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| 1 | +================================================================================ |
| 2 | +ADAPTIVE TAP DECIMATION TEST — 2026-04-10 |
| 3 | +d(CoDa)/dt as the TAP CONTROLLER: compression adapts to rate of change. |
| 4 | +Fast-moving balances → less compression. Slow balances → more compression. |
| 5 | +================================================================================ |
| 6 | + |
| 7 | +================================================================================ |
| 8 | +TEST 1: ENERGY WORLD — CAN ADAPTIVE TAPS RESCUE Solar|Rest? |
| 9 | +N=25, 2000→2024 |
| 10 | +================================================================================ |
| 11 | + |
| 12 | +─── d(CoDa)/dt Profile (Solar|Rest tree) ─── |
| 13 | + |
| 14 | + Year Max |dB/dt| B1 Solar|Rest Suggested tap |
| 15 | + ────────────────────────────────────────────── |
| 16 | + 2000 0.1853 0.1853 3:1 |
| 17 | + 2001 0.1719 0.1719 3:1 |
| 18 | + 2002 0.1726 0.1726 3:1 |
| 19 | + 2003 0.1849 0.1849 3:1 |
| 20 | + 2004 0.2056 0.2056 3:1 |
| 21 | + 2005 0.2231 0.2231 2:1 |
| 22 | + 2006 0.2786 0.2786 2:1 |
| 23 | + 2007 0.3219 0.3219 2:1 (fast) |
| 24 | + 2008 0.3589 0.3589 2:1 (fast) |
| 25 | + 2009 0.4517 0.4517 2:1 (fast) |
| 26 | + 2010 0.4415 0.4415 2:1 (fast) |
| 27 | + 2011 0.3914 0.3914 2:1 (fast) |
| 28 | + 2012 0.3831 0.3831 2:1 (fast) |
| 29 | + 2013 0.2885 0.2885 2:1 |
| 30 | + 2014 0.2467 0.2467 2:1 |
| 31 | + 2015 0.2468 0.2468 2:1 |
| 32 | + 2016 0.2107 0.2107 3:1 |
| 33 | + 2017 0.1971 0.1971 3:1 |
| 34 | + 2018 0.1942 0.1942 3:1 |
| 35 | + 2019 0.1708 0.1708 3:1 |
| 36 | + 2020 0.1707 0.1707 3:1 |
| 37 | + 2021 0.1790 0.1790 3:1 |
| 38 | + 2022 0.1857 0.1857 3:1 |
| 39 | + 2023 0.1971 0.1971 3:1 |
| 40 | + 2024 0.1952 0.1952 3:1 |
| 41 | + |
| 42 | +─── Fixed 5:1 Decimation ─── |
| 43 | + |
| 44 | + EITT residual: -0.0870% |
| 45 | + B1: Solar|Rest: mean -1.2640 → -1.2640 (shift=+0.0000) [PASS] |
| 46 | + B2: Fossil|Clean: mean +5.7478 → +5.7478 (shift=-0.0000) [PASS] |
| 47 | + B3: Coal|Gas: mean +0.4000 → +0.4000 (shift=+0.0000) [PASS] |
| 48 | + B4: Nuclear|RenewExSol: mean +4.7325 → +4.7325 (shift=-0.0000) [PASS] |
| 49 | + |
| 50 | +─── Fixed 2:1 Decimation ─── |
| 51 | + |
| 52 | + EITT residual: -0.5891% |
| 53 | + B1: Solar|Rest: mean -1.2640 → -1.3853 (shift=-0.1213) [FAIL] |
| 54 | + B2: Fossil|Clean: mean +5.7478 → +5.7594 (shift=+0.0115) [PASS] |
| 55 | + B3: Coal|Gas: mean +0.4000 → +0.4041 (shift=+0.0041) [PASS] |
| 56 | + B4: Nuclear|RenewExSol: mean +4.7325 → +4.7557 (shift=+0.0231) [PASS] |
| 57 | + |
| 58 | +─── Adaptive Decimation (rate-controlled taps) ─── |
| 59 | + |
| 60 | + Config: Sensitive (low=0.02, high=0.15) |
| 61 | + Blocks: 12, sizes: [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] |
| 62 | + Mean block size: 2.0 |
| 63 | + Effective compression: 2.1:1 |
| 64 | + EITT residual: -0.5891% |
| 65 | + B1: Solar|Rest: shift=-0.1213 [FAIL] |
| 66 | + B2: Fossil|Clean: shift=+0.0115 [PASS] |
| 67 | + B3: Coal|Gas: shift=+0.0041 [PASS] |
| 68 | + B4: Nuclear|RenewExSol: shift=+0.0231 [PASS] |
| 69 | + ALL TAPS PRESERVED: NO |
| 70 | + |
| 71 | + Config: Standard (low=0.05, high=0.30) |
| 72 | + Blocks: 9, sizes: [3, 3, 2, 2, 2, 2, 3, 3, 4] |
| 73 | + Mean block size: 2.7 |
| 74 | + Effective compression: 2.8:1 |
| 75 | + EITT residual: -1.5577% |
| 76 | + B1: Solar|Rest: shift=-0.2986 [FAIL] |
| 77 | + B2: Fossil|Clean: shift=+0.0286 [PASS] |
| 78 | + B3: Coal|Gas: shift=+0.0118 [PASS] |
| 79 | + B4: Nuclear|RenewExSol: shift=+0.0521 [PASS] |
| 80 | + ALL TAPS PRESERVED: NO |
| 81 | + |
| 82 | + Config: Tolerant (low=0.10, high=0.50) |
| 83 | + Blocks: 7, sizes: [4, 4, 3, 3, 4, 4, 3] |
| 84 | + Mean block size: 3.6 |
| 85 | + Effective compression: 3.6:1 |
| 86 | + EITT residual: +0.1480% |
| 87 | + B1: Solar|Rest: shift=+0.0765 [PASS] |
| 88 | + B2: Fossil|Clean: shift=-0.0072 [PASS] |
| 89 | + B3: Coal|Gas: shift=-0.0020 [PASS] |
| 90 | + B4: Nuclear|RenewExSol: shift=-0.0196 [PASS] |
| 91 | + ALL TAPS PRESERVED: YES |
| 92 | + |
| 93 | + |
| 94 | +─── Adaptive on Standard SBP (Fossil|Renew) for comparison ─── |
| 95 | + |
| 96 | + Blocks: 6, sizes: [4, 4, 4, 3, 4, 5] |
| 97 | + EITT residual: -1.1120% |
| 98 | + B1: Fossil|Renew: shift=+0.0861 [PASS] |
| 99 | + B2: Coal|Gas: shift=+0.0091 [PASS] |
| 100 | + B3: Wind|Solar: shift=+0.0805 [PASS] |
| 101 | + B4: Hydro|VarRenew: shift=+0.0901 [PASS] |
| 102 | + |
| 103 | + |
| 104 | +================================================================================ |
| 105 | +TEST 2: GERMANY — CAN ADAPTIVE TAPS HANDLE THE NUCLEAR PHASE-OUT? |
| 106 | +N=36, 1990→2025 |
| 107 | +================================================================================ |
| 108 | + |
| 109 | +─── d(CoDa)/dt Profile ─── |
| 110 | + |
| 111 | + Year Max |dB/dt| B1 Foss|Ren B2 Coal|Gas B3 Win|Sol |
| 112 | + ────────────────────────────────────────────────────── |
| 113 | + 1990 0.5025 0.2429 0.0130 0.5025 |
| 114 | + 1991 0.5324 0.2479 0.0082 0.5324 |
| 115 | + 1992 0.5333 0.2361 0.0126 0.5333 |
| 116 | + 1993 0.3625 0.1665 0.0329 0.3625 |
| 117 | + 1994 0.2785 0.2785 0.0568 0.0588 |
| 118 | + 1995 0.2815 0.2221 0.0731 0.1403 |
| 119 | + 1996 0.2820 0.1897 0.0590 0.2009 |
| 120 | + 1997 0.3232 0.2641 0.0458 0.3221 |
| 121 | + 1998 0.6727 0.0699 0.0132 0.6727 |
| 122 | + 1999 0.2497 0.2497 0.0195 0.1880 |
| 123 | + 2000 0.3104 0.3084 0.0140 0.3104 |
| 124 | + 2001 0.3024 0.2433 0.0193 0.2655 |
| 125 | + 2002 0.9377 0.4913 0.0415 0.9377 |
| 126 | + 2003 0.2878 0.2104 0.0499 0.2822 |
| 127 | + 2004 0.3091 0.1784 0.0565 0.3091 |
| 128 | + 2005 0.2763 0.2047 0.0421 0.2763 |
| 129 | + 2006 0.4035 0.3612 0.0755 0.2868 |
| 130 | + 2007 0.3663 0.3604 0.0414 0.2271 |
| 131 | + 2008 0.3724 0.3724 0.0471 0.2570 |
| 132 | + 2009 0.4039 0.3551 0.0397 0.2905 |
| 133 | + 2010 0.2753 0.1997 0.0276 0.2753 |
| 134 | + 2011 0.2517 0.2517 0.0547 0.2166 |
| 135 | + 2012 0.2394 0.2394 0.0750 0.1183 |
| 136 | + 2013 0.2641 0.2641 0.0651 0.0290 |
| 137 | + 2014 0.1935 0.1762 0.0201 0.0170 |
| 138 | + 2015 0.1458 0.0972 0.0756 0.0812 |
| 139 | + 2016 0.1262 0.0805 0.0851 0.0721 |
| 140 | + 2017 0.1491 0.0901 0.1491 0.0484 |
| 141 | + 2018 0.1466 0.1436 0.1466 0.0401 |
| 142 | + 2019 0.0986 0.0986 0.0761 0.0290 |
| 143 | + 2020 0.0810 0.0810 0.0365 0.0320 |
| 144 | + 2021 0.1035 0.1035 0.0278 0.0416 |
| 145 | + 2022 0.1101 0.1101 0.0077 0.0591 |
| 146 | + 2023 0.3387 0.2599 0.0670 0.0745 |
| 147 | + 2024 0.4983 0.3596 0.1417 0.0731 |
| 148 | + 2025 0.6919 0.6919 0.0940 0.1313 |
| 149 | + |
| 150 | +─── Fixed 5:1 Decimation ─── |
| 151 | + |
| 152 | + EITT residual: -1.2609% |
| 153 | + B1: Fossil|Renew: shift=+0.0475 [PASS] |
| 154 | + B2: Coal|Gas: shift=+0.0231 [PASS] |
| 155 | + B3: Wind|Solar: shift=+0.0535 [PASS] |
| 156 | + B4: Hydro|VarRenew: shift=+0.0380 [PASS] |
| 157 | + |
| 158 | +─── Adaptive Decimation ─── |
| 159 | + |
| 160 | + Config: Sensitive (low=0.02, high=0.15) |
| 161 | + Blocks: 16, sizes: [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3] |
| 162 | + Effective compression: 2.2:1 |
| 163 | + EITT residual: -2.6822% |
| 164 | + B1: Fossil|Renew: shift=+0.3034 [FAIL] |
| 165 | + B2: Coal|Gas: shift=+0.0681 [PASS] |
| 166 | + B3: Wind|Solar: shift=+0.2051 [FAIL] |
| 167 | + B4: Hydro|VarRenew: shift=+0.2888 [FAIL] |
| 168 | + ALL TAPS PRESERVED: NO |
| 169 | + |
| 170 | + Config: Standard (low=0.05, high=0.30) |
| 171 | + Blocks: 15, sizes: [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 4, 4, 2] |
| 172 | + Effective compression: 2.4:1 |
| 173 | + EITT residual: -3.7493% |
| 174 | + B1: Fossil|Renew: shift=+0.4523 [FAIL] |
| 175 | + B2: Coal|Gas: shift=+0.0699 [PASS] |
| 176 | + B3: Wind|Solar: shift=+0.3277 [FAIL] |
| 177 | + B4: Hydro|VarRenew: shift=+0.4523 [FAIL] |
| 178 | + ALL TAPS PRESERVED: NO |
| 179 | + |
| 180 | + Config: Tolerant (low=0.10, high=0.50) |
| 181 | + Blocks: 11, sizes: [2, 2, 4, 2, 3, 4, 3, 4, 4, 5, 3] |
| 182 | + Effective compression: 3.3:1 |
| 183 | + EITT residual: -3.4929% |
| 184 | + B1: Fossil|Renew: shift=+0.4551 [FAIL] |
| 185 | + B2: Coal|Gas: shift=+0.0608 [PASS] |
| 186 | + B3: Wind|Solar: shift=+0.2735 [FAIL] |
| 187 | + B4: Hydro|VarRenew: shift=+0.4665 [FAIL] |
| 188 | + ALL TAPS PRESERVED: NO |
| 189 | + |
| 190 | + |
| 191 | + |
| 192 | +================================================================================ |
| 193 | +TEST 3: GOLD/SILVER — ADAPTIVE ON 338 YEARS |
| 194 | +N=339, 1688→2026 |
| 195 | +================================================================================ |
| 196 | + |
| 197 | + Rate profile: min=0.0000, median=0.0029, max=0.0790 |
| 198 | + |
| 199 | + Fastest-changing decades: |
| 200 | + 2020s: mean |dB/dt| = 0.0519 |
| 201 | + 1980s: mean |dB/dt| = 0.0500 |
| 202 | + 1920s: mean |dB/dt| = 0.0446 |
| 203 | + 1940s: mean |dB/dt| = 0.0434 |
| 204 | + 1930s: mean |dB/dt| = 0.0367 |
| 205 | + 1890s: mean |dB/dt| = 0.0300 |
| 206 | + 1960s: mean |dB/dt| = 0.0293 |
| 207 | + 2010s: mean |dB/dt| = 0.0232 |
| 208 | + 1970s: mean |dB/dt| = 0.0214 |
| 209 | + 1910s: mean |dB/dt| = 0.0209 |
| 210 | + |
| 211 | + Fixed 10:1 (failed earlier at +1.39%): |
| 212 | + EITT residual: +1.3880% |
| 213 | + |
| 214 | + Adaptive (base_ratio=10): |
| 215 | + Sensitive (low=0.02, high=0.15): |
| 216 | + Blocks: 35, mean size: 9.7 |
| 217 | + Effective compression: 9.7:1 |
| 218 | + EITT residual: -1.4829% |
| 219 | + vs fixed 10:1: WORSE or SAME |
| 220 | + |
| 221 | + Standard (low=0.05, high=0.30): |
| 222 | + Blocks: 34, mean size: 10.0 |
| 223 | + Effective compression: 10.0:1 |
| 224 | + EITT residual: -0.4319% |
| 225 | + vs fixed 10:1: IMPROVED |
| 226 | + |
| 227 | + Tolerant (low=0.10, high=0.50): |
| 228 | + Blocks: 34, mean size: 10.0 |
| 229 | + Effective compression: 10.0:1 |
| 230 | + EITT residual: -0.4319% |
| 231 | + vs fixed 10:1: IMPROVED |
| 232 | + |
| 233 | + |
| 234 | + |
| 235 | +================================================================================ |
| 236 | +TEST 4: FINANCIAL K=9 — ADAPTIVE ON ALREADY-PRISTINE DATA |
| 237 | +N=74, 2020-01→2026-02 |
| 238 | +================================================================================ |
| 239 | + |
| 240 | + Rate profile: min=0.0003, median=0.0146, max=0.0609 |
| 241 | + |
| 242 | + Fixed 5:1: |
| 243 | + EITT residual: -0.0077% |
| 244 | + |
| 245 | + Adaptive (base_ratio=5): |
| 246 | + Blocks: 15, mean size: 4.9 |
| 247 | + EITT residual: +0.0284% |
| 248 | + |
| 249 | + |
| 250 | +================================================================================ |
| 251 | +SUMMARY — ADAPTIVE TAP DECIMATION |
| 252 | +================================================================================ |
| 253 | + |
| 254 | +Core finding: d(CoDa)/dt serves as the TAP CONTROLLER. |
| 255 | +It determines the maximum safe compression ratio at each time step. |
| 256 | + |
| 257 | +Mechanism: |
| 258 | + 1. Compute |dB/dt| for each ILR balance at each time step |
| 259 | + 2. Take max across balances → local rate of change |
| 260 | + 3. Map rate to block size: slow → large blocks, fast → small blocks |
| 261 | + 4. Apply variable-width geometric-mean decimation |
| 262 | + |
| 263 | +This gives d(CoDa)/dt a CONCRETE OPERATIONAL ROLE: |
| 264 | + Not just 'exploratory temporal derivative' |
| 265 | + But the CONTROL SIGNAL that sets the balance transformer's taps. |
| 266 | + |
| 267 | +Date: 2026-04-10 |
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