growth as much 0.032, 1.000 | 0.032, 1.000 only lowering matters, the benchmark's size 0.014, 0.644 | 0.014, 0.644 the benchmark in the dense method only 0.817, 1.000 | 0.000, 0.004 the benchmark in the sparse method only 0.000, 0.003 | 0.826, 0.999 reversed, the benchmark's size 0.000, 0.000 | 0.000, 0.000 noise, the measured shape: expected, but drawn from what is left over in the saved runs (its actual shape) overall decision PASS SMALL PARTIAL REVERSED FAIL INCONCLUSIVE error bar of S no effect 0.0000 0.0000 0.0022 0.0024 0.9954 0.0000 0.00013 half the benchmark 0.4905 0.4475 0.0620 0.0000 0.0000 0.0000 0.00013 the benchmark 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00013 noise, moments sharing a tenth: expected, but 0.1 of the variance shared by a start's moments overall decision PASS SMALL PARTIAL REVERSED FAIL INCONCLUSIVE error bar of S no effect 0.0000 0.0000 0.0024 0.0021 0.9955 0.0001 0.00019 half the benchmark 0.3922 0.1792 0.4230 0.0000 0.0043 0.0013 0.00018 the benchmark 0.9992 0.0000 0.0008 0.0000 0.0000 0.0000 0.00019 noise from 0.5 to 3 times the expected (2,000 repeats each): overall PASS | PASS, SMALL or PARTIAL | FAIL | INCONCLUSIVE no effect x0.5: 0.000 | 0.001 | 0.998 | 0.000 x1: 0.000 | 0.003 | 0.995 | 0.000 x1.5: 0.000 | 0.004 | 0.995 | 0.000 x2: 0.000 | 0.002 | 0.961 | 0.035 x2.5: 0.000 | 0.003 | 0.861 | 0.135 x3: 0.000 | 0.002 | 0.698 | 0.299 half the benchmark x0.5: 0.496 | 1.000 | 0.000 | 0.000 x1: 0.503 | 1.000 | 0.000 | 0.000 x1.5: 0.353 | 0.976 | 0.012 | 0.012 x2: 0.132 | 0.795 | 0.022 | 0.183 x2.5: 0.048 | 0.519 | 0.022 | 0.459 x3: 0.015 | 0.351 | 0.027 | 0.622 the benchmark x0.5: 1.000 | 1.000 | 0.000 | 0.000 x1: 1.000 | 1.000 | 0.000 | 0.000 x1.5: 0.998 | 1.000 | 0.000 | 0.000 x2: 0.924 | 1.000 | 0.000 | 0.000 x2.5: 0.729 | 0.999 | 0.000 | 0.002 x3: 0.449 | 0.983 | 0.000 | 0.017 for comparison, the first draft's 21 starts (the same rule and noise models): expected, 21 starts PASS SMALL PARTIAL REVERSED FAIL INCONCLUSIVE error bar of S no effect 0.0000 0.0000 0.0036 0.0043 0.9918 0.0003 0.00019 the benchmark 0.9998 0.0000 0.0003 0.0000 0.0000 0.0000 0.00019 most cautious, 21 starts PASS SMALL PARTIAL REVERSED FAIL INCONCLUSIVE error bar of S no effect 0.0000 0.0000 0.0031 0.0038 0.6475 0.3456 0.00043 the benchmark 0.3730 0.0000 0.5745 0.0000 0.0003 0.0522 0.00043 False positives: with no effect, the chance of a reading in the predicted direction (PASS, SMALL or PARTIAL) bound: each needs S above 0 by more than 3 error bars, and the error bar is never below SD / sqrt(42); with normal per-start values the chance is at most P(t, 41 degrees of freedom, > 3) = 0.0023, at any noise level. The same bound holds for REVERSED. simulated, each with its own sampling error (+/- one SD of a share from that many repeats): expected overall 0.0020 +/- 0.0003 (REVERSED 0.0019 +/- 0.0003); dense alone 0.0022, sparse alone 0.0027; 20,000 repeats most cautious overall 0.0023 +/- 0.0003 (REVERSED 0.0019 +/- 0.0003); dense alone 0.0023, sparse alone 0.0023; 20,000 repeats the measured shape overall 0.0022 +/- 0.0003 (REVERSED 0.0024 +/- 0.0003); dense alone 0.0028, sparse alone 0.0027; 20,000 repeats moments sharing a tenth overall 0.0024 +/- 0.0003 (REVERSED 0.0021 +/- 0.0003); dense alone 0.0024, sparse alone 0.0024; 20,000 repeats expected, x0.5 overall 0.0010 +/- 0.0007 (REVERSED 0.0015 +/- 0.0009); dense alone 0.0020, sparse alone 0.0035; 2,000 repeats expected, x1 overall 0.0025 +/- 0.0011 (REVERSED 0.0030 +/- 0.0012); dense alone 0.0030, sparse alone 0.0030; 2,000 repeats expected, x1.5 overall 0.0040 +/- 0.0014 (REVERSED 0.0015 +/- 0.0009); dense alone 0.0035, sparse alone 0.0010; 2,000 repeats expected, x2 overall 0.0015 +/- 0.0009 (REVERSED 0.0020 +/- 0.0010); dense alone 0.0030, sparse alone 0.0025; 2,000 repeats expected, x2.5 overall 0.0030 +/- 0.0012 (REVERSED 0.0015 +/- 0.0009); dense alone 0.0020, sparse alone 0.0025; 2,000 repeats expected, x3 overall 0.0020 +/- 0.0010 (REVERSED 0.0010 +/- 0.0007); dense alone 0.0010, sparse alone 0.0025; 2,000 repeats Computing: the replication ran one start (settling, then 2 copies x 6,000 time units) in 154 s per worker, six at once: 80 copy-time-units per second per worker. this plan: 516,600 copy-time-units of base runs + 2,520,000 of branches = 3,036,600; at that pace with 7 workers about 90 minutes Moment table (cause_moments.csv): starts 19 to 60, moments T = 2,000 + offset + 350 m (m = 0 to 9), offset from seed (20261012, seed of the start): 19: 280, 20: 30, 21: 185, 22: 335, 23: 65, 24: 245, 25: 30, 26: 320, 27: 35, 28: 335, 29: 115, 30: 205, 31: 160, 32: 125, 33: 145, 34: 35, 35: 100, 36: 50, 37: 285, 38: 300, 39: 5, 40: 70, 41: 200, 42: 35, 43: 335, 44: 15, 45: 30, 46: 200, 47: 85, 48: 135, 49: 55, 50: 60, 51: 315, 52: 110, 53: 330, 54: 135, 55: 180, 56: 55, 57: 320, 58: 185, 59: 260, 60: 45