E-016b-v3-rootcause.py
Experiments: E-016b · script updated 08-18-2026
E-016b-v3-rootcause.csv
— 331.5 KB, updated 08-18-2026
| # | series | variant | a | y | resid | resid_shifted |
|---|---|---|---|---|---|---|
| 1502 | resid | notail | 4.0 | 30.100000 | 1.0207555989e-01 | -5.6414389502e-02 |
| 1503 | resid | notail | 4.0 | 30.200000 | 1.0227258966e-01 | -5.6217359735e-02 |
| 1504 | resid | notail | 4.0 | 30.300000 | 1.0247006401e-01 | -5.6019885386e-02 |
| 1505 | resid | notail | 4.0 | 30.400000 | 1.0266797832e-01 | -5.5821971071e-02 |
| 1506 | resid | notail | 4.0 | 30.500000 | 1.0286632805e-01 | -5.5623621349e-02 |
| 1507 | resid | notail | 4.0 | 30.600000 | 1.0306510867e-01 | -5.5424840719e-02 |
| 1508 | resid | notail | 4.0 | 30.700000 | 1.0326431577e-01 | -5.5225633623e-02 |
| 1509 | resid | notail | 4.0 | 30.800000 | 1.0346394495e-01 | -5.5026004446e-02 |
| 1510 | resid | notail | 4.0 | 30.900000 | 1.0366399188e-01 | -5.4825957515e-02 |
| 1511 | resid | notail | 4.0 | 31.000000 | 1.0386445229e-01 | -5.4625497103e-02 |
| 1512 | resid | notail | 4.0 | 31.100000 | 1.0406532196e-01 | -5.4424627431e-02 |
| 1513 | resid | notail | 4.0 | 31.200000 | 1.0426659673e-01 | -5.4223352662e-02 |
| 1514 | resid | notail | 4.0 | 31.300000 | 1.0446827248e-01 | -5.4021676912e-02 |
| 1515 | resid | notail | 4.0 | 31.400000 | 1.0467034515e-01 | -5.3819604240e-02 |
| 1516 | resid | notail | 4.0 | 31.500000 | 1.0487281074e-01 | -5.3617138657e-02 |
| 1517 | resid | notail | 4.0 | 31.600000 | 1.0507566527e-01 | -5.3414284124e-02 |
| 1518 | resid | notail | 4.0 | 31.700000 | 1.0527890484e-01 | -5.3211044551e-02 |
| 1519 | resid | notail | 4.0 | 31.800000 | 1.0548252559e-01 | -5.3007423802e-02 |
| 1520 | resid | notail | 4.0 | 31.900000 | 1.0568652370e-01 | -5.2803425691e-02 |
| 1521 | resid | notail | 4.0 | 32.000000 | 1.0589089541e-01 | -5.2599053986e-02 |
| 1522 | resid | notail | 4.0 | 32.100000 | 1.0609563699e-01 | -5.2394312408e-02 |
| 1523 | resid | notail | 4.0 | 32.200000 | 1.0630074476e-01 | -5.2189204633e-02 |
| 1524 | resid | notail | 4.0 | 32.300000 | 1.0650621510e-01 | -5.1983734293e-02 |
| 1525 | resid | notail | 4.0 | 32.400000 | 1.0671204442e-01 | -5.1777904975e-02 |
| 1526 | resid | notail | 4.0 | 32.500000 | 1.0691822917e-01 | -5.1571720221e-02 |
| 1527 | resid | notail | 4.0 | 32.600000 | 1.0712476586e-01 | -5.1365183533e-02 |
| 1528 | resid | notail | 4.0 | 32.700000 | 1.0733165103e-01 | -5.1158298368e-02 |
| 1529 | resid | notail | 4.0 | 32.800000 | 1.0753888125e-01 | -5.0951068145e-02 |
| 1530 | resid | notail | 4.0 | 32.900000 | 1.0774645316e-01 | -5.0743496238e-02 |
| 1531 | resid | notail | 4.0 | 33.000000 | 1.0795436341e-01 | -5.0535585984e-02 |
| 1532 | resid | notail | 4.0 | 33.100000 | 1.0816260871e-01 | -5.0327340680e-02 |
| 1533 | resid | notail | 4.0 | 33.200000 | 1.0837118581e-01 | -5.0118763581e-02 |
| 1534 | resid | notail | 4.0 | 33.300000 | 1.0858009149e-01 | -4.9909857906e-02 |
| 1535 | resid | notail | 4.0 | 33.400000 | 1.0878932256e-01 | -4.9700626837e-02 |
| 1536 | resid | notail | 4.0 | 33.500000 | 1.0899887588e-01 | -4.9491073516e-02 |
| 1537 | resid | notail | 4.0 | 33.600000 | 1.0920874834e-01 | -4.9281201050e-02 |
| 1538 | resid | notail | 4.0 | 33.700000 | 1.0941893688e-01 | -4.9071012510e-02 |
| 1539 | resid | notail | 4.0 | 33.800000 | 1.0962943846e-01 | -4.8860510929e-02 |
| 1540 | resid | notail | 4.0 | 33.900000 | 1.0984025009e-01 | -4.8649699308e-02 |
| 1541 | resid | notail | 4.0 | 34.000000 | 1.1005136878e-01 | -4.8438580611e-02 |
| 1542 | resid | notail | 4.0 | 34.100000 | 1.1026279163e-01 | -4.8227157768e-02 |
| 1543 | resid | notail | 4.0 | 34.200000 | 1.1047451572e-01 | -4.8015433678e-02 |
| 1544 | resid | notail | 4.0 | 34.300000 | 1.1068653819e-01 | -4.7803411202e-02 |
| 1545 | resid | notail | 4.0 | 34.400000 | 1.1089885622e-01 | -4.7591093173e-02 |
| 1546 | resid | notail | 4.0 | 34.500000 | 1.1111146700e-01 | -4.7378482390e-02 |
| 1547 | resid | notail | 4.0 | 34.600000 | 1.1132436777e-01 | -4.7165581619e-02 |
| 1548 | resid | notail | 4.0 | 34.700000 | 1.1153755580e-01 | -4.6952393597e-02 |
| 1549 | resid | notail | 4.0 | 34.800000 | 1.1175102837e-01 | -4.6738921028e-02 |
| 1550 | resid | notail | 4.0 | 34.900000 | 1.1196478281e-01 | -4.6525166588e-02 |
| 1551 | resid | notail | 4.0 | 35.000000 | 1.1217881647e-01 | -4.6311132920e-02 |
| 1552 | resid | notail | 4.0 | 35.100000 | 1.1239312675e-01 | -4.6096822640e-02 |
| 1553 | resid | notail | 4.0 | 35.200000 | 1.1260771106e-01 | -4.5882238333e-02 |
| 1554 | resid | notail | 4.0 | 35.300000 | 1.1282256684e-01 | -4.5667382558e-02 |
| 1555 | resid | notail | 4.0 | 35.400000 | 1.1303769155e-01 | -4.5452257844e-02 |
| 1556 | resid | notail | 4.0 | 35.500000 | 1.1325308270e-01 | -4.5236866690e-02 |
| 1557 | resid | notail | 4.0 | 35.600000 | 1.1346873782e-01 | -4.5021211571e-02 |
| 1558 | resid | notail | 4.0 | 35.700000 | 1.1368465446e-01 | -4.4805294934e-02 |
| 1559 | resid | notail | 4.0 | 35.800000 | 1.1390083020e-01 | -4.4589119198e-02 |
| 1560 | resid | notail | 4.0 | 35.900000 | 1.1411726264e-01 | -4.4372686756e-02 |
| 1561 | resid | notail | 4.0 | 36.000000 | 1.1433394942e-01 | -4.4155999976e-02 |
| 1562 | resid | notail | 4.0 | 36.100000 | 1.1455088819e-01 | -4.3939061200e-02 |
| 1563 | resid | notail | 4.0 | 36.200000 | 1.1476807665e-01 | -4.3721872743e-02 |
| 1564 | resid | notail | 4.0 | 36.300000 | 1.1498551250e-01 | -4.3504436897e-02 |
| 1565 | resid | notail | 4.0 | 36.400000 | 1.1520319346e-01 | -4.3286755930e-02 |
| 1566 | resid | notail | 4.0 | 36.500000 | 1.1542111731e-01 | -4.3068832083e-02 |
| 1567 | resid | notail | 4.0 | 36.600000 | 1.1563928182e-01 | -4.2850667575e-02 |
| 1568 | resid | notail | 4.0 | 36.700000 | 1.1585768479e-01 | -4.2632264601e-02 |
| 1569 | resid | notail | 4.0 | 36.800000 | 1.1607632406e-01 | -4.2413625334e-02 |
| 1570 | resid | notail | 4.0 | 36.900000 | 1.1629519747e-01 | -4.2194751921e-02 |
| 1571 | resid | notail | 4.0 | 37.000000 | 1.1651430290e-01 | -4.1975646489e-02 |
| 1572 | resid | notail | 4.0 | 37.100000 | 1.1673363825e-01 | -4.1756311142e-02 |
| 1573 | resid | notail | 4.0 | 37.200000 | 1.1695320143e-01 | -4.1536747961e-02 |
| 1574 | resid | notail | 4.0 | 37.300000 | 1.1717299039e-01 | -4.1316959005e-02 |
| 1575 | resid | notail | 4.0 | 37.400000 | 1.1739300308e-01 | -4.1096946314e-02 |
| 1576 | resid | notail | 4.0 | 37.500000 | 1.1761323749e-01 | -4.0876711905e-02 |
| 1577 | resid | notail | 4.0 | 37.600000 | 1.1783369162e-01 | -4.0656257774e-02 |
| 1578 | resid | notail | 4.0 | 37.700000 | 1.1805436350e-01 | -4.0435585897e-02 |
| 1579 | resid | notail | 4.0 | 37.800000 | 1.1827525117e-01 | -4.0214698228e-02 |
| 1580 | resid | notail | 4.0 | 37.900000 | 1.1849635269e-01 | -3.9993596704e-02 |
| 1581 | resid | notail | 4.0 | 38.000000 | 1.1871766615e-01 | -3.9772283239e-02 |
| 1582 | resid | notail | 4.0 | 38.100000 | 1.1893918966e-01 | -3.9550759730e-02 |
| 1583 | resid | notail | 4.0 | 38.200000 | 1.1916092134e-01 | -3.9329028052e-02 |
| 1584 | resid | notail | 4.0 | 38.300000 | 1.1938285933e-01 | -3.9107090065e-02 |
| 1585 | resid | notail | 4.0 | 38.400000 | 1.1960500179e-01 | -3.8884947605e-02 |
| 1586 | resid | notail | 4.0 | 38.500000 | 1.1982734690e-01 | -3.8662602493e-02 |
| 1587 | resid | notail | 4.0 | 38.600000 | 1.2004989286e-01 | -3.8440056532e-02 |
| 1588 | resid | notail | 4.0 | 38.700000 | 1.2027263789e-01 | -3.8217311504e-02 |
| 1589 | resid | notail | 4.0 | 38.800000 | 1.2049558022e-01 | -3.7994369175e-02 |
| 1590 | resid | notail | 4.0 | 38.900000 | 1.2071871810e-01 | -3.7771231294e-02 |
| 1591 | resid | notail | 4.0 | 39.000000 | 1.2094204980e-01 | -3.7547899591e-02 |
| 1592 | resid | notail | 4.0 | 39.100000 | 1.2116557361e-01 | -3.7324375780e-02 |
| 1593 | resid | notail | 4.0 | 39.200000 | 1.2138928784e-01 | -3.7100661558e-02 |
| 1594 | resid | notail | 4.0 | 39.300000 | 1.2161319079e-01 | -3.6876758604e-02 |
| 1595 | resid | notail | 4.0 | 39.400000 | 1.2183728081e-01 | -3.6652668582e-02 |
| 1596 | resid | notail | 4.0 | 39.500000 | 1.2206155626e-01 | -3.6428393139e-02 |
| 1597 | resid | notail | 4.0 | 39.600000 | 1.2228601549e-01 | -3.6203933905e-02 |
| 1598 | resid | notail | 4.0 | 39.700000 | 1.2251065690e-01 | -3.5979292497e-02 |
| 1599 | resid | notail | 4.0 | 39.800000 | 1.2273547888e-01 | -3.5754470512e-02 |
| 1600 | resid | notail | 4.0 | 39.900000 | 1.2296047986e-01 | -3.5529469534e-02 |
| 1601 | resid | notail | 4.0 | 40.000000 | 1.2318565826e-01 | -3.5304291133e-02 |
| 1602 | resid | base+pair | 4.0 | 0.100000 | 2.4275614176e-04 | 1.3863937342e+00 |
| 1603 | resid | base+pair | 4.0 | 0.200000 | 4.3152059332e-04 | 1.3865824986e+00 |
| 1604 | resid | base+pair | 4.0 | 0.300000 | 5.6629333078e-04 | 1.3867172714e+00 |
| 1605 | resid | base+pair | 4.0 | 0.400000 | 6.4707435431e-04 | 1.3867980524e+00 |
| 1606 | resid | base+pair | 4.0 | 0.500000 | 6.7386368798e-04 | 1.3868248417e+00 |
| 1607 | resid | base+pair | 4.0 | 0.600000 | 6.4666137988e-04 | 1.3867976394e+00 |
| 1608 | resid | base+pair | 4.0 | 0.700000 | 5.6546750199e-04 | 1.3867164455e+00 |
| 1609 | resid | base+pair | 4.0 | 0.800000 | 4.3028215027e-04 | 1.3865812602e+00 |
| 1610 | resid | base+pair | 4.0 | 0.900000 | 2.4110544463e-04 | 1.3863920835e+00 |
| 1611 | resid | base+pair | 4.0 | 1.000000 | -2.0624710451e-06 | 1.3861489156e+00 |
| 1612 | resid | base+pair | 4.0 | 1.100000 | -2.9922142895e-04 | 1.3858517566e+00 |
| 1613 | resid | base+pair | 4.0 | 1.200000 | -6.5037123729e-04 | 1.3855006068e+00 |
| 1614 | resid | base+pair | 4.0 | 1.300000 | -1.0555116804e-03 | 1.3850954663e+00 |
| 1615 | resid | base+pair | 4.0 | 1.400000 | -1.5146425185e-03 | 1.3846363355e+00 |
| 1616 | resid | base+pair | 4.0 | 1.500000 | -2.0277634880e-03 | 1.3841232145e+00 |
| 1617 | resid | base+pair | 4.0 | 1.600000 | -2.5948743013e-03 | 1.3835561037e+00 |
| 1618 | resid | base+pair | 4.0 | 1.700000 | -3.2159746469e-03 | 1.3829350034e+00 |
| 1619 | resid | base+pair | 4.0 | 1.800000 | -3.8910641893e-03 | 1.3822599138e+00 |
| 1620 | resid | base+pair | 4.0 | 1.900000 | -4.6201425690e-03 | 1.3815308355e+00 |
| 1621 | resid | base+pair | 4.0 | 2.000000 | -5.4032094027e-03 | 1.3807477686e+00 |
| 1622 | resid | base+pair | 4.0 | 2.100000 | -6.2402642831e-03 | 1.3799107137e+00 |
| 1623 | resid | base+pair | 4.0 | 2.200000 | -7.1313067788e-03 | 1.3790196712e+00 |
| 1624 | resid | base+pair | 4.0 | 2.300000 | -8.0763364347e-03 | 1.3780746416e+00 |
| 1625 | resid | base+pair | 4.0 | 2.400000 | -9.0753527715e-03 | 1.3770756253e+00 |
| 1626 | resid | base+pair | 4.0 | 2.500000 | -1.0128355286e-02 | 1.3760226227e+00 |
| 1627 | resid | base+pair | 4.0 | 2.600000 | -1.1235343452e-02 | 1.3749156346e+00 |
| 1628 | resid | base+pair | 4.0 | 2.700000 | -1.2396316717e-02 | 1.3737546613e+00 |
| 1629 | resid | base+pair | 4.0 | 2.800000 | -1.3611274507e-02 | 1.3725397035e+00 |
| 1630 | resid | base+pair | 4.0 | 2.900000 | -1.4880216223e-02 | 1.3712707618e+00 |
| 1631 | resid | base+pair | 4.0 | 3.000000 | -1.6203141242e-02 | 1.3699478368e+00 |
| 1632 | resid | base+pair | 4.0 | 3.100000 | -1.7580048918e-02 | 1.3685709291e+00 |
| 1633 | resid | base+pair | 4.0 | 3.200000 | -1.9010938579e-02 | 1.3671400394e+00 |
| 1634 | resid | base+pair | 4.0 | 3.300000 | -2.0495809531e-02 | 1.3656551685e+00 |
| 1635 | resid | base+pair | 4.0 | 3.400000 | -2.2034661056e-02 | 1.3641163170e+00 |
| 1636 | resid | base+pair | 4.0 | 3.500000 | -2.3627492411e-02 | 1.3625234856e+00 |
| 1637 | resid | base+pair | 4.0 | 3.600000 | -2.5274302829e-02 | 1.3608766752e+00 |
| 1638 | resid | base+pair | 4.0 | 3.700000 | -2.6975091521e-02 | 1.3591758865e+00 |
| 1639 | resid | base+pair | 4.0 | 3.800000 | -2.8729857671e-02 | 1.3574211204e+00 |
| 1640 | resid | base+pair | 4.0 | 3.900000 | -3.0538600442e-02 | 1.3556123776e+00 |
| 1641 | resid | base+pair | 4.0 | 4.000000 | -3.2401318972e-02 | 1.3537496591e+00 |
| 1642 | resid | base+pair | 4.0 | 4.100000 | -3.4318012375e-02 | 1.3518329656e+00 |
| 1643 | resid | base+pair | 4.0 | 4.200000 | -3.6288679740e-02 | 1.3498622983e+00 |
| 1644 | resid | base+pair | 4.0 | 4.300000 | -3.8313320133e-02 | 1.3478376579e+00 |
| 1645 | resid | base+pair | 4.0 | 4.400000 | -4.0391932598e-02 | 1.3457590454e+00 |
| 1646 | resid | base+pair | 4.0 | 4.500000 | -4.2524516152e-02 | 1.3436264619e+00 |
| 1647 | resid | base+pair | 4.0 | 4.600000 | -4.4711069789e-02 | 1.3414399082e+00 |
| 1648 | resid | base+pair | 4.0 | 4.700000 | -4.6951592480e-02 | 1.3391993855e+00 |
| 1649 | resid | base+pair | 4.0 | 4.800000 | -4.9246083172e-02 | 1.3369048949e+00 |
| 1650 | resid | base+pair | 4.0 | 4.900000 | -5.1594540787e-02 | 1.3345564372e+00 |
| 1651 | resid | base+pair | 4.0 | 5.000000 | -5.3996964224e-02 | 1.3321540138e+00 |
| 1652 | resid | base+pair | 4.0 | 5.100000 | -5.6453352358e-02 | 1.3296976257e+00 |
| 1653 | resid | base+pair | 4.0 | 5.200000 | -5.8963704039e-02 | 1.3271872740e+00 |
| 1654 | resid | base+pair | 4.0 | 5.300000 | -6.1528018095e-02 | 1.3246229599e+00 |
| 1655 | resid | base+pair | 4.0 | 5.400000 | -6.4146293329e-02 | 1.3220046847e+00 |
| 1656 | resid | base+pair | 4.0 | 5.500000 | -6.6818528520e-02 | 1.3193324495e+00 |
| 1657 | resid | base+pair | 4.0 | 5.600000 | -6.9544722424e-02 | 1.3166062556e+00 |
| 1658 | resid | base+pair | 4.0 | 5.700000 | -7.2324873771e-02 | 1.3138261043e+00 |
| 1659 | resid | base+pair | 4.0 | 5.800000 | -7.5158981271e-02 | 1.3109919968e+00 |
| 1660 | resid | base+pair | 4.0 | 5.900000 | -7.8047043605e-02 | 1.3081039344e+00 |
| 1661 | resid | base+pair | 4.0 | 6.000000 | -8.0989059435e-02 | 1.3051619186e+00 |
| 1662 | resid | base+pair | 4.0 | 6.100000 | -8.3985027395e-02 | 1.3021659506e+00 |
| 1663 | resid | base+pair | 4.0 | 6.200000 | -8.7034946099e-02 | 1.2991160319e+00 |
| 1664 | resid | base+pair | 4.0 | 6.300000 | -9.0138814134e-02 | 1.2960121639e+00 |
| 1665 | resid | base+pair | 4.0 | 6.400000 | -9.3296630065e-02 | 1.2928543480e+00 |
| 1666 | resid | base+pair | 4.0 | 6.500000 | -9.6508392432e-02 | 1.2896425856e+00 |
| 1667 | resid | base+pair | 4.0 | 6.600000 | -9.9774099752e-02 | 1.2863768783e+00 |
| 1668 | resid | base+pair | 4.0 | 6.700000 | -1.0309375052e-01 | 1.2830572275e+00 |
| 1669 | resid | base+pair | 4.0 | 6.800000 | -1.0646734320e-01 | 1.2796836348e+00 |
| 1670 | resid | base+pair | 4.0 | 6.900000 | -1.0989487624e-01 | 1.2762561018e+00 |
| 1671 | resid | base+pair | 4.0 | 7.000000 | -1.1337634806e-01 | 1.2727746300e+00 |
| 1672 | resid | base+pair | 4.0 | 7.100000 | -1.1691175705e-01 | 1.2692392210e+00 |
| 1673 | resid | base+pair | 4.0 | 7.200000 | -1.2050110160e-01 | 1.2656498764e+00 |
| 1674 | resid | base+pair | 4.0 | 7.300000 | -1.2414438005e-01 | 1.2620065980e+00 |
| 1675 | resid | base+pair | 4.0 | 7.400000 | -1.2784159073e-01 | 1.2583093873e+00 |
| 1676 | resid | base+pair | 4.0 | 7.500000 | -1.3159273194e-01 | 1.2545582461e+00 |
| 1677 | resid | base+pair | 4.0 | 7.600000 | -1.3539780195e-01 | 1.2507531761e+00 |
| 1678 | resid | base+pair | 4.0 | 7.700000 | -1.3925679903e-01 | 1.2468941790e+00 |
| 1679 | resid | base+pair | 4.0 | 7.800000 | -1.4316972139e-01 | 1.2429812566e+00 |
| 1680 | resid | base+pair | 4.0 | 7.900000 | -1.4713656726e-01 | 1.2390144108e+00 |
| 1681 | resid | base+pair | 4.0 | 8.000000 | -1.5115733481e-01 | 1.2349936432e+00 |
| 1682 | resid | base+pair | 4.0 | 8.100000 | -1.5523202220e-01 | 1.2309189558e+00 |
| 1683 | resid | base+pair | 4.0 | 8.200000 | -1.5936062756e-01 | 1.2267903505e+00 |
| 1684 | resid | base+pair | 4.0 | 8.300000 | -1.6354314901e-01 | 1.2226078290e+00 |
| 1685 | resid | base+pair | 4.0 | 8.400000 | -1.6777958464e-01 | 1.2183713934e+00 |
| 1686 | resid | base+pair | 4.0 | 8.500000 | -1.7206993250e-01 | 1.2140810455e+00 |
| 1687 | resid | base+pair | 4.0 | 8.600000 | -1.7641419065e-01 | 1.2097367874e+00 |
| 1688 | resid | base+pair | 4.0 | 8.700000 | -1.8081235709e-01 | 1.2053386209e+00 |
| 1689 | resid | base+pair | 4.0 | 8.800000 | -1.8526442981e-01 | 1.2008865482e+00 |
| 1690 | resid | base+pair | 4.0 | 8.900000 | -1.8977040680e-01 | 1.1963805712e+00 |
| 1691 | resid | base+pair | 4.0 | 9.000000 | -1.9433028598e-01 | 1.1918206920e+00 |
| 1692 | resid | base+pair | 4.0 | 9.100000 | -1.9894406529e-01 | 1.1872069127e+00 |
| 1693 | resid | base+pair | 4.0 | 9.200000 | -2.0361174262e-01 | 1.1825392354e+00 |
| 1694 | resid | base+pair | 4.0 | 9.300000 | -2.0833331584e-01 | 1.1778176622e+00 |
| 1695 | resid | base+pair | 4.0 | 9.400000 | -2.1310878280e-01 | 1.1730421952e+00 |
| 1696 | resid | base+pair | 4.0 | 9.500000 | -2.1793814133e-01 | 1.1682128367e+00 |
| 1697 | resid | base+pair | 4.0 | 9.600000 | -2.2282138924e-01 | 1.1633295888e+00 |
| 1698 | resid | base+pair | 4.0 | 9.700000 | -2.2775852429e-01 | 1.1583924537e+00 |
| 1699 | resid | base+pair | 4.0 | 9.800000 | -2.3274954425e-01 | 1.1534014338e+00 |
| 1700 | resid | base+pair | 4.0 | 9.900000 | -2.3779444685e-01 | 1.1483565312e+00 |
| 1701 | resid | base+pair | 4.0 | 10.000000 | -2.4289322979e-01 | 1.1432577482e+00 |
| 1702 | resid | base+pair | 4.0 | 10.100000 | -2.4804589075e-01 | 1.1381050873e+00 |
| 1703 | resid | base+pair | 4.0 | 10.200000 | -2.5325242741e-01 | 1.1328985506e+00 |
| 1704 | resid | base+pair | 4.0 | 10.300000 | -2.5851283739e-01 | 1.1276381406e+00 |
| 1705 | resid | base+pair | 4.0 | 10.400000 | -2.6382711830e-01 | 1.1223238597e+00 |
| 1706 | resid | base+pair | 4.0 | 10.500000 | -2.6919526774e-01 | 1.1169557103e+00 |
| 1707 | resid | base+pair | 4.0 | 10.600000 | -2.7461728327e-01 | 1.1115336948e+00 |
| 1708 | resid | base+pair | 4.0 | 10.700000 | -2.8009316243e-01 | 1.1060578156e+00 |
| 1709 | resid | base+pair | 4.0 | 10.800000 | -2.8562290273e-01 | 1.1005280753e+00 |
| 1710 | resid | base+pair | 4.0 | 10.900000 | -2.9120650169e-01 | 1.0949444763e+00 |
| 1711 | resid | base+pair | 4.0 | 11.000000 | -2.9684395675e-01 | 1.0893070213e+00 |
| 1712 | resid | base+pair | 4.0 | 11.100000 | -3.0253526537e-01 | 1.0836157127e+00 |
| 1713 | resid | base+pair | 4.0 | 11.200000 | -3.0828042498e-01 | 1.0778705530e+00 |
| 1714 | resid | base+pair | 4.0 | 11.300000 | -3.1407943297e-01 | 1.0720715451e+00 |
| 1715 | resid | base+pair | 4.0 | 11.400000 | -3.1993228672e-01 | 1.0662186913e+00 |
| 1716 | resid | base+pair | 4.0 | 11.500000 | -3.2583898357e-01 | 1.0603119945e+00 |
| 1717 | resid | base+pair | 4.0 | 11.600000 | -3.3179952087e-01 | 1.0543514572e+00 |
| 1718 | resid | base+pair | 4.0 | 11.700000 | -3.3781389590e-01 | 1.0483370821e+00 |
| 1719 | resid | base+pair | 4.0 | 11.800000 | -3.4388210596e-01 | 1.0422688721e+00 |
| 1720 | resid | base+pair | 4.0 | 11.900000 | -3.5000414830e-01 | 1.0361468297e+00 |
| 1721 | resid | base+pair | 4.0 | 12.000000 | -3.5618002016e-01 | 1.0299709579e+00 |
| 1722 | resid | base+pair | 4.0 | 12.100000 | -3.6240971874e-01 | 1.0237412593e+00 |
| 1723 | resid | base+pair | 4.0 | 12.200000 | -3.6869324123e-01 | 1.0174577368e+00 |
| 1724 | resid | base+pair | 4.0 | 12.300000 | -3.7503058479e-01 | 1.0111203932e+00 |
| 1725 | resid | base+pair | 4.0 | 12.400000 | -3.8142174657e-01 | 1.0047292315e+00 |
| 1726 | resid | base+pair | 4.0 | 12.500000 | -3.8786672368e-01 | 9.9828425435e-01 |
| 1727 | resid | base+pair | 4.0 | 12.600000 | -3.9436551321e-01 | 9.9178546482e-01 |
| 1728 | resid | base+pair | 4.0 | 12.700000 | -4.0091811222e-01 | 9.8523286580e-01 |
| 1729 | resid | base+pair | 4.0 | 12.800000 | -4.0752451778e-01 | 9.7862646025e-01 |
| 1730 | resid | base+pair | 4.0 | 12.900000 | -4.1418472688e-01 | 9.7196625114e-01 |
| 1731 | resid | base+pair | 4.0 | 13.000000 | -4.2089873655e-01 | 9.6525224148e-01 |
| 1732 | resid | base+pair | 4.0 | 13.100000 | -4.2766654373e-01 | 9.5848443429e-01 |
| 1733 | resid | base+pair | 4.0 | 13.200000 | -4.3448814540e-01 | 9.5166283262e-01 |
| 1734 | resid | base+pair | 4.0 | 13.300000 | -4.4136353847e-01 | 9.4478743955e-01 |
| 1735 | resid | base+pair | 4.0 | 13.400000 | -4.4829271985e-01 | 9.3785825817e-01 |
| 1736 | resid | base+pair | 4.0 | 13.500000 | -4.5527568642e-01 | 9.3087529161e-01 |
| 1737 | resid | base+pair | 4.0 | 13.600000 | -4.6231243503e-01 | 9.2383854299e-01 |
| 1738 | resid | base+pair | 4.0 | 13.700000 | -4.6940296252e-01 | 9.1674801550e-01 |
| 1739 | resid | base+pair | 4.0 | 13.800000 | -4.7654726570e-01 | 9.0960371232e-01 |
| 1740 | resid | base+pair | 4.0 | 13.900000 | -4.8374534135e-01 | 9.0240563667e-01 |
| 1741 | resid | base+pair | 4.0 | 14.000000 | -4.9099718624e-01 | 8.9515379179e-01 |
| 1742 | resid | base+pair | 4.0 | 14.100000 | -4.9830279710e-01 | 8.8784818093e-01 |
| 1743 | resid | base+pair | 4.0 | 14.200000 | -5.0566217065e-01 | 8.8048880738e-01 |
| 1744 | resid | base+pair | 4.0 | 14.300000 | -5.1307530357e-01 | 8.7307567445e-01 |
| 1745 | resid | base+pair | 4.0 | 14.400000 | -5.2054219255e-01 | 8.6560878547e-01 |
| 1746 | resid | base+pair | 4.0 | 14.500000 | -5.2806283423e-01 | 8.5808814380e-01 |
| 1747 | resid | base+pair | 4.0 | 14.600000 | -5.3563722521e-01 | 8.5051375281e-01 |
| 1748 | resid | base+pair | 4.0 | 14.700000 | -5.4326536212e-01 | 8.4288561591e-01 |
| 1749 | resid | base+pair | 4.0 | 14.800000 | -5.5094724150e-01 | 8.3520373652e-01 |
| 1750 | resid | base+pair | 4.0 | 14.900000 | -5.5868285993e-01 | 8.2746811809e-01 |
| 1751 | resid | base+pair | 4.0 | 15.000000 | -5.6647221393e-01 | 8.1967876410e-01 |
| 1752 | resid | base+pair | 4.0 | 15.100000 | -5.7431529999e-01 | 8.1183567803e-01 |
| 1753 | resid | base+pair | 4.0 | 15.200000 | -5.8221211460e-01 | 8.0393886342e-01 |
| 1754 | resid | base+pair | 4.0 | 15.300000 | -5.9016265423e-01 | 7.9598832380e-01 |
| 1755 | resid | base+pair | 4.0 | 15.400000 | -5.9816691529e-01 | 7.8798406273e-01 |
| 1756 | resid | base+pair | 4.0 | 15.500000 | -6.0622489421e-01 | 7.7992608381e-01 |
| 1757 | resid | base+pair | 4.0 | 15.600000 | -6.1433658737e-01 | 7.7181439066e-01 |
| 1758 | resid | base+pair | 4.0 | 15.700000 | -6.2250199113e-01 | 7.6364898690e-01 |
| 1759 | resid | base+pair | 4.0 | 15.800000 | -6.3072110183e-01 | 7.5542987620e-01 |
| 1760 | resid | base+pair | 4.0 | 15.900000 | -6.3899391579e-01 | 7.4715706224e-01 |
| 1761 | resid | base+pair | 4.0 | 16.000000 | -6.4732042930e-01 | 7.3883054872e-01 |
| 1762 | resid | base+pair | 4.0 | 16.100000 | -6.5570063864e-01 | 7.3045033938e-01 |
| 1763 | resid | base+pair | 4.0 | 16.200000 | -6.6413454005e-01 | 7.2201643797e-01 |
| 1764 | resid | base+pair | 4.0 | 16.300000 | -6.7262212975e-01 | 7.1352884827e-01 |
| 1765 | resid | base+pair | 4.0 | 16.400000 | -6.8116340395e-01 | 7.0498757408e-01 |
| 1766 | resid | base+pair | 4.0 | 16.500000 | -6.8975835881e-01 | 6.9639261921e-01 |
| 1767 | resid | base+pair | 4.0 | 16.600000 | -6.9840699050e-01 | 6.8774398752e-01 |
| 1768 | resid | base+pair | 4.0 | 16.700000 | -7.0710929514e-01 | 6.7904168288e-01 |
| 1769 | resid | base+pair | 4.0 | 16.800000 | -7.1586526885e-01 | 6.7028570918e-01 |
| 1770 | resid | base+pair | 4.0 | 16.900000 | -7.2467490769e-01 | 6.6147607033e-01 |
| 1771 | resid | base+pair | 4.0 | 17.000000 | -7.3353820774e-01 | 6.5261277028e-01 |
| 1772 | resid | base+pair | 4.0 | 17.100000 | -7.4245516503e-01 | 6.4369581300e-01 |
| 1773 | resid | base+pair | 4.0 | 17.200000 | -7.5142577557e-01 | 6.3472520245e-01 |
| 1774 | resid | base+pair | 4.0 | 17.300000 | -7.6045003536e-01 | 6.2570094267e-01 |
| 1775 | resid | base+pair | 4.0 | 17.400000 | -7.6952794036e-01 | 6.1662303767e-01 |
| 1776 | resid | base+pair | 4.0 | 17.500000 | -7.7865948651e-01 | 6.0749149152e-01 |
| 1777 | resid | base+pair | 4.0 | 17.600000 | -7.8784466974e-01 | 5.9830630829e-01 |
| 1778 | resid | base+pair | 4.0 | 17.700000 | -7.9708348594e-01 | 5.8906749209e-01 |
| 1779 | resid | base+pair | 4.0 | 17.800000 | -8.0637593098e-01 | 5.7977504704e-01 |
| 1780 | resid | base+pair | 4.0 | 17.900000 | -8.1572200073e-01 | 5.7042897730e-01 |
| 1781 | resid | base+pair | 4.0 | 18.000000 | -8.2512169099e-01 | 5.6102928703e-01 |
| 1782 | resid | base+pair | 4.0 | 18.100000 | -8.3457499759e-01 | 5.5157598043e-01 |
| 1783 | resid | base+pair | 4.0 | 18.200000 | -8.4408191630e-01 | 5.4206906173e-01 |
| 1784 | resid | base+pair | 4.0 | 18.300000 | -8.5364244287e-01 | 5.3250853515e-01 |
| 1785 | resid | base+pair | 4.0 | 18.400000 | -8.6325657305e-01 | 5.2289440498e-01 |
| 1786 | resid | base+pair | 4.0 | 18.500000 | -8.7292430254e-01 | 5.1322667548e-01 |
| 1787 | resid | base+pair | 4.0 | 18.600000 | -8.8264562703e-01 | 5.0350535099e-01 |
| 1788 | resid | base+pair | 4.0 | 18.700000 | -8.9242054220e-01 | 4.9373043583e-01 |
| 1789 | resid | base+pair | 4.0 | 18.800000 | -9.0224904367e-01 | 4.8390193436e-01 |
| 1790 | resid | base+pair | 4.0 | 18.900000 | -9.1213112707e-01 | 4.7401985096e-01 |
| 1791 | resid | base+pair | 4.0 | 19.000000 | -9.2206678799e-01 | 4.6408419003e-01 |
| 1792 | resid | base+pair | 4.0 | 19.100000 | -9.3205602201e-01 | 4.5409495601e-01 |
| 1793 | resid | base+pair | 4.0 | 19.200000 | -9.4209882468e-01 | 4.4405215335e-01 |
| 1794 | resid | base+pair | 4.0 | 19.300000 | -9.5219519152e-01 | 4.3395578650e-01 |
| 1795 | resid | base+pair | 4.0 | 19.400000 | -9.6234511804e-01 | 4.2380585999e-01 |
| 1796 | resid | base+pair | 4.0 | 19.500000 | -9.7254859971e-01 | 4.1360237831e-01 |
| 1797 | resid | base+pair | 4.0 | 19.600000 | -9.8280563200e-01 | 4.0334534603e-01 |
| 1798 | resid | base+pair | 4.0 | 19.700000 | -9.9311621033e-01 | 3.9303476769e-01 |
| 1799 | resid | base+pair | 4.0 | 19.800000 | -1.0034803301e+00 | 3.8267064790e-01 |
| 1800 | resid | base+pair | 4.0 | 19.900000 | -1.0138979868e+00 | 3.7225299125e-01 |
| 1801 | resid | base+pair | 4.0 | 20.000000 | -1.0243691756e+00 | 3.6178180240e-01 |
| 1802 | resid | base+pair | 4.0 | 20.100000 | -1.0348938920e+00 | 3.5125708600e-01 |
| 1803 | resid | base+pair | 4.0 | 20.200000 | -1.0454721313e+00 | 3.4067884672e-01 |
| 1804 | resid | base+pair | 4.0 | 20.300000 | -1.0561038888e+00 | 3.3004708927e-01 |
| 1805 | resid | base+pair | 4.0 | 20.400000 | -1.0667891596e+00 | 3.1936181838e-01 |
| 1806 | resid | base+pair | 4.0 | 20.500000 | -1.0775279392e+00 | 3.0862303880e-01 |
| 1807 | resid | base+pair | 4.0 | 20.600000 | -1.0883202227e+00 | 2.9783075531e-01 |
| 1808 | resid | base+pair | 4.0 | 20.700000 | -1.0991660053e+00 | 2.8698497269e-01 |
| 1809 | resid | base+pair | 4.0 | 20.800000 | -1.1100652823e+00 | 2.7608569577e-01 |
| 1810 | resid | base+pair | 4.0 | 20.900000 | -1.1210180486e+00 | 2.6513292939e-01 |
| 1811 | resid | base+pair | 4.0 | 21.000000 | -1.1320242996e+00 | 2.5412667841e-01 |
| 1812 | resid | base+pair | 4.0 | 21.100000 | -1.1430840303e+00 | 2.4306694773e-01 |
| 1813 | resid | base+pair | 4.0 | 21.200000 | -1.1541972358e+00 | 2.3195374225e-01 |
| 1814 | resid | base+pair | 4.0 | 21.300000 | -1.1653639111e+00 | 2.2078706691e-01 |
| 1815 | resid | base+pair | 4.0 | 21.400000 | -1.1765840514e+00 | 2.0956692666e-01 |
| 1816 | resid | base+pair | 4.0 | 21.500000 | -1.1878576515e+00 | 1.9829332649e-01 |
| 1817 | resid | base+pair | 4.0 | 21.600000 | -1.1991847066e+00 | 1.8696627139e-01 |
| 1818 | resid | base+pair | 4.0 | 21.700000 | -1.2105652116e+00 | 1.7558576640e-01 |
| 1819 | resid | base+pair | 4.0 | 21.800000 | -1.2219991615e+00 | 1.6415181655e-01 |
| 1820 | resid | base+pair | 4.0 | 21.900000 | -1.2334865511e+00 | 1.5266442693e-01 |
| 1821 | resid | base+pair | 4.0 | 22.000000 | -1.2450273754e+00 | 1.4112360262e-01 |
| 1822 | resid | base+pair | 4.0 | 22.100000 | -1.2566216293e+00 | 1.2952934874e-01 |
| 1823 | resid | base+pair | 4.0 | 22.200000 | -1.2682693076e+00 | 1.1788167044e-01 |
| 1824 | resid | base+pair | 4.0 | 22.300000 | -1.2799704052e+00 | 1.0618057287e-01 |
| 1825 | resid | base+pair | 4.0 | 22.400000 | -1.2917249168e+00 | 9.4426061224e-02 |
| 1826 | resid | base+pair | 4.0 | 22.500000 | -1.3035328373e+00 | 8.2618140703e-02 |
| 1827 | resid | base+pair | 4.0 | 22.600000 | -1.3153941615e+00 | 7.0756816542e-02 |
| 1828 | resid | base+pair | 4.0 | 22.700000 | -1.3273088840e+00 | 5.8842093994e-02 |
| 1829 | resid | base+pair | 4.0 | 22.800000 | -1.3392769997e+00 | 4.6873978335e-02 |
| 1830 | resid | base+pair | 4.0 | 22.900000 | -1.3512985032e+00 | 3.4852474865e-02 |
| 1831 | resid | base+pair | 4.0 | 23.000000 | -1.3633733891e+00 | 2.2777588906e-02 |
| 1832 | resid | base+pair | 4.0 | 23.100000 | -1.3755016522e+00 | 1.0649325802e-02 |
| 1833 | resid | base+pair | 4.0 | 23.200000 | -1.3876832871e+00 | -1.5323090782e-03 |
| 1834 | resid | base+pair | 4.0 | 23.300000 | -1.3999182884e+00 | -1.3767310346e-02 |
| 1835 | resid | base+pair | 4.0 | 23.400000 | -1.4122066506e+00 | -2.6055672587e-02 |
| 1836 | resid | base+pair | 4.0 | 23.500000 | -1.4245483684e+00 | -3.8397390366e-02 |
| 1837 | resid | base+pair | 4.0 | 23.600000 | -1.4369434362e+00 | -5.0792458225e-02 |
| 1838 | resid | base+pair | 4.0 | 23.700000 | -1.4493918487e+00 | -6.3240870682e-02 |
| 1839 | resid | base+pair | 4.0 | 23.800000 | -1.4618936003e+00 | -7.5742622235e-02 |
| 1840 | resid | base+pair | 4.0 | 23.900000 | -1.4744486854e+00 | -8.8297707357e-02 |
| 1841 | resid | base+pair | 4.0 | 24.000000 | -1.4870570985e+00 | -1.0090612050e-01 |
| 1842 | resid | base+pair | 4.0 | 24.100000 | -1.4997188341e+00 | -1.1356785609e-01 |
| 1843 | resid | base+pair | 4.0 | 24.200000 | -1.5124338866e+00 | -1.2628290853e-01 |
| 1844 | resid | base+pair | 4.0 | 24.300000 | -1.5252022502e+00 | -1.3905127221e-01 |
| 1845 | resid | base+pair | 4.0 | 24.400000 | -1.5380239195e+00 | -1.5187294149e-01 |
| 1846 | resid | base+pair | 4.0 | 24.500000 | -1.5508988887e+00 | -1.6474791070e-01 |
| 1847 | resid | base+pair | 4.0 | 24.600000 | -1.5638271522e+00 | -1.7767617417e-01 |
| 1848 | resid | base+pair | 4.0 | 24.700000 | -1.5768087042e+00 | -1.9065772617e-01 |
| 1849 | resid | base+pair | 4.0 | 24.800000 | -1.5898435390e+00 | -2.0369256100e-01 |
| 1850 | resid | base+pair | 4.0 | 24.900000 | -1.6029316509e+00 | -2.1678067288e-01 |
| 1851 | resid | base+pair | 4.0 | 25.000000 | -1.6160730341e+00 | -2.2992205605e-01 |
| 1852 | resid | base+pair | 4.0 | 25.100000 | -1.6292676827e+00 | -2.4311670471e-01 |
| 1853 | resid | base+pair | 4.0 | 25.200000 | -1.6425155911e+00 | -2.5636461304e-01 |
| 1854 | resid | base+pair | 4.0 | 25.300000 | -1.6558167532e+00 | -2.6966577519e-01 |
| 1855 | resid | base+pair | 4.0 | 25.400000 | -1.6691711633e+00 | -2.8302018531e-01 |
| 1856 | resid | base+pair | 4.0 | 25.500000 | -1.6825788155e+00 | -2.9642783750e-01 |
| 1857 | resid | base+pair | 4.0 | 25.600000 | -1.6960397039e+00 | -3.0988872586e-01 |
| 1858 | resid | base+pair | 4.0 | 25.700000 | -1.7095538225e+00 | -3.2340284445e-01 |
| 1859 | resid | base+pair | 4.0 | 25.800000 | -1.7231211653e+00 | -3.3697018732e-01 |
| 1860 | resid | base+pair | 4.0 | 25.900000 | -1.7367417265e+00 | -3.5059074849e-01 |
| 1861 | resid | base+pair | 4.0 | 26.000000 | -1.7504155000e+00 | -3.6426452196e-01 |
| 1862 | resid | base+pair | 4.0 | 26.100000 | -1.7641424797e+00 | -3.7799150171e-01 |
| 1863 | resid | base+pair | 4.0 | 26.200000 | -1.7779226597e+00 | -3.9177168169e-01 |
| 1864 | resid | base+pair | 4.0 | 26.300000 | -1.7917560339e+00 | -4.0560505584e-01 |
| 1865 | resid | base+pair | 4.0 | 26.400000 | -1.8056425961e+00 | -4.1949161807e-01 |
| 1866 | resid | base+pair | 4.0 | 26.500000 | -1.8195823403e+00 | -4.3343136227e-01 |
| 1867 | resid | base+pair | 4.0 | 26.600000 | -1.8335752603e+00 | -4.4742428230e-01 |
| 1868 | resid | base+pair | 4.0 | 26.700000 | -1.8476213500e+00 | -4.6147037201e-01 |
| 1869 | resid | base+pair | 4.0 | 26.800000 | -1.8617206032e+00 | -4.7556962522e-01 |
| 1870 | resid | base+pair | 4.0 | 26.900000 | -1.8758730138e+00 | -4.8972203573e-01 |
| 1871 | resid | base+pair | 4.0 | 27.000000 | -1.8900785753e+00 | -5.0392759731e-01 |
| 1872 | resid | base+pair | 4.0 | 27.100000 | -1.9043372817e+00 | -5.1818630372e-01 |
| 1873 | resid | base+pair | 4.0 | 27.200000 | -1.9186491267e+00 | -5.3249814869e-01 |
| 1874 | resid | base+pair | 4.0 | 27.300000 | -1.9330141040e+00 | -5.4686312593e-01 |
| 1875 | resid | base+pair | 4.0 | 27.400000 | -1.9474322072e+00 | -5.6128122913e-01 |
| 1876 | resid | base+pair | 4.0 | 27.500000 | -1.9619034300e+00 | -5.7575245196e-01 |
| 1877 | resid | base+pair | 4.0 | 27.600000 | -1.9764277661e+00 | -5.9027678805e-01 |
| 1878 | resid | base+pair | 4.0 | 27.700000 | -1.9910052091e+00 | -6.0485423104e-01 |
| 1879 | resid | base+pair | 4.0 | 27.800000 | -2.0056357525e+00 | -6.1948477451e-01 |
| 1880 | resid | base+pair | 4.0 | 27.900000 | -2.0203193901e+00 | -6.3416841204e-01 |
| 1881 | resid | base+pair | 4.0 | 28.000000 | -2.0350561152e+00 | -6.4890513720e-01 |
| 1882 | resid | base+pair | 4.0 | 28.100000 | -2.0498459215e+00 | -6.6369494351e-01 |
| 1883 | resid | base+pair | 4.0 | 28.200000 | -2.0646888025e+00 | -6.7853782448e-01 |
| 1884 | resid | base+pair | 4.0 | 28.300000 | -2.0795847516e+00 | -6.9343377360e-01 |
| 1885 | resid | base+pair | 4.0 | 28.400000 | -2.0945337624e+00 | -7.0838278433e-01 |
| 1886 | resid | base+pair | 4.0 | 28.500000 | -2.1095358281e+00 | -7.2338485012e-01 |
| 1887 | resid | base+pair | 4.0 | 28.600000 | -2.1245909424e+00 | -7.3843996440e-01 |
| 1888 | resid | base+pair | 4.0 | 28.700000 | -2.1396990986e+00 | -7.5354812055e-01 |
| 1889 | resid | base+pair | 4.0 | 28.800000 | -2.1548602900e+00 | -7.6870931197e-01 |
| 1890 | resid | base+pair | 4.0 | 28.900000 | -2.1700745100e+00 | -7.8392353200e-01 |
| 1891 | resid | base+pair | 4.0 | 29.000000 | -2.1853417520e+00 | -7.9919077397e-01 |
| 1892 | resid | base+pair | 4.0 | 29.100000 | -2.2006620092e+00 | -8.1451103120e-01 |
| 1893 | resid | base+pair | 4.0 | 29.200000 | -2.2160352750e+00 | -8.2988429698e-01 |
| 1894 | resid | base+pair | 4.0 | 29.300000 | -2.2314615426e+00 | -8.4531056458e-01 |
| 1895 | resid | base+pair | 4.0 | 29.400000 | -2.2469408053e+00 | -8.6078982723e-01 |
| 1896 | resid | base+pair | 4.0 | 29.500000 | -2.2624730562e+00 | -8.7632207817e-01 |
| 1897 | resid | base+pair | 4.0 | 29.600000 | -2.2780582886e+00 | -8.9190731060e-01 |
| 1898 | resid | base+pair | 4.0 | 29.700000 | -2.2936964957e+00 | -9.0754551769e-01 |
| 1899 | resid | base+pair | 4.0 | 29.800000 | -2.3093876706e+00 | -9.2323669260e-01 |
| 1900 | resid | base+pair | 4.0 | 29.900000 | -2.3251318065e+00 | -9.3898082846e-01 |
| 1901 | resid | base+pair | 4.0 | 30.000000 | -2.3409288964e+00 | -9.5477791840e-01 |
| 1902 | resid | base+pair | 4.0 | 30.100000 | -2.3567789335e+00 | -9.7062795550e-01 |
| 1903 | resid | base+pair | 4.0 | 30.200000 | -2.3726819109e+00 | -9.8653093283e-01 |
| 1904 | resid | base+pair | 4.0 | 30.300000 | -2.3886378215e+00 | -1.0024868434e+00 |
| 1905 | resid | base+pair | 4.0 | 30.400000 | -2.4046466584e+00 | -1.0184956804e+00 |
| 1906 | resid | base+pair | 4.0 | 30.500000 | -2.4207084146e+00 | -1.0345574366e+00 |
| 1907 | resid | base+pair | 4.0 | 30.600000 | -2.4368230831e+00 | -1.0506721051e+00 |
| 1908 | resid | base+pair | 4.0 | 30.700000 | -2.4529906569e+00 | -1.0668396789e+00 |
| 1909 | resid | base+pair | 4.0 | 30.800000 | -2.4692111289e+00 | -1.0830601509e+00 |
| 1910 | resid | base+pair | 4.0 | 30.900000 | -2.4854844920e+00 | -1.0993335139e+00 |
| 1911 | resid | base+pair | 4.0 | 31.000000 | -2.5018107390e+00 | -1.1156597610e+00 |
| 1912 | resid | base+pair | 4.0 | 31.100000 | -2.5181898630e+00 | -1.1320388850e+00 |
| 1913 | resid | base+pair | 4.0 | 31.200000 | -2.5346218567e+00 | -1.1484708787e+00 |
| 1914 | resid | base+pair | 4.0 | 31.300000 | -2.5511067129e+00 | -1.1649557349e+00 |
| 1915 | resid | base+pair | 4.0 | 31.400000 | -2.5676444245e+00 | -1.1814934465e+00 |
| 1916 | resid | base+pair | 4.0 | 31.500000 | -2.5842349843e+00 | -1.1980840063e+00 |
| 1917 | resid | base+pair | 4.0 | 31.600000 | -2.6008783850e+00 | -1.2147274069e+00 |
| 1918 | resid | base+pair | 4.0 | 31.700000 | -2.6175746193e+00 | -1.2314236413e+00 |
| 1919 | resid | base+pair | 4.0 | 31.800000 | -2.6343236800e+00 | -1.2481727020e+00 |
| 1920 | resid | base+pair | 4.0 | 31.900000 | -2.6511255598e+00 | -1.2649745818e+00 |
| 1921 | resid | base+pair | 4.0 | 32.000000 | -2.6679802514e+00 | -1.2818292734e+00 |
| 1922 | resid | base+pair | 4.0 | 32.100000 | -2.6848877474e+00 | -1.2987367694e+00 |
| 1923 | resid | base+pair | 4.0 | 32.200000 | -2.7018480404e+00 | -1.3156970624e+00 |
| 1924 | resid | base+pair | 4.0 | 32.300000 | -2.7188611231e+00 | -1.3327101451e+00 |
| 1925 | resid | base+pair | 4.0 | 32.400000 | -2.7359269881e+00 | -1.3497760100e+00 |
| 1926 | resid | base+pair | 4.0 | 32.500000 | -2.7530456278e+00 | -1.3668946498e+00 |
| 1927 | resid | base+pair | 4.0 | 32.600000 | -2.7702170350e+00 | -1.3840660569e+00 |
| 1928 | resid | base+pair | 4.0 | 32.700000 | -2.7874412020e+00 | -1.4012902240e+00 |
| 1929 | resid | base+pair | 4.0 | 32.800000 | -2.8047181215e+00 | -1.4185671434e+00 |
| 1930 | resid | base+pair | 4.0 | 32.900000 | -2.8220477858e+00 | -1.4358968078e+00 |
| 1931 | resid | base+pair | 4.0 | 33.000000 | -2.8394301875e+00 | -1.4532792095e+00 |
| 1932 | resid | base+pair | 4.0 | 33.100000 | -2.8568653190e+00 | -1.4707143410e+00 |
| 1933 | resid | base+pair | 4.0 | 33.200000 | -2.8743531727e+00 | -1.4882021947e+00 |
| 1934 | resid | base+pair | 4.0 | 33.300000 | -2.8918937410e+00 | -1.5057427630e+00 |
| 1935 | resid | base+pair | 4.0 | 33.400000 | -2.9094870163e+00 | -1.5233360383e+00 |
| 1936 | resid | base+pair | 4.0 | 33.500000 | -2.9271329909e+00 | -1.5409820129e+00 |
| 1937 | resid | base+pair | 4.0 | 33.600000 | -2.9448316572e+00 | -1.5586806792e+00 |
| 1938 | resid | base+pair | 4.0 | 33.700000 | -2.9625830075e+00 | -1.5764320295e+00 |
| 1939 | resid | base+pair | 4.0 | 33.800000 | -2.9803870341e+00 | -1.5942360561e+00 |
| 1940 | resid | base+pair | 4.0 | 33.900000 | -2.9982437292e+00 | -1.6120927512e+00 |
| 1941 | resid | base+pair | 4.0 | 34.000000 | -3.0161530851e+00 | -1.6300021071e+00 |
| 1942 | resid | base+pair | 4.0 | 34.100000 | -3.0341150940e+00 | -1.6479641160e+00 |
| 1943 | resid | base+pair | 4.0 | 34.200000 | -3.0521297482e+00 | -1.6659787702e+00 |
| 1944 | resid | base+pair | 4.0 | 34.300000 | -3.0701970398e+00 | -1.6840460617e+00 |
| 1945 | resid | base+pair | 4.0 | 34.400000 | -3.0883169609e+00 | -1.7021659829e+00 |
| 1946 | resid | base+pair | 4.0 | 34.500000 | -3.1064895038e+00 | -1.7203385257e+00 |
| 1947 | resid | base+pair | 4.0 | 34.600000 | -3.1247146605e+00 | -1.7385636824e+00 |
| 1948 | resid | base+pair | 4.0 | 34.700000 | -3.1429924231e+00 | -1.7568414451e+00 |
| 1949 | resid | base+pair | 4.0 | 34.800000 | -3.1613227837e+00 | -1.7751718057e+00 |
| 1950 | resid | base+pair | 4.0 | 34.900000 | -3.1797057344e+00 | -1.7935547564e+00 |
| 1951 | resid | base+pair | 4.0 | 35.000000 | -3.1981412672e+00 | -1.8119902892e+00 |
| 1952 | resid | base+pair | 4.0 | 35.100000 | -3.2166293742e+00 | -1.8304783961e+00 |
| 1953 | resid | base+pair | 4.0 | 35.200000 | -3.2351700472e+00 | -1.8490190692e+00 |
| 1954 | resid | base+pair | 4.0 | 35.300000 | -3.2537632783e+00 | -1.8676123003e+00 |
| 1955 | resid | base+pair | 4.0 | 35.400000 | -3.2724090595e+00 | -1.8862580814e+00 |
| 1956 | resid | base+pair | 4.0 | 35.500000 | -3.2911073826e+00 | -1.9049564045e+00 |
| 1957 | resid | base+pair | 4.0 | 35.600000 | -3.3098582395e+00 | -1.9237072615e+00 |
| 1958 | resid | base+pair | 4.0 | 35.700000 | -3.3286616223e+00 | -1.9425106443e+00 |
| 1959 | resid | base+pair | 4.0 | 35.800000 | -3.3475175226e+00 | -1.9613665446e+00 |
| 1960 | resid | base+pair | 4.0 | 35.900000 | -3.3664259325e+00 | -1.9802749544e+00 |
| 1961 | resid | base+pair | 4.0 | 36.000000 | -3.3853868436e+00 | -1.9992358656e+00 |
| 1962 | resid | base+pair | 4.0 | 36.100000 | -3.4044002478e+00 | -2.0182492698e+00 |
| 1963 | resid | base+pair | 4.0 | 36.200000 | -3.4234661369e+00 | -2.0373151589e+00 |
| 1964 | resid | base+pair | 4.0 | 36.300000 | -3.4425845026e+00 | -2.0564335246e+00 |
| 1965 | resid | base+pair | 4.0 | 36.400000 | -3.4617553367e+00 | -2.0756043587e+00 |
| 1966 | resid | base+pair | 4.0 | 36.500000 | -3.4809786309e+00 | -2.0948276529e+00 |
| 1967 | resid | base+pair | 4.0 | 36.600000 | -3.5002543769e+00 | -2.1141033989e+00 |
| 1968 | resid | base+pair | 4.0 | 36.700000 | -3.5195825664e+00 | -2.1334315884e+00 |
| 1969 | resid | base+pair | 4.0 | 36.800000 | -3.5389631910e+00 | -2.1528122129e+00 |
| 1970 | resid | base+pair | 4.0 | 36.900000 | -3.5583962423e+00 | -2.1722452643e+00 |
| 1971 | resid | base+pair | 4.0 | 37.000000 | -3.5778817121e+00 | -2.1917307340e+00 |
| 1972 | resid | base+pair | 4.0 | 37.100000 | -3.5974195918e+00 | -2.2112686137e+00 |
| 1973 | resid | base+pair | 4.0 | 37.200000 | -3.6170098730e+00 | -2.2308588950e+00 |
| 1974 | resid | base+pair | 4.0 | 37.300000 | -3.6366525473e+00 | -2.2505015693e+00 |
| 1975 | resid | base+pair | 4.0 | 37.400000 | -3.6563476063e+00 | -2.2701966283e+00 |
| 1976 | resid | base+pair | 4.0 | 37.500000 | -3.6760950414e+00 | -2.2899440634e+00 |
| 1977 | resid | base+pair | 4.0 | 37.600000 | -3.6958948441e+00 | -2.3097438661e+00 |
| 1978 | resid | base+pair | 4.0 | 37.700000 | -3.7157470060e+00 | -2.3295960279e+00 |
| 1979 | resid | base+pair | 4.0 | 37.800000 | -3.7356515183e+00 | -2.3495005403e+00 |
| 1980 | resid | base+pair | 4.0 | 37.900000 | -3.7556083726e+00 | -2.3694573946e+00 |
| 1981 | resid | base+pair | 4.0 | 38.000000 | -3.7756175603e+00 | -2.3894665823e+00 |
| 1982 | resid | base+pair | 4.0 | 38.100000 | -3.7956790728e+00 | -2.4095280948e+00 |
| 1983 | resid | base+pair | 4.0 | 38.200000 | -3.8157929014e+00 | -2.4296419233e+00 |
| 1984 | resid | base+pair | 4.0 | 38.300000 | -3.8359590374e+00 | -2.4498080594e+00 |
| 1985 | resid | base+pair | 4.0 | 38.400000 | -3.8561774722e+00 | -2.4700264942e+00 |
| 1986 | resid | base+pair | 4.0 | 38.500000 | -3.8764481972e+00 | -2.4902972191e+00 |
| 1987 | resid | base+pair | 4.0 | 38.600000 | -3.8967712035e+00 | -2.5106202255e+00 |
| 1988 | resid | base+pair | 4.0 | 38.700000 | -3.9171464824e+00 | -2.5309955044e+00 |
| 1989 | resid | base+pair | 4.0 | 38.800000 | -3.9375740252e+00 | -2.5514230472e+00 |
| 1990 | resid | base+pair | 4.0 | 38.900000 | -3.9580538231e+00 | -2.5719028451e+00 |
| 1991 | resid | base+pair | 4.0 | 39.000000 | -3.9785858674e+00 | -2.5924348893e+00 |
| 1992 | resid | base+pair | 4.0 | 39.100000 | -3.9991701490e+00 | -2.6130191710e+00 |
| 1993 | resid | base+pair | 4.0 | 39.200000 | -4.0198066594e+00 | -2.6336556813e+00 |
| 1994 | resid | base+pair | 4.0 | 39.300000 | -4.0404953895e+00 | -2.6543444114e+00 |
| 1995 | resid | base+pair | 4.0 | 39.400000 | -4.0612363305e+00 | -2.6750853524e+00 |
| 1996 | resid | base+pair | 4.0 | 39.500000 | -4.0820294734e+00 | -2.6958784954e+00 |
| 1997 | resid | base+pair | 4.0 | 39.600000 | -4.1028748095e+00 | -2.7167238314e+00 |
| 1998 | resid | base+pair | 4.0 | 39.700000 | -4.1237723296e+00 | -2.7376213516e+00 |
| 1999 | resid | base+pair | 4.0 | 39.800000 | -4.1447220249e+00 | -2.7585710469e+00 |
| 2000 | resid | base+pair | 4.0 | 39.900000 | -4.1657238864e+00 | -2.7795729084e+00 |
| 2001 | resid | base+pair | 4.0 | 40.000000 | -4.1867779051e+00 | -2.8006269270e+00 |
E-016b-v3-rootcause.json
— 6.9 KB, updated 08-18-2026
JSON sidecar (click to expand)
{
"experiment": "E-016b",
"task": "2.6: root-cause E-016 V3 Poisson-reconstruction failure",
"script": "research/numerics/scripts/E-016b-v3-rootcause.py",
"parameters": {
"a_sweep": [
4.0,
10.0
],
"h": 0.01,
"lambda": -1.0,
"y_grid": [
0.1,
40.0,
400
],
"z_max": 300.0
},
"report": {
"4.0": {
"T1_kappa_re": -0.9914379801328772,
"T1_kappa_im": -1.4222222222222223,
"T2_census": {
"n_real": 381,
"z1": 1.1260734006983593,
"z_last": 299.8646747694667,
"lattice_count_window": 381.9718634205488
},
"T2_winding": {
"0.3927": {
"winding": 1.9971283856655768,
"real_zeros_inside": 0,
"excess": 1.9971283856655768
},
"1.1781": {
"winding": 3.957366770074305,
"real_zeros_inside": 2,
"excess": 1.9573667700743052
},
"0.0000": {
"winding": 1.9960937479061762,
"real_zeros_inside": 0,
"excess": 1.9960937479061762
},
"0.0001": {
"winding": 1.9960937500549862,
"real_zeros_inside": 0,
"excess": 1.9960937500549862
},
"0.0100": {
"winding": 1.996094371929568,
"real_zeros_inside": 0,
"excess": 1.996094371929568
},
"0.1000": {
"winding": 1.9961562249900062,
"real_zeros_inside": 0,
"excess": 1.9961562249900062
},
"2.0000": {
"winding": 5.942871677547558,
"real_zeros_inside": 4,
"excess": 1.9428716775475579
},
"5.0000": {
"winding": 12.077973882052314,
"real_zeros_inside": 10,
"excess": 2.077973882052314
}
},
"T2_imag_pair": {
"eps": 5.829287623947368e-09,
"W_at_ieps": 2.825742938081395e-49,
"scan_min": 5.749824935036285e-06,
"scan_at_y": 0.0001
},
"T3_A_over_y_fit": 0.6343007263567857,
"T3_two_over_pi": 0.6366197723675814,
"T3_mean_shift": -1.2815872994129114,
"T4_variants": {
"base": {
"resid_y0.5": 1.2739134084231456,
"resid_y5": 0.07332699024962142,
"resid_y20": -0.9925381870041659,
"shape_rms_rel": 1.0497908515365875
},
"trunc60": {
"resid_y0.5": 1.2766229564752873,
"resid_y5": -0.14349117160523672,
"resid_y20": -4.94373487936198,
"shape_rms_rel": 4.338262071341213
},
"trunc100": {
"resid_y0.5": 1.27526491761311,
"resid_y5": -0.034968760716001634,
"resid_y20": -3.0133337980338,
"shape_rms_rel": 2.809762823982386
},
"notail": {
"resid_y0.5": 1.2745883033553684,
"resid_y5": 0.14081030856832366,
"resid_y20": 0.08570192959282363,
"shape_rms_rel": 0.2895380312354026
},
"base+pair": {
"resid_y0.5": 0.0006738636879826121,
"resid_y5": -0.05399696422389488,
"resid_y20": -1.0243691756225448,
"shape_rms_rel": 0.9421400227183758
},
"mp60": {
"resid_y0.5": 1.276622956475289,
"resid_y5": -0.14349117160523361,
"resid_y20": -4.943734879361979,
"shape_rms_rel": 4.338262071341214
}
},
"T4_mp60": {
"n_relocated": 75,
"max_abs_dz": 1.2434497875801753e-12
},
"T5_sinc_est_max": 0.0002055923399439411
},
"10.0": {
"T1_kappa_re": -3.6447054985051435,
"T1_kappa_im": -4.397114393679149,
"T2_census": {
"n_real": 954,
"z1": 0.44959700551214055,
"z_last": 299.89357740917427,
"lattice_count_window": 954.9296585513721
},
"T2_winding": {
"0.1571": {
"winding": 1.9971325652242644,
"real_zeros_inside": 0,
"excess": 1.9971325652242644
},
"0.4712": {
"winding": 3.9589810973742314,
"real_zeros_inside": 2,
"excess": 1.9589810973742314
},
"0.0000": {
"winding": 1.996093695657393,
"real_zeros_inside": 0,
"excess": 1.996093695657393
},
"0.0001": {
"winding": 1.9960937503824123,
"real_zeros_inside": 0,
"excess": 1.9960937503824123
},
"0.0100": {
"winding": 1.9960976525143628,
"real_zeros_inside": 0,
"excess": 1.9960976525143628
},
"0.1000": {
"winding": 1.9964955397146036,
"real_zeros_inside": 0,
"excess": 1.9964955397146036
},
"2.0000": {
"winding": 12.085419712205663,
"real_zeros_inside": 10,
"excess": 2.0854197122056632
},
"5.0000": {
"winding": 31.975335381644364,
"real_zeros_inside": 30,
"excess": 1.9753353816443635
}
},
"T2_imag_pair": {
"eps": 2.0797966440236883e-09,
"W_at_ieps": 1.6504059507421108e-26,
"scan_min": 0.01459451355707131,
"scan_at_y": 0.0001
},
"T3_A_over_y_fit": 0.6308206254641555,
"T3_two_over_pi": 0.6366197723675814,
"T3_mean_shift": -3.3631535473854246,
"T4_variants": {
"base": {
"resid_y0.5": 1.2749261380781172,
"resid_y5": -0.007753707743303639,
"resid_y20": -2.530820269504034,
"shape_rms_rel": 1.0143675095987894
},
"trunc60": {
"resid_y0.5": 1.2816709492693397,
"resid_y5": -0.5465597395886301,
"resid_y20": -12.354286478739445,
"shape_rms_rel": 4.43884573453234
},
"trunc100": {
"resid_y0.5": 1.278305028486991,
"resid_y5": -0.27789168396584607,
"resid_y20": -7.57271682340175,
"shape_rms_rel": 2.860573136578675
},
"notail": {
"resid_y0.5": 1.2766145378113016,
"resid_y5": 0.16107079639175792,
"resid_y20": 0.16663165033476446,
"shape_rms_rel": 0.11754357982145858
},
"base+pair": {
"resid_y0.5": 0.0016865933429546232,
"resid_y5": -0.13507766221681994,
"resid_y20": -2.5626512581224135,
"shape_rms_rel": 0.9793208614044097
},
"mp60": {
"resid_y0.5": 1.2816709492693397,
"resid_y5": -0.5465597395886301,
"resid_y20": -12.354286478739445,
"shape_rms_rel": 4.438845734532339
}
},
"T4_mp60": {
"n_relocated": 190,
"max_abs_dz": 1.0587086762825493e-12
},
"T5_sinc_est_max": 0.0002055923399439411
}
},
"elapsed_seconds": 702.8,
"timestamp_utc": "2026-08-18T17:19:13.123417+00:00"
}
Source code
Python script (click to expand)
"""E-016b — root-cause the E-016 V3 (zero-Poisson reconstruction) failure.
E-016 V3: rho_W^analytic (Galerkin z-derivative) vs rho_W^recon (located
real zeros + Euler-Maclaurin lattice tail) mismatch rel ~0.3 at a=4.
Residual (D-024 sec.4): +1.274 (y=0.5), +0.637 (1), +0.313 (2), +0.073
(5), -0.179 (10), -0.993 (20). Note 2/(pi*y) = 1.2732, 0.6366, 0.3183 —
the low-y residual matches a MISSING zero pair at |z|~0 to 4 digits.
Tests (D-024 sec.4 candidates + new hypothesis):
T1. kappa = W'/W(0): exact gauge arithmetic gives kappa = 0 by symmetry
(x symmetric, c real). Numeric confirmation. => candidate (a) dead.
T2. Zero census + ARGUMENT PRINCIPLE on circles |z|=r: the real-gauge
brentq scan can only find REAL zeros. If Galerkin W has a complex
pair near 0 (candidate: purely imaginary +/-i*eps, self-conjugate
under the mirror symmetries), the winding number exceeds the real-
zero count. If found: locate eps by scanning |W(iy)|.
T3. Residual shape on a fine y-grid: test A/y law; report A vs 2/pi.
T4. Recon variants: (i) base (zeros<=300 + EM tail); (ii) trunc60;
(iii) trunc100; (iv) notail; (v) mp60 (zeros<=60 relocated at
dps 50 + EM tail from 60 — float64 contamination test, D-024 (c));
(vi) base+pair (recon + exact contribution of the T2 imaginary
pair, (2/pi) y/(y^2-eps^2) — decisive if T2 fires).
T5. Sinc-artifact zeros of hat h at z=2*pi*k/h (=628k, beyond window):
analytic size of their rho contribution (expected ~1e-4, dismiss).
Outputs: research/numerics/data/E-016b-v3-rootcause.csv (+ .json)
"""
import importlib.util
import json
import sys
import time
from datetime import datetime, timezone
from pathlib import Path
import mpmath as mp
import numpy as np
import scipy.optimize
REPO = Path(__file__).resolve().parents[3]
DATA = REPO / "research" / "numerics" / "data"
CSV = DATA / "E-016b-v3-rootcause.csv"
JSON = DATA / "E-016b-v3-rootcause.json"
# ---- import E-016 machinery (runs the sieve once, ~15 s) ---------------
_spec = importlib.util.spec_from_file_location(
"E16", Path(__file__).with_name("E-016-herglotz-fine-structure.py"))
E16 = importlib.util.module_from_spec(_spec)
_spec.loader.exec_module(E16)
A_SWEEP = [4.0, 10.0]
H = E16.H_MAIN
LAM = E16.LAM_SHIFT
Y_GRID = np.linspace(0.1, 40.0, 400)
Z_MAX = 300.0
N_GRID = 40000
WIND_RADII_FRAC = [0.5, 1.5] # in units of pi/a, plus absolute below
WIND_RADII_ABS = [1e-6, 1e-4, 1e-2, 0.1, 2.0, 5.0]
def locate_real_zeros(cp, x, h, z_max=Z_MAX, n_grid=N_GRID):
"""Real-axis sign-change + brentq on g(z) = z Im Vp - Re Vp (E-016)."""
zg = np.linspace(1e-3, z_max, n_grid)
Vpr, _ = E16.V_and_dV(zg, cp, x, h)
g = zg * Vpr.imag - Vpr.real
def g_direct(zz):
V = E16.hat_FT(np.array([zz]), h)[0] * complex(
np.exp(1j * zz * x) @ cp)
return zz * V.imag - V.real
idx = np.flatnonzero(np.sign(g[:-1]) * np.sign(g[1:]) < 0)
zeros = []
for i in idx:
try:
zeros.append(scipy.optimize.brentq(g_direct, zg[i], zg[i + 1],
xtol=1e-13, rtol=1e-13))
except ValueError:
pass
return np.array(zeros)
def winding(cp, cm, x, h, r, n_pts=512):
"""Argument-principle zero count of W(theta=pi) on |z|=r."""
phi = np.linspace(0, 2 * np.pi, n_pts, endpoint=False)
z = r * np.exp(1j * phi)
Vp, dVp = E16.V_and_dV(z, cp, x, h)
Vm, dVm = E16.V_and_dV(z, cm, x, h)
W, _ = E16.W_and_dW(z, Vp, dVp, Vm, dVm, np.pi)
dphi = np.diff(np.unwrap(np.angle(W)))
return float(dphi.sum() / (2 * np.pi))
def imag_pair_scan(cp, cm, x, h, y_max=3.0):
"""Scan |W(iy)| for a minimum -> candidate purely-imaginary pair."""
ys = np.linspace(1e-4, y_max, 30000)
z = 1j * ys
Vp, _ = E16.V_and_dV(z, cp, x, h)
Vm, _ = E16.V_and_dV(z, cm, x, h)
W = (z - 1j) * Vp - (z + 1j) * Vm # theta = pi
aw = np.abs(W)
i = int(np.argmin(aw))
# polish with mpmath findroot on W(iy)=0 (real unknown y)
mp.mp.dps = 50
cpm = [mp.mpf(float(v)) for v in cp]
cmm = [mp.mpf(float(v)) for v in cm]
xm = [mp.mpf(float(v)) for v in x]
def Wimag(yy):
yy = mp.mpf(yy)
Sp = sum(c * mp.e ** (1j * yy * xx) for c, xx in zip(cpm, xm))
Sm = sum(c * mp.e ** (1j * yy * xx) for c, xx in zip(cmm, xm))
hh = mp.mpf(h)
hat = hh * (mp.sin(yy * hh / 2) / (yy * hh / 2)) ** 2
Vpv, Vmv = hat * Sp, hat * Sm
W = 1j * (yy - 1) * Vpv - 1j * (yy + 1) * Vmv # W(i*yy), th=pi
return mp.im(W) # mirror symmetry: W(iy) = i * (real)
try:
root = mp.findroot(Wimag, mp.mpf(float(ys[i])),
solver="secant", tol=mp.mpf("1e-40"))
eps = float(root)
resid = float(abs(Wimag(root)))
return eps, resid, float(aw[i]), float(ys[i])
except (ValueError, ZeroDivisionError):
return None, None, float(aw[i]), float(ys[i])
def em_tail(y, z_start, d_lat):
return (y / d_lat) * (np.pi / 2.0 - np.arctan(z_start / y))
def recon_rho(y, zeros_pos, d_lat, z_tail_start=None, extra_pairs=()):
"""Poisson density from positive zeros (doubled) + EM tail + explicit
extra pairs (purely imaginary +/-i*eps: 2y/(y^2 - eps^2))."""
y = np.asarray(y, dtype=float)
zeros_pos = np.asarray(zeros_pos, dtype=float)
if zeros_pos.size:
s = 2.0 * np.sum(y[:, None] / (y[:, None] ** 2
+ zeros_pos[None, :] ** 2), axis=1)
else:
s = np.zeros_like(y)
if z_tail_start is not None:
s = s + 2.0 * em_tail(y, z_tail_start, d_lat)
for eps in extra_pairs:
s = s + 2.0 * y / (y**2 - eps**2)
return s / np.pi
def mp_relocate(cp, x, h, zeros_pos, z_hi=60.0):
"""Re-locate zeros <= z_hi with mpmath dps 50 (float64 contamination
test). Bisection on the real gauge, 80 iterations."""
mp.mp.dps = 50
cpm = [mp.mpf(float(v)) for v in cp]
xm = [mp.mpf(float(v)) for v in x]
hh = mp.mpf(h)
def g_mp(zz):
zz = mp.mpf(zz)
S = sum(c * mp.e ** (1j * zz * xx) for c, xx in zip(cpm, xm))
hat = hh * (mp.sin(zz * hh / 2) / (zz * hh / 2)) ** 2
V = hat * S
return zz * mp.im(V) - mp.re(V)
out = []
for z0 in zeros_pos:
if z0 > z_hi:
continue
lo, hi = mp.mpf(float(z0)) - mp.mpf("0.05"), \
mp.mpf(float(z0)) + mp.mpf("0.05")
flo, fhi = g_mp(lo), g_mp(hi)
if flo * fhi > 0:
out.append((float(z0), None))
continue
for _ in range(80):
mid = (lo + hi) / 2
fm = g_mp(mid)
if flo * fm <= 0:
hi, fhi = mid, fm
else:
lo, flo = mid, fm
out.append((float(z0), float((lo + hi) / 2)))
return out
def main() -> int:
if CSV.exists() and "--force" not in sys.argv:
print(f"cached: {CSV} (use --force to recompute)")
return 0
t0 = time.time()
rows = []
report = {}
for a in A_SWEEP:
print(f"a={a}: build + solve ...", flush=True)
x, hh, Q, M, b = E16.build(a, H)
n = len(x)
cp, T = E16.solve_v(Q, M, b[+1.0], LAM, n)
cm, _ = E16.solve_v(Q, M, b[-1.0], LAM, n)
np_ = float(cp @ T @ cp)
nm = float(cm @ T @ cm)
cm = cm * np.sqrt(np_ / nm)
d_lat = np.pi / a
# analytic rho_W at theta=pi on the fine grid
ziy = 1j * Y_GRID
Vp, dVp = E16.V_and_dV(ziy, cp, x, hh)
Vm, dVm = E16.V_and_dV(ziy, cm, x, hh)
W, dW = E16.W_and_dW(ziy, Vp, dVp, Vm, dVm, np.pi)
rho_an = -np.imag(dW / W) / np.pi
# T1: kappa = W'/W(0)
z0 = np.array([0.0 + 0.0j])
Vp0, dVp0 = E16.V_and_dV(z0, cp, x, hh)
Vm0, dVm0 = E16.V_and_dV(z0, cm, x, hh)
W0, dW0 = E16.W_and_dW(z0, Vp0, dVp0, Vm0, dVm0, np.pi)
kappa = complex(dW0[0] / W0[0])
print(f" T1 kappa = {kappa:.3e}", flush=True)
# T2: census + argument principle
zeros = locate_real_zeros(cp, x, hh)
census = {"n_real": int(len(zeros)), "z1": float(zeros[0]),
"z_last": float(zeros[-1]),
"lattice_count_window": a * Z_MAX / np.pi}
radii = [f * d_lat for f in WIND_RADII_FRAC] + WIND_RADII_ABS
wind = {}
for r in radii:
w = winding(cp, cm, x, hh, r)
n_real_in = int(2 * np.sum(zeros < r))
wind[f"{r:.4f}"] = {"winding": w, "real_zeros_inside": n_real_in,
"excess": w - n_real_in}
print(f" T2 winding: {wind}", flush=True)
eps, eps_resid, scan_min, scan_at = None, None, None, None
if any(abs(v["excess"]) > 0.5 for v in wind.values()):
eps, eps_resid, scan_min, scan_at = imag_pair_scan(cp, cm, x, hh)
print(f" T2 imaginary pair: eps={eps} |W(i*eps)|={eps_resid:.2e} "
f"(scan min {scan_min:.3e} at y={scan_at:.4f})", flush=True)
# T3: residual shape (base variant), A/y fit at small y
z_tail = zeros[-1] + d_lat / 2.0
rec_base = recon_rho(Y_GRID, zeros, d_lat, z_tail)
resid = rho_an - rec_base
sel_small = (Y_GRID >= 0.3) & (Y_GRID <= 2.0)
A_fit = float(np.mean(resid[sel_small] * Y_GRID[sel_small]))
# mean-shift removed version for shape comparison
shift = float(np.mean(resid))
# T4: variants
z60 = zeros[zeros <= 60.0]
z100 = zeros[zeros <= 100.0]
variants = {
"base": rec_base,
"trunc60": recon_rho(Y_GRID, z60, d_lat, z60[-1] + d_lat / 2),
"trunc100": recon_rho(Y_GRID, z100, d_lat, z100[-1] + d_lat / 2),
"notail": recon_rho(Y_GRID, zeros, d_lat, None),
}
if eps is not None and eps_resid is not None and eps_resid < 1e-20:
variants["base+pair"] = recon_rho(
Y_GRID, zeros, d_lat, z_tail, extra_pairs=(eps,))
print(" T4 mp60 relocation (dps 50) ...", flush=True)
reloc = mp_relocate(cp, x, hh, zeros, 60.0)
n_ok = sum(1 for _, r in reloc if r is not None)
max_dz = max((abs(z0 - r) for z0, r in reloc if r is not None),
default=0.0)
z60mp = np.array([r for _, r in reloc if r is not None])
variants["mp60"] = recon_rho(Y_GRID, z60mp, d_lat,
z60mp[-1] + d_lat / 2)
var_summary = {}
for name, rec in variants.items():
res = rho_an - rec
res_shifted = res - np.mean(res)
var_summary[name] = {
"resid_y0.5": float(res[np.argmin(abs(Y_GRID - 0.5))]),
"resid_y5": float(res[np.argmin(abs(Y_GRID - 5.0))]),
"resid_y20": float(res[np.argmin(abs(Y_GRID - 20.0))]),
"shape_rms_rel": float(np.sqrt(np.mean(res_shifted**2))
/ np.sqrt(np.mean(rho_an**2))),
}
for y, rv, rsv in zip(Y_GRID, res, res_shifted):
rows.append(f"resid,{name},{a},{y:.6f},{rv:.10e},{rsv:.10e}")
for y, rv in zip(Y_GRID, rho_an):
rows.append(f"rho_analytic,-,{a},{y:.6f},{rv:.10e},")
# T5: sinc-artifact zero contribution estimate (analytic formula)
k = np.arange(1, 20)
zk = 2 * np.pi * k / hh
sinc_est = float(np.max(
(4.0 / np.pi) * np.max(Y_GRID) * np.sum(1.0 / zk**2)))
report[str(a)] = {
"T1_kappa_re": kappa.real, "T1_kappa_im": kappa.imag,
"T2_census": census, "T2_winding": wind,
"T2_imag_pair": {"eps": eps, "W_at_ieps": eps_resid,
"scan_min": scan_min, "scan_at_y": scan_at},
"T3_A_over_y_fit": A_fit, "T3_two_over_pi": 2.0 / np.pi,
"T3_mean_shift": shift,
"T4_variants": var_summary,
"T4_mp60": {"n_relocated": n_ok, "max_abs_dz": max_dz},
"T5_sinc_est_max": sinc_est,
}
print(f" T3 A/y fit: A={A_fit:.4f} vs 2/pi={2/np.pi:.4f} "
f"shift={shift:.4f}", flush=True)
print(f" T4 variants: {json.dumps(var_summary, indent=1)}",
flush=True)
with CSV.open("w", encoding="utf-8", newline="") as f:
f.write("series,variant,a,y,resid,resid_shifted\n")
f.write("\n".join(rows) + "\n")
meta = {
"experiment": "E-016b",
"task": "2.6: root-cause E-016 V3 Poisson-reconstruction failure",
"script": "research/numerics/scripts/E-016b-v3-rootcause.py",
"parameters": {"a_sweep": A_SWEEP, "h": H, "lambda": LAM,
"y_grid": [0.1, 40.0, 400], "z_max": Z_MAX},
"report": report,
"elapsed_seconds": round(time.time() - t0, 1),
"timestamp_utc": datetime.now(timezone.utc).isoformat(),
}
JSON.write_text(json.dumps(meta, indent=2), encoding="utf-8")
print(f"wrote {CSV.name}, {JSON.name}")
return 0
if __name__ == "__main__":
raise SystemExit(main())