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Warning [2] Undefined array key "lockoutexpiry" - Line: 550 - File: global.php PHP 8.0.26 (Linux)
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Warning [2] Undefined array key "avatartype" - Line: 811 - File: global.php PHP 8.0.26 (Linux)
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Warning [2] Undefined property: MyLanguage::$lang_select_default - Line: 5196 - File: inc/functions.php PHP 8.0.26 (Linux)
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Warning [2] Undefined array key "additionalgroups" - Line: 7360 - File: inc/functions.php PHP 8.0.26 (Linux)
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Warning [2] Undefined array key "additionalgroups" - Line: 7360 - File: inc/functions.php PHP 8.0.26 (Linux)
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Warning [2] Undefined array key "mybb" - Line: 1997 - File: inc/functions.php PHP 8.0.26 (Linux)
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Warning [2] Undefined property: MyLanguage::$ratings_update_error - Line: 5 - File: showthread.php(768) : eval()'d code PHP 8.0.26 (Linux)
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Warning [2] Undefined variable $postsdone - Line: 901 - File: showthread.php PHP 8.0.26 (Linux)
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Warning [2] Undefined array key 9 - Line: 907 - File: showthread.php PHP 8.0.26 (Linux)
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Warning [2] Undefined array key 130 - Line: 907 - File: showthread.php PHP 8.0.26 (Linux)
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Warning [2] Undefined array key 132 - Line: 907 - File: showthread.php PHP 8.0.26 (Linux)
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Warning [2] Undefined array key 154 - Line: 907 - File: showthread.php PHP 8.0.26 (Linux)
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Warning [2] Undefined array key 159 - Line: 907 - File: showthread.php PHP 8.0.26 (Linux)
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Warning [2] Undefined array key 160 - Line: 907 - File: showthread.php PHP 8.0.26 (Linux)
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Warning [2] Undefined array key 170 - Line: 907 - File: showthread.php PHP 8.0.26 (Linux)
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Warning [2] Undefined array key 175 - Line: 907 - File: showthread.php PHP 8.0.26 (Linux)
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Warning [2] Undefined array key 394 - Line: 907 - File: showthread.php PHP 8.0.26 (Linux)
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Warning [2] Undefined array key 396 - Line: 907 - File: showthread.php PHP 8.0.26 (Linux)
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Warning [2] Undefined array key 401 - Line: 907 - File: showthread.php PHP 8.0.26 (Linux)
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Warning [2] Undefined array key 404 - Line: 907 - File: showthread.php PHP 8.0.26 (Linux)
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Warning [2] Undefined array key 406 - Line: 907 - File: showthread.php PHP 8.0.26 (Linux)
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Warning [2] Undefined array key 407 - Line: 907 - File: showthread.php PHP 8.0.26 (Linux)
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Warning [2] Undefined array key 408 - Line: 907 - File: showthread.php PHP 8.0.26 (Linux)
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Warning [2] Undefined array key 409 - Line: 907 - File: showthread.php PHP 8.0.26 (Linux)
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Warning [2] Undefined array key 410 - Line: 907 - File: showthread.php PHP 8.0.26 (Linux)
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Warning [2] Undefined array key 411 - Line: 907 - File: showthread.php PHP 8.0.26 (Linux)
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/showthread.php 907 errorHandler->error
Warning [2] Undefined array key 412 - Line: 907 - File: showthread.php PHP 8.0.26 (Linux)
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Warning [2] Undefined array key 413 - Line: 907 - File: showthread.php PHP 8.0.26 (Linux)
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Warning [2] Undefined array key 414 - Line: 907 - File: showthread.php PHP 8.0.26 (Linux)
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Warning [2] Undefined array key 418 - Line: 907 - File: showthread.php PHP 8.0.26 (Linux)
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Warning [2] Undefined array key 423 - Line: 907 - File: showthread.php PHP 8.0.26 (Linux)
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Warning [2] Undefined array key 425 - Line: 907 - File: showthread.php PHP 8.0.26 (Linux)
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Warning [2] Undefined array key 428 - Line: 907 - File: showthread.php PHP 8.0.26 (Linux)
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Warning [2] Undefined array key 429 - Line: 907 - File: showthread.php PHP 8.0.26 (Linux)
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Warning [2] Undefined array key 518 - Line: 907 - File: showthread.php PHP 8.0.26 (Linux)
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Warning [2] Undefined array key 520 - Line: 907 - File: showthread.php PHP 8.0.26 (Linux)
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Warning [2] Undefined array key 524 - Line: 907 - File: showthread.php PHP 8.0.26 (Linux)
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Warning [2] Undefined array key 525 - Line: 907 - File: showthread.php PHP 8.0.26 (Linux)
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Warning [2] Undefined array key 527 - Line: 907 - File: showthread.php PHP 8.0.26 (Linux)
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/showthread.php 907 errorHandler->error
Warning [2] Undefined array key 528 - Line: 907 - File: showthread.php PHP 8.0.26 (Linux)
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/showthread.php 907 errorHandler->error
Warning [2] Undefined array key 530 - Line: 907 - File: showthread.php PHP 8.0.26 (Linux)
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/showthread.php 907 errorHandler->error
Warning [2] Undefined array key 533 - Line: 907 - File: showthread.php PHP 8.0.26 (Linux)
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Warning [2] Undefined array key 534 - Line: 907 - File: showthread.php PHP 8.0.26 (Linux)
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/showthread.php 907 errorHandler->error
Warning [2] Undefined array key 535 - Line: 907 - File: showthread.php PHP 8.0.26 (Linux)
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/showthread.php 907 errorHandler->error
Warning [2] Undefined array key 536 - Line: 907 - File: showthread.php PHP 8.0.26 (Linux)
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/showthread.php 907 errorHandler->error
Warning [2] Undefined array key 542 - Line: 907 - File: showthread.php PHP 8.0.26 (Linux)
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/showthread.php 907 errorHandler->error
Warning [2] Undefined array key 545 - Line: 907 - File: showthread.php PHP 8.0.26 (Linux)
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Warning [2] Undefined array key 547 - Line: 907 - File: showthread.php PHP 8.0.26 (Linux)
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/showthread.php 907 errorHandler->error
Warning [2] Undefined array key 551 - Line: 907 - File: showthread.php PHP 8.0.26 (Linux)
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Warning [2] Undefined array key 555 - Line: 907 - File: showthread.php PHP 8.0.26 (Linux)
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/showthread.php 907 errorHandler->error
Warning [2] Undefined array key 557 - Line: 907 - File: showthread.php PHP 8.0.26 (Linux)
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Warning [2] Undefined array key 559 - Line: 907 - File: showthread.php PHP 8.0.26 (Linux)
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Warning [2] Undefined array key 560 - Line: 907 - File: showthread.php PHP 8.0.26 (Linux)
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Warning [2] Undefined array key 562 - Line: 907 - File: showthread.php PHP 8.0.26 (Linux)
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Warning [2] Undefined array key 639 - Line: 907 - File: showthread.php PHP 8.0.26 (Linux)
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Warning [2] Undefined array key 680 - Line: 907 - File: showthread.php PHP 8.0.26 (Linux)
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Warning [2] Undefined array key 693 - Line: 907 - File: showthread.php PHP 8.0.26 (Linux)
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Warning [2] Undefined array key 695 - Line: 907 - File: showthread.php PHP 8.0.26 (Linux)
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Warning [2] Undefined array key 696 - Line: 907 - File: showthread.php PHP 8.0.26 (Linux)
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Warning [2] Undefined array key 697 - Line: 907 - File: showthread.php PHP 8.0.26 (Linux)
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Warning [2] Undefined array key 698 - Line: 907 - File: showthread.php PHP 8.0.26 (Linux)
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Warning [2] Undefined array key 699 - Line: 907 - File: showthread.php PHP 8.0.26 (Linux)
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Warning [2] Undefined array key 701 - Line: 907 - File: showthread.php PHP 8.0.26 (Linux)
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
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File Line Function
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
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File Line Function
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
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File Line Function
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
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File Line Function
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File Line Function
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File Line Function
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
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File Line Function
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
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File Line Function
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File Line Function
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File Line Function
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File Line Function
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File Line Function
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File Line Function
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
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File Line Function
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File Line Function
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File Line Function
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File Line Function
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File Line Function
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File Line Function
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File Line Function
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File Line Function
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File Line Function
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File Line Function
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File Line Function
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File Line Function
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File Line Function
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File Line Function
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File Line Function
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
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File Line Function
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
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File Line Function
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File Line Function
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
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File Line Function
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File Line Function
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File Line Function
/showthread.php 907 errorHandler->error
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File Line Function
/showthread.php 1630 errorHandler->error
/showthread.php 1632 buildtree
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File Line Function
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File Line Function
/showthread.php 1630 errorHandler->error
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File Line Function
/showthread.php 1630 errorHandler->error
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/showthread.php 919 buildtree
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File Line Function
/showthread.php 1630 errorHandler->error
/showthread.php 1632 buildtree
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Warning [2] Undefined array key 170 - Line: 1630 - File: showthread.php PHP 8.0.26 (Linux)
File Line Function
/showthread.php 1630 errorHandler->error
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Warning [2] Undefined array key 175 - Line: 1630 - File: showthread.php PHP 8.0.26 (Linux)
File Line Function
/showthread.php 1630 errorHandler->error
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/showthread.php 919 buildtree
Warning [2] Undefined array key 394 - Line: 1630 - File: showthread.php PHP 8.0.26 (Linux)
File Line Function
/showthread.php 1630 errorHandler->error
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/showthread.php 919 buildtree
Warning [2] Undefined array key 396 - Line: 1630 - File: showthread.php PHP 8.0.26 (Linux)
File Line Function
/showthread.php 1630 errorHandler->error
/showthread.php 1632 buildtree
/showthread.php 919 buildtree
Warning [2] Undefined array key 398 - Line: 1630 - File: showthread.php PHP 8.0.26 (Linux)
File Line Function
/showthread.php 1630 errorHandler->error
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/showthread.php 919 buildtree
Warning [2] Undefined array key 401 - Line: 1630 - File: showthread.php PHP 8.0.26 (Linux)
File Line Function
/showthread.php 1630 errorHandler->error
/showthread.php 1632 buildtree
/showthread.php 919 buildtree
Warning [2] Undefined array key 402 - Line: 1630 - File: showthread.php PHP 8.0.26 (Linux)
File Line Function
/showthread.php 1630 errorHandler->error
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/showthread.php 919 buildtree
Warning [2] Undefined array key 404 - Line: 1630 - File: showthread.php PHP 8.0.26 (Linux)
File Line Function
/showthread.php 1630 errorHandler->error
/showthread.php 1632 buildtree
/showthread.php 919 buildtree
Warning [2] Undefined array key 407 - Line: 1630 - File: showthread.php PHP 8.0.26 (Linux)
File Line Function
/showthread.php 1630 errorHandler->error
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/showthread.php 1632 buildtree
/showthread.php 919 buildtree
Warning [2] Undefined array key 408 - Line: 1630 - File: showthread.php PHP 8.0.26 (Linux)
File Line Function
/showthread.php 1630 errorHandler->error
/showthread.php 1632 buildtree
/showthread.php 919 buildtree
Warning [2] Undefined array key 409 - Line: 1630 - File: showthread.php PHP 8.0.26 (Linux)
File Line Function
/showthread.php 1630 errorHandler->error
/showthread.php 1632 buildtree
/showthread.php 919 buildtree
Warning [2] Undefined array key 410 - Line: 1630 - File: showthread.php PHP 8.0.26 (Linux)
File Line Function
/showthread.php 1630 errorHandler->error
/showthread.php 1632 buildtree
/showthread.php 919 buildtree
Warning [2] Undefined array key 411 - Line: 1630 - File: showthread.php PHP 8.0.26 (Linux)
File Line Function
/showthread.php 1630 errorHandler->error
/showthread.php 1632 buildtree
/showthread.php 919 buildtree
Warning [2] Undefined array key 412 - Line: 1630 - File: showthread.php PHP 8.0.26 (Linux)
File Line Function
/showthread.php 1630 errorHandler->error
/showthread.php 1632 buildtree
/showthread.php 919 buildtree
Warning [2] Undefined array key 413 - Line: 1630 - File: showthread.php PHP 8.0.26 (Linux)
File Line Function
/showthread.php 1630 errorHandler->error
/showthread.php 1632 buildtree
/showthread.php 919 buildtree
Warning [2] Undefined array key 414 - Line: 1630 - File: showthread.php PHP 8.0.26 (Linux)
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Bell's theorem - for or against Hidden Variables?
#30
What about time?  Why would it not be a hidden variable, considering that it is not a real quantity independent of spacetime?  Spacetime dependence, then, would dictate that the time parameter demands specification of measure space, and once that is done one cannot avoid including the parameter as integrated into the measure.  

The conventional way to do measurements of Bell-Aspect quantum correlations is described by Richard Gill:  "The experiment is about *counting*. There are two measurement devices which have binary settings ('1' or '2'). There is a binary outcome. ('+' or '-') At the end of the experiment you have 16 counts. So many times you saw outcome '++' and the setting was '11', so many times '+-' and the setting was '12' ... so many times '--' and the setting was '22'. Quantum mechanics predicts the probabilities of outcomes given settings e.g. Prob('-+' | '21').  The physicist's correlation is just the probability of equal outcomes minus the probability of different outcomes." *

Now if Bell-Aspect is a simple discrete counting function as Richard claims, and pairwise measures have 16 possible binary outcomes, let's try using the ultimate discrete counting device -- prime numbers.

Because all odd primes are congruent (mod 2), and unity is not considered a prime, let's take the ordered sequence of the first 8 primes on the natural line: 3, 5, 7, 11, 13, 17, 19, 23

This is the densest sequence of primes > 2 of cardinality 8, with the interesting properties that all pairs are congruent (mod 2), regardless of order, and 23 is the least prime that is not a member of a twin pair.

If we take quantum correlations as signed terms, as Richard describes, then every term has a corresponding negative value, for 16 unique counts.  That's too many, though -- we should have only 4 each (+) and ( - ) values, for 4 pairwise outcomes.  Look:

We find exactly four primes in the sequence with the Sophie Germain property
(P and 2P + 1 are both prime):  {3, 5, 11, 23}.  Let’s call this set (+).  Call ( - ) the remaining set {7, 13, 17, 19}

The one property that these combined sets have, that the conventional 4 X 4 correlation matrix does not – is reversibility. Here is why:

{+1, + 1, + 1, + 1} and {- 1, - 1, - 1, -1} with an upper bound (CHSH bound) of 2, cannot describe an evolution of particle interactions – what EPR would call hidden variables – that a wave function captures by symmetry of motion that implies reversibility of states.

We can see this clearly, by writing the delta between each term of the ordered sequences:

(+) 3 5 11 23

       + + + -
       4 8 6 4  
        - - - +

( - ) 7 13 17 19



So we generate the positive set as {3+4, 5+8, 11+6, 23-4}

The negative set is                       {7-4, 13-8, 17-6, 19+4}


So while the fundamental linear assumption of the 4 X 4 matrix is a terminating order of + + + - or - - - + (+ 3 – 1 or – 3 + 1), our continuous function is compelled to be reversible to the origin.

The delta terms all cancel, so we haven’t lost any consistency with the natural integer sequence (to which in fact, recursion is a native property). We’ve gained additional information though, of a time parameter that is sensitive to initial condition – is the origin positive or negative?

As we demonstrated, regarding the algebraic closure of the complex plane, the double-zero origin of C demands positivity parity starting condition  -- the 2 + 1 condition gives us the prime 3.  The counting function still holds, when measuring quantum correlations; however, the three delta terms are hidden variables (one term is redundant).

Karl Hess and Walter Philipp introduced the time parameter ("timelike correlated parameter") to the Bell inequality, with the same result.  “An example of outcomes for the products of equation 3.1   A(a,lambda)A(b,lambda) + A(a,lambda)A(c,lambda) – A(b,lambda)A(c,lambda) =/< + 1 that violate Bell’s inequality is + 1 for the terms with the plus sign and – 1 for the last term with the minus sign.  Because  - (-1) = + 1 the sum of the three terms is then + 3, which indeed violates the Bell inequality Eq (3.1)”  

In terms of computability, recursion native to the real line is equivalent to time reversibility native to general relativity cosmology, and dependent on initial condition.

* Gill, Paul Snively's blog, 2015
** Karl Hess, Einstein was Right p.47
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RE: Bell's theorem - for or against Hidden Variables? - by Thomas Ray - 06-16-2016, 03:18 PM

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