Cause test: October 12, 2026. N = 4,000 per group, K = 1.90, eps = 0.1; starts 19 to 60 (42), 10 moments each.
Pre-registered: cause_test_prereg.md (SHA-256 1c44034e64f4ec74d5afba7080cf1df1e96262680583f785447b153f3ce61112), locked 2026-10-12 16:58 Halifax.
Run: 462 tasks in 37 pieces, 2026-10-12 17:27 Halifax to 2026-10-12 20:25 Halifax.
A toy model (two groups of phase oscillators): this shows structure in the model, not proof beyond it.

Question: If coherence is raised or lowered at a chosen moment, does the growth of a tiny gap 200 to 500 time units later change in the direction the correlation predicts, compared with a matched sham?

DECISION: FAIL: no effect of the interventions as large as half the benchmark. The correlation in the untouched runs is then most likely carried by something else, such as a slower feature of the state that drives both.

Manipulation checks
  moments carried out: 420 of 420 (fewest in a start: 10 of 10); at most 21 may be missing
  dense: every branch carried out inside its band True; same oscillators and sizes True (largest relative difference in sum of squared moves 0.0e+00); gap as it was True (largest 4.4e-10); M1 holds
  sparse: every branch carried out inside its band True; same oscillators and sizes True (largest relative difference in sum of squared moves 0.0e+00); gap as it was True (largest 1.6e-10); M1 holds
  M2: Phi = 0.511 pooled (dense 0.515, sparse 0.507); floor 0.181: holds

Primary measure: later growth over (T + 200, T + 500], each arm minus its own sham; each start's moments averaged, then the two methods, then the 42 starts (error bar: the larger of resampled and SD/sqrt(42))
  S = (D_down - D_up)/2   +0.00031 (error bar 0.00015; +2.1 error bars; above 0 in 24 of 42)
  D_up (up - sham)        -0.00158 (error bar 0.00027; -6.0 error bars; above 0 in 8 of 42)
  D_down (down - sham)    -0.00096 (error bar 0.00024; -4.0 error bars; above 0 in 12 of 42)
  delta = 1/2 x 0.1602 x |dC| = 0.00104 (|dC| = 0.01303)
  clear (S > 3 error bars): False; sides: False; methods agree: False; excluded (S + 2 error bars < delta): True

Each method's own reading (beside the decision, not the decision)
  dense: FAIL
    S -0.00025 (error bar 0.00018; -1.4 error bars; above 0 in 18 of 42); D_up -0.00118 (error bar 0.00034; -3.5 error bars; above 0 in 12 of 42); D_down -0.00169 (error bar 0.00035; -4.8 error bars; above 0 in 9 of 42); delta 0.00104; M1 holds; Phi 0.515
  sparse: PARTIAL (down is not clearly above its sham)
    S +0.00087 (error bar 0.00020; +4.3 error bars; above 0 in 30 of 42); D_up -0.00198 (error bar 0.00038; -5.2 error bars; above 0 in 7 of 42); D_down -0.00023 (error bar 0.00040; -0.6 error bars; above 0 in 20 of 42); delta 0.00104; M1 holds; Phi 0.507
  dense S - sparse S: -0.00113 (error bar 0.00024; -4.6 error bars; above 0 in 8 of 42)

Also reported (fixed before the run, not used for the decision)
  P = (D_up + D_down)/2, a change of this size either way: pooled -0.00127 (error bar 0.00020; -6.3 error bars; above 0 in 6 of 42): slows later growth; dense -0.00144 (error bar 0.00029; -4.9 error bars; above 0 in 10 of 42): slows later growth; sparse -0.00110 (error bar 0.00033; -3.3 error bars; above 0 in 16 of 42): slows later growth
  sham against none (G_sham - G_none): dense +0.00095 (error bar 0.00032; +3.0 error bars; above 0 in 29 of 42); sparse +0.00226 (error bar 0.00037; +6.1 error bars; above 0 in 35 of 42)
  causal slope -S/|dC|: -0.0238 (error bar 0.0116); benchmark -0.1602; scaled by 0.363/Phi: -0.0169 (0.0082)
  growth over (T, T + 200]: pooled S -0.00491 (0.00016), D_up +0.00596 (0.00025), D_down -0.00386 (0.00029); dense S -0.00535 (0.00019), D_up +0.00717 (0.00031), D_down -0.00353 (0.00032); sparse S -0.00447 (0.00019), D_up +0.00475 (0.00032), D_down -0.00419 (0.00034)
  growth over (T, T + 500]: pooled S -0.00178 (0.00012), D_up +0.00144 (0.00020), D_down -0.00212 (0.00019); dense S -0.00229 (0.00014), D_up +0.00216 (0.00028), D_down -0.00243 (0.00026); sparse S -0.00126 (0.00015), D_up +0.00072 (0.00024), D_down -0.00181 (0.00027)
  coherence paths: Phi against sham: dense up 0.591, down 0.439; sparse up 0.506, down 0.508; share of the up - down difference left over (T + 200, T + 500]: pooled 0.297, dense 0.318, sparse 0.275

What the changes did to the state, just after the change (moments carried out; average over the starts, with its error bar, and the range over moments). Reported, not used for the decision.
  dense
    R_A after / before: up +1.4999 [+1.4993, +1.5001]; down +0.4999 [+0.4993, +0.5001]; sham +0.9999 [+0.9993, +1.0001] | up - sham +0.5000 (0.0000); down - sham -0.5000 (0.0000)
    R_B after / before: up +1.4999 [+1.4993, +1.5001]; down +0.4999 [+0.4993, +0.5001]; sham +0.9999 [+0.9993, +1.0001] | up - sham +0.5000 (0.0000); down - sham -0.5000 (0.0000)
    change in C: up +0.01302 [+0.00218, +0.03345]; down -0.01303 [-0.03352, -0.00218]; sham -0.00000 [-0.00004, +0.00000] | up - sham +0.01303 (0.00028); down - sham -0.01303 (0.00028)
    change in C / C: up +0.4999 [+0.4994, +0.5000]; down -0.5001 [-0.5006, -0.5000]; sham -0.0001 [-0.0006, +0.0001] | up - sham +0.5000 (0.0000); down - sham -0.5000 (0.0000)
    change in psi_A: up -0.00006 [-0.00768, +0.00761]; down +0.00019 [-0.02291, +0.02304]; sham -0.00008 [-0.01609, +0.01825] | up - sham +0.00002 (0.00027); down - sham +0.00027 (0.00056)
    change in psi_B: up +0.00033 [-0.01176, +0.01053]; down -0.00100 [-0.03188, +0.03533]; sham +0.00019 [-0.01688, +0.01651] | up - sham +0.00014 (0.00037); down - sham -0.00119 (0.00067)
    change in psi_A - psi_B: up -0.00039 [-0.01307, +0.01405]; down +0.00118 [-0.04214, +0.03967]; sham -0.00027 [-0.02408, +0.02101] | up - sham -0.00012 (0.00045); down - sham +0.00146 (0.00095)
    change in |z2| A: up +0.000206 [-0.005233, +0.006834]; down -0.000008 [-0.002869, +0.002796]; sham +0.000048 [-0.002447, +0.002636] | up - sham +0.000158 (0.000049); down - sham -0.000056 (0.000047)
    change in |z2| B: up +0.000231 [-0.004468, +0.006623]; down -0.000017 [-0.002518, +0.002904]; sham +0.000042 [-0.002234, +0.002975] | up - sham +0.000188 (0.000040); down - sham -0.000059 (0.000042)
    change in |z3| A: up -0.000008 [-0.003642, +0.002298]; down +0.000004 [-0.002355, +0.003263]; sham -0.000011 [-0.002328, +0.003746] | up - sham +0.000003 (0.000050); down - sham +0.000015 (0.000039)
    change in |z3| B: up -0.000002 [-0.002517, +0.003347]; down +0.000014 [-0.003127, +0.002279]; sham -0.000042 [-0.001894, +0.002108] | up - sham +0.000040 (0.000039); down - sham +0.000056 (0.000043)
    change in |z4| A: up -0.000011 [-0.003625, +0.003731]; down +0.000027 [-0.003646, +0.002817]; sham +0.000019 [-0.002896, +0.003125] | up - sham -0.000030 (0.000062); down - sham +0.000008 (0.000058)
    change in |z4| B: up +0.000009 [-0.002757, +0.004490]; down -0.000018 [-0.004976, +0.002549]; sham +0.000034 [-0.003311, +0.004258] | up - sham -0.000025 (0.000070); down - sham -0.000051 (0.000053)
  sparse
    R_A after / before: up +1.4990 [+1.4878, +1.5036]; down +0.4990 [+0.4878, +0.5036]; sham +0.9990 [+0.9886, +1.0063] | up - sham +0.5000 (0.0001); down - sham -0.5000 (0.0001)
    R_B after / before: up +1.4991 [+1.4887, +1.5040]; down +0.4991 [+0.4887, +0.5040]; sham +0.9992 [+0.9865, +1.0069] | up - sham +0.4999 (0.0002); down - sham -0.5001 (0.0002)
    change in C: up +0.01299 [+0.00219, +0.03313]; down -0.01307 [-0.03384, -0.00218]; sham -0.00004 [-0.00061, +0.00012] | up - sham +0.01303 (0.00028); down - sham -0.01303 (0.00028)
    change in C / C: up +0.4989 [+0.4912, +0.5025]; down -0.5011 [-0.5088, -0.4975]; sham -0.0010 [-0.0097, +0.0049] | up - sham +0.4999 (0.0001); down - sham -0.5001 (0.0001)
    change in psi_A: up +0.00025 [-0.03649, +0.03312]; down +0.00134 [-0.09384, +0.11305]; sham -0.00045 [-0.04684, +0.06244] | up - sham +0.00070 (0.00104); down - sham +0.00178 (0.00201)
    change in psi_B: up +0.00064 [-0.03292, +0.03678]; down -0.00227 [-0.10968, +0.12851]; sham -0.00019 [-0.05191, +0.05025] | up - sham +0.00083 (0.00082); down - sham -0.00208 (0.00201)
    change in psi_A - psi_B: up -0.00039 [-0.04552, +0.04526]; down +0.00361 [-0.16257, +0.18935]; sham -0.00026 [-0.06907, +0.07784] | up - sham -0.00014 (0.00120); down - sham +0.00386 (0.00271)
    change in |z2| A: up +0.001940 [-0.013227, +0.026260]; down +0.001033 [-0.008488, +0.020507]; sham +0.001425 [-0.011209, +0.024994] | up - sham +0.000515 (0.000103); down - sham -0.000392 (0.000089)
    change in |z2| B: up +0.001823 [-0.009777, +0.025711]; down +0.001073 [-0.010358, +0.015286]; sham +0.001473 [-0.007714, +0.020188] | up - sham +0.000350 (0.000106); down - sham -0.000400 (0.000093)
    change in |z3| A: up +0.000576 [-0.010430, +0.017857]; down +0.000315 [-0.010517, +0.010269]; sham +0.000221 [-0.005193, +0.008722] | up - sham +0.000355 (0.000161); down - sham +0.000095 (0.000142)
    change in |z3| B: up +0.000520 [-0.015035, +0.018177]; down +0.000116 [-0.013280, +0.012245]; sham -0.000215 [-0.008215, +0.005060] | up - sham +0.000734 (0.000138); down - sham +0.000330 (0.000145)
    change in |z4| A: up +0.000243 [-0.011085, +0.017978]; down +0.000305 [-0.010380, +0.013567]; sham +0.000214 [-0.013374, +0.014466] | up - sham +0.000029 (0.000129); down - sham +0.000090 (0.000153)
    change in |z4| B: up +0.000140 [-0.012053, +0.014535]; down +0.000005 [-0.010235, +0.011251]; sham +0.000125 [-0.012606, +0.010281] | up - sham +0.000015 (0.000122); down - sham -0.000120 (0.000157)
  |z2| before (A, B): 0.01187, 0.01240; after: dense up 0.01208, 0.01263; dense down 0.01186, 0.01238; dense sham 0.01192, 0.01244; sparse up 0.01381, 0.01422; sparse down 0.01290, 0.01347; sparse sham 0.01329, 0.01387
  |z3| before (A, B): 0.01293, 0.01304; after: dense up 0.01293, 0.01304; dense down 0.01294, 0.01306; dense sham 0.01292, 0.01300; sparse up 0.01351, 0.01356; sparse down 0.01325, 0.01316; sparse sham 0.01316, 0.01283
  |z4| before (A, B): 0.01291, 0.01357; after: dense up 0.01290, 0.01358; dense down 0.01294, 0.01355; dense sham 0.01293, 0.01360; sparse up 0.01316, 0.01371; sparse down 0.01322, 0.01358; sparse sham 0.01313, 0.01370

The moves themselves (matched by construction; kept apart from their effects above)
  dense: up sum of squares 3.542 (largest 18.51), moved 7744, largest move 0.0326 (largest 0.0727), rms 0.0197; down sum of squares 3.542 (largest 18.51), moved 7744, largest move 0.0326 (largest 0.0727), rms 0.0197; sham sum of squares 3.542 (largest 18.51), moved 7744, largest move 0.0326 (largest 0.0727), rms 0.0197
  sparse: up sum of squares 37.2 (largest 204), moved 774, largest move 0.3331 (largest 0.7859), rms 0.2010; down sum of squares 37.2 (largest 204), moved 774, largest move 0.3331 (largest 0.7859), rms 0.2010; sham sum of squares 37.2 (largest 204), moved 774, largest move 0.3331 (largest 0.7859), rms 0.2010

Moments not carried out: 0

How much the moments of a start go together (intraclass correlation; design effect)
  pooled: S -0.010 (0.91); up -0.012 (0.89); down -0.035 (0.68)
  dense: S -0.024 (0.78); up -0.014 (0.87); down -0.017 (0.84)
  sparse: S +0.002 (1.02); up -0.010 (0.91); down -0.000 (1.00)

From the base runs (the 42 untouched new starts)
  long-run rate, t = 3,000 to 6,000: +0.0139 (0.0003); Test 16: +0.0147 (0.0006): agree (within 3 combined error bars)
  Test 17's conditional coefficient on these starts (its own code; not part of this decision): -0.1589 (error bar 0.0144; -11.0 error bars; below 0 in 39 of 42)

Per start: S, D_up, D_down (pooled); S dense, S sparse; moments carried out
  19: -0.00011 -0.00173 -0.00194 | -0.00164 +0.00142 | 10
  20: +0.00051 -0.00414 -0.00312 | +0.00021 +0.00081 | 10
  21: -0.00100 -0.00154 -0.00354 | -0.00261 +0.00061 | 10
  22: +0.00157 -0.00346 -0.00033 | +0.00084 +0.00229 | 10
  23: -0.00002 -0.00116 -0.00119 | -0.00045 +0.00042 | 10
  24: +0.00118 -0.00195 +0.00040 | +0.00004 +0.00231 | 10
  25: -0.00022 -0.00178 -0.00221 | -0.00119 +0.00076 | 10
  26: -0.00077 +0.00164 +0.00009 | -0.00045 -0.00110 | 10
  27: -0.00053 +0.00068 -0.00038 | -0.00065 -0.00040 | 10
  28: +0.00055 -0.00068 +0.00041 | -0.00006 +0.00115 | 10
  29: -0.00035 +0.00044 -0.00027 | -0.00009 -0.00062 | 10
  30: +0.00111 -0.00209 +0.00014 | -0.00004 +0.00227 | 10
  31: +0.00098 +0.00051 +0.00246 | -0.00025 +0.00221 | 10
  32: +0.00089 -0.00324 -0.00146 | -0.00073 +0.00250 | 10
  33: +0.00134 -0.00421 -0.00153 | +0.00118 +0.00149 | 10
  34: +0.00015 +0.00085 +0.00115 | +0.00059 -0.00029 | 10
  35: -0.00062 -0.00086 -0.00211 | -0.00108 -0.00017 | 10
  36: -0.00043 +0.00031 -0.00055 | -0.00081 -0.00005 | 10
  37: -0.00192 +0.00120 -0.00264 | -0.00194 -0.00190 | 10
  38: +0.00081 -0.00228 -0.00066 | +0.00138 +0.00025 | 10
  39: +0.00091 -0.00174 +0.00009 | +0.00051 +0.00132 | 10
  40: +0.00092 -0.00475 -0.00291 | +0.00085 +0.00099 | 10
  41: +0.00137 -0.00408 -0.00134 | +0.00215 +0.00059 | 10
  42: +0.00070 -0.00072 +0.00068 | -0.00023 +0.00163 | 10
  43: -0.00009 -0.00077 -0.00096 | -0.00117 +0.00098 | 10
  44: +0.00135 -0.00450 -0.00180 | -0.00117 +0.00386 | 10
  45: -0.00023 -0.00104 -0.00150 | +0.00095 -0.00141 | 10
  46: -0.00102 -0.00042 -0.00246 | -0.00136 -0.00068 | 10
  47: +0.00084 -0.00176 -0.00007 | +0.00078 +0.00091 | 10
  48: -0.00170 +0.00097 -0.00244 | -0.00227 -0.00113 | 10
  49: -0.00017 -0.00117 -0.00151 | -0.00013 -0.00021 | 10
  50: +0.00058 -0.00181 -0.00065 | +0.00055 +0.00061 | 10
  51: +0.00157 -0.00131 +0.00183 | +0.00002 +0.00312 | 10
  52: -0.00186 -0.00179 -0.00552 | -0.00311 -0.00062 | 10
  53: -0.00015 -0.00264 -0.00294 | -0.00165 +0.00134 | 10
  54: +0.00024 -0.00045 +0.00003 | +0.00015 +0.00034 | 10
  55: +0.00122 -0.00147 +0.00097 | +0.00003 +0.00241 | 10
  56: +0.00059 -0.00084 +0.00033 | -0.00042 +0.00159 | 10
  57: +0.00141 -0.00355 -0.00073 | +0.00160 +0.00122 | 10
  58: +0.00150 -0.00340 -0.00039 | +0.00111 +0.00190 | 10
  59: -0.00007 -0.00061 -0.00076 | -0.00108 +0.00094 | 10
  60: +0.00198 -0.00502 -0.00106 | +0.00094 +0.00303 | 10

Deviations from the plan: none