diff --git a/research/k8-phase-local-gauges/BOUNDARY-COMPARISON.json b/research/k8-phase-local-gauges/BOUNDARY-COMPARISON.json new file mode 100644 index 0000000000..80f572588f --- /dev/null +++ b/research/k8-phase-local-gauges/BOUNDARY-COMPARISON.json @@ -0,0 +1,234 @@ +{ + "status": "PASS_ZERO_BOUNDARY_PRICE_COMPARISON", + "pr1259_head": "61367611154266a982fe25e1a6243a8aad77227d", + "orientations": { + "backward": { + "predecessor_minima_checked": 16, + "rows": [ + { + "helper": 264, + "unrestricted_delta_per_component": -110, + "reset_delta_per_component": -110, + "reset_price_per_component": 0 + }, + { + "helper": 265, + "unrestricted_delta_per_component": -155, + "reset_delta_per_component": -151, + "reset_price_per_component": 4 + }, + { + "helper": 266, + "unrestricted_delta_per_component": -160, + "reset_delta_per_component": -158, + "reset_price_per_component": 2 + }, + { + "helper": 267, + "unrestricted_delta_per_component": -167, + "reset_delta_per_component": -165, + "reset_price_per_component": 2 + }, + { + "helper": 268, + "unrestricted_delta_per_component": -119, + "reset_delta_per_component": -119, + "reset_price_per_component": 0 + }, + { + "helper": 269, + "unrestricted_delta_per_component": -111, + "reset_delta_per_component": -111, + "reset_price_per_component": 0 + }, + { + "helper": 270, + "unrestricted_delta_per_component": -162, + "reset_delta_per_component": -162, + "reset_price_per_component": 0 + }, + { + "helper": 271, + "unrestricted_delta_per_component": -161, + "reset_delta_per_component": -161, + "reset_price_per_component": 0 + }, + { + "helper": 272, + "unrestricted_delta_per_component": -100, + "reset_delta_per_component": -100, + "reset_price_per_component": 0 + }, + { + "helper": 274, + "unrestricted_delta_per_component": -123, + "reset_delta_per_component": -119, + "reset_price_per_component": 4 + }, + { + "helper": 276, + "unrestricted_delta_per_component": -172, + "reset_delta_per_component": -170, + "reset_price_per_component": 2 + }, + { + "helper": 278, + "unrestricted_delta_per_component": -127, + "reset_delta_per_component": -121, + "reset_price_per_component": 6 + }, + { + "helper": 279, + "unrestricted_delta_per_component": -108, + "reset_delta_per_component": -106, + "reset_price_per_component": 2 + }, + { + "helper": 280, + "unrestricted_delta_per_component": -137, + "reset_delta_per_component": -133, + "reset_price_per_component": 4 + }, + { + "helper": 281, + "unrestricted_delta_per_component": -59, + "reset_delta_per_component": -57, + "reset_price_per_component": 2 + }, + { + "helper": 283, + "unrestricted_delta_per_component": -163, + "reset_delta_per_component": -159, + "reset_price_per_component": 4 + }, + { + "helper": 359, + "unrestricted_delta_per_component": -259, + "reset_delta_per_component": -259, + "reset_price_per_component": 0 + }, + { + "helper": 427, + "unrestricted_delta_per_component": -263, + "reset_delta_per_component": -261, + "reset_price_per_component": 2 + } + ], + "rejection_controls": 2 + }, + "forward": { + "predecessor_minima_checked": 16, + "rows": [ + { + "helper": 264, + "unrestricted_delta_per_component": -110, + "reset_delta_per_component": -110, + "reset_price_per_component": 0 + }, + { + "helper": 265, + "unrestricted_delta_per_component": -155, + "reset_delta_per_component": -151, + "reset_price_per_component": 4 + }, + { + "helper": 266, + "unrestricted_delta_per_component": -160, + "reset_delta_per_component": -158, + "reset_price_per_component": 2 + }, + { + "helper": 267, + "unrestricted_delta_per_component": -167, + "reset_delta_per_component": -165, + "reset_price_per_component": 2 + }, + { + "helper": 268, + "unrestricted_delta_per_component": -119, + "reset_delta_per_component": -119, + "reset_price_per_component": 0 + }, + { + "helper": 269, + "unrestricted_delta_per_component": -111, + "reset_delta_per_component": -111, + "reset_price_per_component": 0 + }, + { + "helper": 270, + "unrestricted_delta_per_component": -162, + "reset_delta_per_component": -162, + "reset_price_per_component": 0 + }, + { + "helper": 271, + "unrestricted_delta_per_component": -161, + "reset_delta_per_component": -161, + "reset_price_per_component": 0 + }, + { + "helper": 272, + "unrestricted_delta_per_component": -100, + "reset_delta_per_component": -100, + "reset_price_per_component": 0 + }, + { + "helper": 274, + "unrestricted_delta_per_component": -123, + "reset_delta_per_component": -119, + "reset_price_per_component": 4 + }, + { + "helper": 276, + "unrestricted_delta_per_component": -172, + "reset_delta_per_component": -170, + "reset_price_per_component": 2 + }, + { + "helper": 278, + "unrestricted_delta_per_component": -127, + "reset_delta_per_component": -121, + "reset_price_per_component": 6 + }, + { + "helper": 279, + "unrestricted_delta_per_component": -108, + "reset_delta_per_component": -106, + "reset_price_per_component": 2 + }, + { + "helper": 280, + "unrestricted_delta_per_component": -137, + "reset_delta_per_component": -133, + "reset_price_per_component": 4 + }, + { + "helper": 281, + "unrestricted_delta_per_component": -59, + "reset_delta_per_component": -57, + "reset_price_per_component": 2 + }, + { + "helper": 283, + "unrestricted_delta_per_component": -163, + "reset_delta_per_component": -159, + "reset_price_per_component": 4 + }, + { + "helper": 359, + "unrestricted_delta_per_component": -259, + "reset_delta_per_component": -259, + "reset_price_per_component": 0 + }, + { + "helper": 427, + "unrestricted_delta_per_component": -263, + "reset_delta_per_component": -261, + "reset_price_per_component": 2 + } + ], + "rejection_controls": 2 + } + } +} diff --git a/research/k8-phase-local-gauges/CERTIFICATE.json b/research/k8-phase-local-gauges/CERTIFICATE.json new file mode 100644 index 0000000000..854ae83769 --- /dev/null +++ b/research/k8-phase-local-gauges/CERTIFICATE.json @@ -0,0 +1 @@ +{"base":"dadfea6e8a78ff6ba901705f87532a71c6f5bbb8","excluded_helpers":[224,240,256],"on_pr1214":{"backward":{"after":{"charged_payload_bits":192,"complex_primitives":147924,"paid_profile":{"1":2412,"2":418,"3":432,"4":142,"5":82,"8":8},"prefix_bits":68,"prefix_l1":"14824960514781440791821/64","real_primitives":73962},"baseline_endpoint":{"all_restored":true,"centre_columns":8,"data_helper_columns":704,"dirty_helper_columns":480,"formal_input_columns":712},"before":{"charged_payload_bits":192,"complex_primitives":148442,"paid_profile":{"1":2412,"2":418,"3":432,"4":142,"5":82,"8":8},"prefix_bits":68,"prefix_l1":"14824960514781440791821/64","real_primitives":74221},"candidate_endpoint":{"all_restored":true,"centre_columns":8,"data_helper_columns":704,"dirty_helper_columns":480,"formal_input_columns":712},"candidate_sha256":"82a1001932186d1c54d000a95e606d3f9d257047108a479321dc8b77b6a89d36","delta":-259,"helper":359,"helpers":477,"inserted_scales":28,"original_before":{"charged_payload_bits":192,"complex_primitives":149018,"paid_profile":{"1":2412,"2":418,"3":432,"4":142,"5":82,"8":8},"prefix_bits":68,"prefix_l1":"14824960514781440791821/64","real_primitives":74509},"rows":[[225,-75,7,551],[226,-56,9,527],[227,-72,7,727],[228,-16,9,48],[229,-62,7,809],[230,-88,9,869],[231,-34,9,482],[232,-54,9,524],[233,-67,9,743],[234,-58,6,483],[235,-80,8,685],[236,-43,9,1147],[237,-62,8,799],[238,-56,9,473],[239,-61,8,1372],[241,-183,7,587],[242,-40,12,549],[243,-194,8,711],[244,-112,11,577],[245,-140,7,575],[246,-135,11,418],[247,-132,11,519],[248,-107,11,477],[249,-128,10,541],[250,-153,7,545],[251,-66,8,439],[252,-129,11,511],[253,-122,8,470],[254,-152,10,513],[255,-185,8,572],[257,-190,7,381],[258,-64,12,896],[259,-166,8,1293],[260,-120,11,247],[261,-143,7,395],[262,-136,11,602],[263,-121,11,325],[264,-110,11,253],[265,-148,10,917],[266,-159,7,425],[267,-165,8,337],[268,-120,11,265],[269,-111,8,233],[270,-162,10,333],[271,-161,8,284],[272,-100,10,344],[273,-20,7,72],[274,-119,12,608],[275,-14,7,98],[276,-169,11,813],[277,-18,7,99],[278,-121,11,501],[279,-106,11,555],[280,-133,11,746],[281,-57,9,222],[282,-10,6,96],[283,-159,14,622],[284,-139,11,422],[285,-44,9,481],[286,-155,11,300],[287,-112,10,259],[288,-94,10,281],[289,-20,7,72],[290,-106,12,320],[291,-14,7,98],[292,-173,11,407],[293,-18,7,99],[294,-120,11,423],[295,-106,11,369],[296,-129,11,516],[297,-63,9,253],[298,-10,6,96],[299,-142,12,472],[300,-132,11,282],[301,-35,9,336],[302,-161,11,495],[303,-107,10,422],[304,-91,10,261],[305,-20,7,72],[306,-107,10,208],[307,-14,7,98],[308,-165,9,409],[309,-18,7,99],[310,-108,9,282],[311,-4,7,91],[312,-161,11,383],[313,-59,9,447],[314,-10,6,96],[315,-144,14,674],[316,-100,11,495],[317,-24,9,468],[318,-151,11,273],[319,-107,10,231],[320,-112,9,286],[321,-22,7,70],[322,-100,9,247],[323,-14,7,102],[324,-162,9,295],[325,-16,7,102],[326,-114,9,240],[327,-4,9,88],[328,-47,11,146],[329,-57,9,172],[330,-11,6,96],[331,-148,12,334],[332,-101,11,213],[333,-29,9,137],[334,-154,11,285],[335,-142,9,364],[336,-163,9,386],[337,-22,7,70],[338,-127,11,1031],[339,-14,7,102],[340,-160,11,322],[341,-16,7,102],[342,-129,11,630],[343,-144,11,540],[344,-50,11,208],[345,-60,9,231],[346,-11,6,96],[347,-154,14,792],[348,-184,11,743],[349,-27,9,239],[350,-163,11,333],[351,-145,12,441],[352,-119,9,258],[353,-22,7,70],[354,-143,11,1097],[355,-14,7,102],[356,-161,11,322],[357,-16,7,102],[358,-112,11,290],[359,-259,11,1121],[360,-61,11,255],[361,-55,9,271],[362,-11,6,96],[363,-142,12,328],[364,-107,11,391],[365,-34,9,158],[366,-151,11,297],[367,-147,10,346],[368,-146,9,399],[369,-22,7,70],[370,-99,8,215],[371,-14,7,102],[372,-138,8,346],[373,-16,7,102],[374,-106,8,290],[375,-108,8,239],[376,-44,11,136],[377,-55,9,203],[378,-11,6,96],[379,-171,14,483],[380,-101,11,238],[381,-35,9,190],[382,-158,11,340],[383,-132,12,361],[384,-112,9,255],[385,-22,7,70],[386,-106,8,203],[387,-14,7,102],[388,-157,8,295],[389,-16,7,102],[390,-105,8,236],[391,-142,8,418],[392,-51,11,204],[393,-50,9,153],[394,-11,6,96],[395,-150,12,407],[396,-99,11,239],[397,-33,9,206],[398,-151,11,269],[399,-141,12,342],[400,-38,9,187],[401,-199,7,389],[402,-178,7,333],[403,-197,7,435],[404,-106,7,186],[405,-144,7,269],[406,-102,7,204],[407,-130,7,325],[408,-96,8,145],[409,-109,9,356],[410,-139,6,339],[411,-188,8,325],[412,-104,8,159],[413,-102,8,152],[414,-141,8,303],[415,-146,8,289],[416,-36,9,230],[417,-179,7,293],[418,-159,7,312],[419,-183,7,385],[420,-104,7,177],[421,-153,7,347],[422,-128,7,466],[423,-108,7,192],[424,-95,8,153],[425,-109,9,293],[426,-132,6,271],[427,-77,8,469],[428,-94,8,185],[429,-100,8,157],[430,-186,8,406],[431,-149,8,228],[432,-63,8,194],[433,-45,7,163],[434,-32,9,174],[435,-53,7,215],[436,-18,9,52],[437,-35,7,161],[438,-58,9,156],[439,-16,9,92],[440,-14,9,74],[441,-28,9,116],[442,-37,6,165],[443,-39,8,101],[444,-16,9,65],[445,-42,8,111],[446,-27,9,103],[447,-48,8,164],[448,0,7,10],[449,0,7,10],[450,0,7,10],[451,0,7,10],[452,0,7,9],[453,0,7,9],[454,0,7,9],[455,0,7,9],[456,-32,9,129],[457,-28,9,157],[458,-45,9,389],[459,-28,9,341],[460,-20,8,107],[461,-17,8,115],[462,-21,8,139],[463,-28,8,162],[464,-25,9,82],[465,-41,9,362],[466,-34,9,205],[467,-36,9,193],[468,-22,8,174],[469,-22,8,91],[470,-25,8,115],[471,-33,8,326],[472,-1,5,36],[473,0,5,11],[474,-1,4,80],[475,-6,4,68],[476,-6,4,15],[477,-11,4,159],[478,-18,8,69],[479,-17,8,401],[480,-18,8,145],[481,-14,8,52],[482,-26,9,63],[483,-22,9,69],[484,0,6,8],[485,0,6,8],[486,-6,4,78],[487,-2,4,24],[488,-19,4,75],[489,-8,4,71],[490,-12,8,57],[491,-14,8,89],[492,-19,8,97],[493,-14,8,175],[494,-28,9,73],[495,-29,9,167],[496,-7,5,171],[497,0,5,16],[498,-8,6,30],[499,-94,7,161],[500,0,4,9],[501,-2,4,9],[502,-7,9,67],[503,-8,9,94],[504,-14,9,60],[505,-16,9,63],[506,-5,11,27],[507,-24,9,69],[508,0,6,8],[509,0,6,8],[510,-2,4,9],[511,-158,7,266],[512,-2,4,9],[513,-4,4,11],[514,-12,9,47],[515,-8,9,67],[516,-14,9,57],[517,-15,9,122],[518,-6,11,31],[519,-26,9,61],[520,-4,5,142],[521,0,5,11],[522,-6,4,45],[523,-4,4,35],[524,-5,4,23],[525,-16,4,149],[526,0,4,5],[527,-1,4,195],[528,0,4,11],[529,0,4,48],[530,-30,6,63],[531,0,7,7],[532,0,6,10],[533,0,6,10],[534,-8,4,61],[535,-4,4,77],[536,-12,4,65],[537,-3,4,20],[538,-2,4,7],[539,-5,4,18],[540,-2,4,7],[541,0,4,9],[542,-28,6,58],[543,0,7,7],[544,-5,5,57],[545,0,5,11],[546,-38,6,126],[547,-33,6,110],[548,-27,7,81],[549,-23,6,87],[550,0,4,5],[551,-2,4,33],[552,0,4,11],[553,-3,4,53],[554,-4,6,22],[555,0,7,7],[556,0,6,10],[557,0,6,10],[558,-26,7,92],[559,-3,6,45],[560,-35,6,93],[561,-14,6,70],[562,-2,4,9],[563,-4,4,27],[564,0,4,11],[565,0,4,13],[566,-4,7,13],[567,0,7,7],[568,-28,5,87],[569,-6,5,24],[570,-23,5,78],[571,-2,5,31],[572,0,4,6],[573,0,4,5],[574,0,4,6],[575,0,4,5],[576,-10,4,30],[577,-8,4,36],[578,-11,4,60],[579,-7,4,36],[580,0,4,6],[581,0,4,6],[582,0,4,6],[583,0,4,6],[584,0,7,12],[585,0,7,12],[586,-2,7,13],[587,0,7,12],[588,0,7,8],[589,0,6,6],[590,0,7,7],[591,0,7,7],[592,-4,11,112],[593,-8,8,44],[594,-21,7,367],[595,0,7,30],[596,-14,6,276],[597,0,6,23],[598,-1,5,57],[599,0,5,23],[600,-20,11,174],[601,-10,8,73],[602,-16,7,267],[603,-2,7,40],[604,-16,6,266],[605,-2,6,42],[606,-3,5,105],[607,-4,5,73],[608,-15,11,82],[609,-33,8,247],[610,-21,7,138],[611,-7,7,82],[612,-13,6,84],[613,-1,6,53],[614,0,5,33],[615,-6,5,165],[616,-16,10,206],[617,-18,8,59],[618,-19,9,334],[619,-2,7,204],[620,-16,6,308],[621,-8,6,222],[622,-8,5,33],[623,-8,5,36],[624,-36,8,122],[625,-15,8,50],[626,-22,7,146],[627,-1,7,36],[628,-31,6,132],[629,-11,6,41],[630,-10,5,79],[631,-10,5,159],[632,-17,9,92],[633,-13,8,44],[634,-17,7,106],[635,-5,7,57],[636,-17,6,104],[637,-8,6,62],[638,-8,5,36],[639,-8,5,36],[640,-21,9,78],[641,-19,8,50],[642,-22,7,131],[643,-6,7,45],[644,-17,6,130],[645,-10,6,54],[646,-8,5,36],[647,-9,5,60],[648,-15,9,212],[649,-6,8,93],[650,-29,7,446],[651,-9,7,42],[652,-30,6,421],[653,-9,6,78],[654,-9,5,154],[655,-2,5,28],[656,-5,9,209],[657,-11,8,81],[658,-16,7,401],[659,-3,7,45],[660,-19,6,434],[661,-5,6,78],[662,-2,5,145],[663,-2,5,28],[664,-2,12,39],[665,-6,8,29],[666,-9,9,87],[667,0,7,33],[668,-9,6,86],[669,0,6,24],[670,0,5,24],[671,0,5,24],[672,-2,10,39],[673,-6,8,29],[674,-8,7,65],[675,0,7,36],[676,-12,6,54],[677,0,6,26],[678,0,5,24],[679,0,5,24],[680,0,11,35],[681,-6,8,33],[682,-6,7,33],[683,0,7,23],[684,-6,6,26],[685,0,6,22],[686,0,5,22],[687,0,5,22],[688,0,11,35],[689,-6,8,33],[690,-6,7,33],[691,0,7,23],[692,-6,6,26],[693,0,6,22],[694,0,5,22],[695,0,5,22],[696,0,11,35],[697,-6,8,33],[698,-6,7,33],[699,0,7,23],[700,-6,6,26],[701,0,6,22],[702,0,5,22],[703,0,5,22]],"schedule":[{"bounds":[0,2],"delta":-92,"path":[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2],"run":1,"states":3,"terms":[[1381,2,true],[1427,2,true],[1472,2,true],[1540,2,true],[1602,2,true],[1672,2,true],[1736,2,true],[1802,2,true],[2266,2,true],[2339,2,true],[2404,2,true],[2478,2,true],[2552,2,true],[2623,2,true],[2688,2,true],[2762,2,true],[3540,2,true],[3863,2,true],[3983,2,true],[4154,2,true],[4975,2,true],[5046,2,true],[5119,2,true],[5194,2,true],[5267,2,true],[5338,2,true],[5405,2,true],[5479,2,true],[5960,2,true],[6039,2,true],[6119,2,true],[6197,2,true]],"vertices":96},{"bounds":[-1,1],"delta":-2,"path":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0],"run":707,"states":3,"terms":[[8879,0,true],[8939,0,true],[8943,0,true],[8944,0,true],[8945,0,true],[8946,0,true],[8947,0,true],[8948,0,true],[8949,-1,true],[8952,0,true],[8953,0,true],[8954,0,true],[8956,0,true],[8957,0,true],[8958,0,true],[8975,1,true],[8989,1,true],[9003,-1,true]],"vertices":54},{"bounds":[-7,3],"delta":-165,"path":[0,0,0,0,1,1,2,3,3,-7,-7,-3,-3,-3,-2,-4,-4,-4,-4,-3,-3,-3,-4,-4,-4,-4,-4,-4,-4,-4,-4,-4,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-4,-4,-4,-2,-1,-1,-1,-1,-1,-1,-5,-5,-5,-5,-5,-3,0,-1,-1,-1,-2,-2,-1,-1,-1,-4,-4,-4,-4,-4,-3,-3,-3,0,0,1,1],"run":4833,"states":11,"terms":[[19242,-1,true],[19256,0,true],[19311,0,true],[19329,0,true],[19341,1,true],[19345,1,true],[23468,2,true],[24019,3,true],[24027,3,true],[24047,-7,true],[24048,-7,true],[24049,-2,false],[24050,-3,true],[24051,-3,true],[24052,-2,true],[24053,-4,true],[24054,-3,false],[24055,-5,true],[24056,-4,true],[24057,-1,true],[24058,-3,true],[24059,0,true],[24060,-4,true],[24061,-5,true],[24062,-4,true],[24063,-4,true],[24064,-1,true],[24065,-4,true],[24066,-2,true],[24067,-4,true],[24068,-5,true],[24069,-4,true],[24070,-1,true],[24071,-1,false],[24072,-1,false],[24073,-1,false],[24074,-1,false],[24075,-1,false],[24076,-1,false],[24077,-1,false],[24078,-1,false],[24079,-1,true],[24080,-4,true],[24081,-1,true],[24082,-1,true],[24083,-4,true],[24084,-1,true],[24085,-1,true],[24086,-1,true],[24087,-1,true],[24088,-4,true],[24089,-4,true],[24090,-4,true],[24091,-2,false],[24092,-1,false],[24093,-5,true],[24094,-1,false],[24095,-1,true],[24096,-4,false],[24097,-1,true],[24098,-5,true],[24099,-5,true],[24100,-5,true],[24101,0,true],[24102,-5,true],[24103,-3,false],[24104,0,true],[24105,-1,true],[24106,-5,true],[24107,-1,true],[24108,-2,true],[24109,-3,true],[24110,-1,false],[24111,-1,false],[24112,-1,false],[24113,-5,true],[24114,-4,true],[24115,-4,true],[24116,-4,true],[24117,-4,true],[24118,-3,true],[24119,-4,true],[24120,-3,true],[24121,0,true],[24122,-3,true],[24158,1,true],[24437,2,false]],"vertices":957}],"total_vertices":94261},"forward":{"after":{"charged_payload_bits":192,"complex_primitives":147908,"paid_profile":{"1":2412,"2":418,"3":432,"4":142,"5":82,"8":8},"prefix_bits":52,"prefix_l1":"2765345294379392599/1024","real_primitives":73954},"baseline_endpoint":{"all_restored":true,"centre_columns":8,"data_helper_columns":704,"dirty_helper_columns":480,"formal_input_columns":712},"before":{"charged_payload_bits":192,"complex_primitives":148426,"paid_profile":{"1":2412,"2":418,"3":432,"4":142,"5":82,"8":8},"prefix_bits":52,"prefix_l1":"2765345294379392599/1024","real_primitives":74213},"candidate_endpoint":{"all_restored":true,"centre_columns":8,"data_helper_columns":704,"dirty_helper_columns":480,"formal_input_columns":712},"candidate_sha256":"0e1e33ab6e83f48bf65a0dcd7c860767078045bfd93be0012e2ab861dd0bae1a","delta":-259,"helper":359,"helpers":477,"inserted_scales":28,"original_before":{"charged_payload_bits":192,"complex_primitives":149002,"paid_profile":{"1":2412,"2":418,"3":432,"4":142,"5":82,"8":8},"prefix_bits":52,"prefix_l1":"2765345294379392599/1024","real_primitives":74501},"rows":[[225,-75,7,551],[226,-56,9,527],[227,-72,7,727],[228,-16,9,48],[229,-62,7,809],[230,-88,9,869],[231,-34,9,482],[232,-54,9,524],[233,-67,9,743],[234,-58,6,483],[235,-80,8,685],[236,-43,9,1147],[237,-62,8,799],[238,-56,9,473],[239,-61,8,1372],[241,-183,7,587],[242,-40,12,549],[243,-194,8,711],[244,-112,11,577],[245,-140,7,575],[246,-135,11,418],[247,-132,11,519],[248,-107,11,477],[249,-128,10,541],[250,-153,7,545],[251,-66,8,439],[252,-129,11,511],[253,-122,8,470],[254,-152,10,513],[255,-185,8,572],[257,-190,7,381],[258,-64,12,896],[259,-166,8,1293],[260,-120,11,247],[261,-143,7,395],[262,-136,11,602],[263,-121,11,325],[264,-110,11,253],[265,-148,10,917],[266,-159,7,425],[267,-165,8,337],[268,-120,11,265],[269,-111,8,233],[270,-162,10,333],[271,-161,8,284],[272,-100,10,344],[273,-20,7,72],[274,-119,12,608],[275,-14,7,98],[276,-169,11,813],[277,-18,7,99],[278,-121,11,501],[279,-106,11,555],[280,-133,11,746],[281,-57,9,222],[282,-10,6,96],[283,-159,14,622],[284,-139,11,422],[285,-44,9,481],[286,-155,11,300],[287,-112,10,259],[288,-94,10,281],[289,-20,7,72],[290,-106,12,320],[291,-14,7,98],[292,-173,11,407],[293,-18,7,99],[294,-120,11,423],[295,-106,11,369],[296,-129,11,516],[297,-63,9,253],[298,-10,6,96],[299,-142,12,472],[300,-132,11,282],[301,-35,9,336],[302,-161,11,495],[303,-107,10,422],[304,-91,10,261],[305,-20,7,72],[306,-107,10,208],[307,-14,7,98],[308,-165,9,409],[309,-18,7,99],[310,-108,9,282],[311,-4,7,91],[312,-161,11,383],[313,-59,9,447],[314,-10,6,96],[315,-144,14,674],[316,-100,11,495],[317,-24,9,468],[318,-151,11,273],[319,-107,10,231],[320,-112,9,286],[321,-22,7,70],[322,-100,9,247],[323,-14,7,102],[324,-162,9,295],[325,-16,7,102],[326,-114,9,240],[327,-4,9,88],[328,-47,11,146],[329,-57,9,172],[330,-11,6,96],[331,-148,12,334],[332,-101,11,213],[333,-29,9,137],[334,-154,11,285],[335,-142,9,364],[336,-163,9,386],[337,-22,7,70],[338,-127,11,1031],[339,-14,7,102],[340,-160,11,322],[341,-16,7,102],[342,-129,11,630],[343,-144,11,540],[344,-50,11,208],[345,-60,9,231],[346,-11,6,96],[347,-154,14,792],[348,-184,11,743],[349,-27,9,239],[350,-163,11,333],[351,-145,12,441],[352,-119,9,258],[353,-22,7,70],[354,-143,11,1097],[355,-14,7,102],[356,-161,11,322],[357,-16,7,102],[358,-112,11,290],[359,-259,11,1121],[360,-61,11,255],[361,-55,9,271],[362,-11,6,96],[363,-142,12,328],[364,-107,11,391],[365,-34,9,158],[366,-151,11,297],[367,-147,10,346],[368,-146,9,399],[369,-22,7,70],[370,-99,8,215],[371,-14,7,102],[372,-138,8,346],[373,-16,7,102],[374,-106,8,290],[375,-108,8,239],[376,-44,11,136],[377,-55,9,203],[378,-11,6,96],[379,-171,14,483],[380,-101,11,238],[381,-35,9,190],[382,-158,11,340],[383,-132,12,361],[384,-112,9,255],[385,-22,7,70],[386,-106,8,203],[387,-14,7,102],[388,-157,8,295],[389,-16,7,102],[390,-105,8,236],[391,-142,8,418],[392,-51,11,204],[393,-50,9,153],[394,-11,6,96],[395,-150,12,407],[396,-99,11,239],[397,-33,9,206],[398,-151,11,269],[399,-141,12,342],[400,-38,9,187],[401,-199,7,389],[402,-178,7,333],[403,-197,7,435],[404,-106,7,186],[405,-144,7,269],[406,-102,7,204],[407,-130,7,325],[408,-96,8,145],[409,-109,9,356],[410,-139,6,339],[411,-188,8,325],[412,-104,8,159],[413,-102,8,152],[414,-141,8,303],[415,-146,8,289],[416,-36,9,230],[417,-179,7,293],[418,-159,7,312],[419,-183,7,385],[420,-104,7,177],[421,-153,7,347],[422,-128,7,466],[423,-108,7,192],[424,-95,8,153],[425,-109,9,293],[426,-132,6,271],[427,-77,8,469],[428,-94,8,185],[429,-100,8,157],[430,-186,8,406],[431,-149,8,228],[432,-63,8,194],[433,-45,7,163],[434,-32,9,174],[435,-53,7,215],[436,-18,9,52],[437,-35,7,161],[438,-58,9,156],[439,-16,9,92],[440,-14,9,74],[441,-28,9,116],[442,-37,6,165],[443,-39,8,101],[444,-16,9,65],[445,-42,8,111],[446,-27,9,103],[447,-48,8,164],[448,0,7,10],[449,0,7,10],[450,0,7,10],[451,0,7,10],[452,0,7,9],[453,0,7,9],[454,0,7,9],[455,0,7,9],[456,-32,9,129],[457,-28,9,157],[458,-45,9,389],[459,-28,9,341],[460,-20,8,107],[461,-17,8,115],[462,-21,8,139],[463,-28,8,162],[464,-25,9,82],[465,-41,9,362],[466,-34,9,205],[467,-36,9,193],[468,-22,8,174],[469,-22,8,91],[470,-25,8,115],[471,-33,8,326],[472,-1,5,36],[473,0,5,11],[474,-1,4,80],[475,-6,4,68],[476,-6,4,15],[477,-11,4,159],[478,-18,8,69],[479,-17,8,401],[480,-18,8,145],[481,-14,8,52],[482,-26,9,63],[483,-22,9,69],[484,0,6,8],[485,0,6,8],[486,-6,4,78],[487,-2,4,24],[488,-19,4,75],[489,-8,4,71],[490,-12,8,57],[491,-14,8,89],[492,-19,8,97],[493,-14,8,175],[494,-28,9,73],[495,-29,9,167],[496,-7,5,171],[497,0,5,16],[498,-8,6,30],[499,-94,7,161],[500,0,4,9],[501,-2,4,9],[502,-7,9,67],[503,-8,9,94],[504,-14,9,60],[505,-16,9,63],[506,-5,11,27],[507,-24,9,69],[508,0,6,8],[509,0,6,8],[510,-2,4,9],[511,-158,7,266],[512,-2,4,9],[513,-4,4,11],[514,-12,9,47],[515,-8,9,67],[516,-14,9,57],[517,-15,9,122],[518,-6,11,31],[519,-26,9,61],[520,-4,5,142],[521,0,5,11],[522,-6,4,45],[523,-4,4,35],[524,-5,4,23],[525,-16,4,149],[526,0,4,5],[527,-1,4,195],[528,0,4,11],[529,0,4,48],[530,-30,6,63],[531,0,7,7],[532,0,6,10],[533,0,6,10],[534,-8,4,61],[535,-4,4,77],[536,-12,4,65],[537,-3,4,20],[538,-2,4,7],[539,-5,4,18],[540,-2,4,7],[541,0,4,9],[542,-28,6,58],[543,0,7,7],[544,-5,5,57],[545,0,5,11],[546,-38,6,126],[547,-33,6,110],[548,-27,7,81],[549,-23,6,87],[550,0,4,5],[551,-2,4,33],[552,0,4,11],[553,-3,4,53],[554,-4,6,22],[555,0,7,7],[556,0,6,10],[557,0,6,10],[558,-26,7,92],[559,-3,6,45],[560,-35,6,93],[561,-14,6,70],[562,-2,4,9],[563,-4,4,27],[564,0,4,11],[565,0,4,13],[566,-4,7,13],[567,0,7,7],[568,-28,5,87],[569,-6,5,24],[570,-23,5,78],[571,-2,5,31],[572,0,4,6],[573,0,4,5],[574,0,4,6],[575,0,4,5],[576,-10,4,30],[577,-8,4,36],[578,-11,4,60],[579,-7,4,36],[580,0,4,6],[581,0,4,6],[582,0,4,6],[583,0,4,6],[584,0,7,12],[585,0,7,12],[586,-2,7,13],[587,0,7,12],[588,0,7,8],[589,0,6,6],[590,0,7,7],[591,0,7,7],[592,-4,11,112],[593,-8,8,44],[594,-21,7,367],[595,0,7,30],[596,-14,6,276],[597,0,6,23],[598,-1,5,57],[599,0,5,23],[600,-20,11,174],[601,-10,8,73],[602,-16,7,267],[603,-2,7,40],[604,-16,6,266],[605,-2,6,42],[606,-3,5,105],[607,-4,5,73],[608,-15,11,82],[609,-33,8,247],[610,-21,7,138],[611,-7,7,82],[612,-13,6,84],[613,-1,6,53],[614,0,5,33],[615,-6,5,165],[616,-16,10,206],[617,-18,8,59],[618,-19,9,334],[619,-2,7,204],[620,-16,6,308],[621,-8,6,222],[622,-8,5,33],[623,-8,5,36],[624,-36,8,122],[625,-15,8,50],[626,-22,7,146],[627,-1,7,36],[628,-31,6,132],[629,-11,6,41],[630,-10,5,79],[631,-10,5,159],[632,-17,9,92],[633,-13,8,44],[634,-17,7,106],[635,-5,7,57],[636,-17,6,104],[637,-8,6,62],[638,-8,5,36],[639,-8,5,36],[640,-21,9,78],[641,-19,8,50],[642,-22,7,131],[643,-6,7,45],[644,-17,6,130],[645,-10,6,54],[646,-8,5,36],[647,-9,5,60],[648,-15,9,212],[649,-6,8,93],[650,-29,7,446],[651,-9,7,42],[652,-30,6,421],[653,-9,6,78],[654,-9,5,154],[655,-2,5,28],[656,-5,9,209],[657,-11,8,81],[658,-16,7,401],[659,-3,7,45],[660,-19,6,434],[661,-5,6,78],[662,-2,5,145],[663,-2,5,28],[664,-2,12,39],[665,-6,8,29],[666,-9,9,87],[667,0,7,33],[668,-9,6,86],[669,0,6,24],[670,0,5,24],[671,0,5,24],[672,-2,10,39],[673,-6,8,29],[674,-8,7,65],[675,0,7,36],[676,-12,6,54],[677,0,6,26],[678,0,5,24],[679,0,5,24],[680,0,11,35],[681,-6,8,33],[682,-6,7,33],[683,0,7,23],[684,-6,6,26],[685,0,6,22],[686,0,5,22],[687,0,5,22],[688,0,11,35],[689,-6,8,33],[690,-6,7,33],[691,0,7,23],[692,-6,6,26],[693,0,6,22],[694,0,5,22],[695,0,5,22],[696,0,11,35],[697,-6,8,33],[698,-6,7,33],[699,0,7,23],[700,-6,6,26],[701,0,6,22],[702,0,5,22],[703,0,5,22]],"schedule":[{"bounds":[-2,0],"delta":-92,"path":[-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2],"run":1,"states":3,"terms":[[1381,-2,true],[1427,-2,true],[1472,-2,true],[1540,-2,true],[1602,-2,true],[1672,-2,true],[1736,-2,true],[1802,-2,true],[2266,-2,true],[2339,-2,true],[2404,-2,true],[2478,-2,true],[2552,-2,true],[2623,-2,true],[2688,-2,true],[2762,-2,true],[3540,-2,true],[3863,-2,true],[3983,-2,true],[4154,-2,true],[4975,-2,true],[5046,-2,true],[5119,-2,true],[5194,-2,true],[5267,-2,true],[5338,-2,true],[5405,-2,true],[5479,-2,true],[5960,-2,true],[6039,-2,true],[6119,-2,true],[6197,-2,true]],"vertices":96},{"bounds":[-1,1],"delta":-2,"path":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,0],"run":707,"states":3,"terms":[[8879,0,true],[8939,0,true],[8943,0,true],[8944,0,true],[8945,0,true],[8946,0,true],[8947,0,true],[8948,0,true],[8949,1,true],[8952,0,true],[8953,0,true],[8954,0,true],[8956,0,true],[8957,0,true],[8958,0,true],[8975,-1,true],[8989,-1,true],[9003,1,true]],"vertices":54},{"bounds":[-3,7],"delta":-165,"path":[0,0,0,0,-1,-1,-2,-3,-3,7,7,3,3,3,2,4,4,4,4,3,3,3,4,4,4,4,4,4,4,4,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,2,1,1,1,1,1,1,5,5,5,5,5,3,0,1,1,1,2,2,1,1,1,4,4,4,4,4,3,3,3,0,0,-1,-1],"run":4833,"states":11,"terms":[[19242,1,true],[19256,0,true],[19311,0,true],[19329,0,true],[19341,-1,true],[19345,-1,true],[23468,-2,true],[24019,-3,true],[24027,-3,true],[24047,7,true],[24048,7,true],[24049,2,false],[24050,3,true],[24051,3,true],[24052,2,true],[24053,4,true],[24054,3,false],[24055,5,true],[24056,4,true],[24057,1,true],[24058,3,true],[24059,0,true],[24060,4,true],[24061,5,true],[24062,4,true],[24063,4,true],[24064,1,true],[24065,4,true],[24066,2,true],[24067,4,true],[24068,5,true],[24069,4,true],[24070,1,true],[24071,1,false],[24072,1,false],[24073,1,false],[24074,1,false],[24075,1,false],[24076,1,false],[24077,1,false],[24078,1,false],[24079,1,true],[24080,4,true],[24081,1,true],[24082,1,true],[24083,4,true],[24084,1,true],[24085,1,true],[24086,1,true],[24087,1,true],[24088,4,true],[24089,4,true],[24090,4,true],[24091,2,false],[24092,1,false],[24093,5,true],[24094,1,false],[24095,1,true],[24096,4,false],[24097,1,true],[24098,5,true],[24099,5,true],[24100,5,true],[24101,0,true],[24102,5,true],[24103,3,false],[24104,0,true],[24105,1,true],[24106,5,true],[24107,1,true],[24108,2,true],[24109,3,true],[24110,1,false],[24111,1,false],[24112,1,false],[24113,5,true],[24114,4,true],[24115,4,true],[24116,4,true],[24117,4,true],[24118,3,true],[24119,4,true],[24120,3,true],[24121,0,true],[24122,3,true],[24158,-1,true],[24437,-2,false]],"vertices":957}],"total_vertices":94261}},"orientations":{"backward":{"after":{"charged_payload_bits":192,"complex_primitives":148496,"paid_profile":{"1":2412,"2":418,"3":432,"4":142,"5":82,"8":8},"prefix_bits":68,"prefix_l1":"14824960514781440791821/64","real_primitives":74248},"baseline_endpoint":{"all_restored":true,"centre_columns":8,"data_helper_columns":704,"dirty_helper_columns":480,"formal_input_columns":712},"before":{"charged_payload_bits":192,"complex_primitives":149018,"paid_profile":{"1":2412,"2":418,"3":432,"4":142,"5":82,"8":8},"prefix_bits":68,"prefix_l1":"14824960514781440791821/64","real_primitives":74509},"candidate_endpoint":{"all_restored":true,"centre_columns":8,"data_helper_columns":704,"dirty_helper_columns":480,"formal_input_columns":712},"candidate_sha256":"377407bbbf06c4e16978c3a6a1ea019422ff7ce19b3a7d3d602870c9eec31864","delta":-261,"helper":427,"helpers":477,"inserted_scales":22,"rows":[[225,-75,7,551],[226,-56,9,527],[227,-72,7,727],[228,-16,9,48],[229,-62,7,809],[230,-88,9,869],[231,-34,9,482],[232,-54,9,524],[233,-67,9,743],[234,-58,6,483],[235,-80,8,685],[236,-43,9,1147],[237,-62,8,799],[238,-56,9,473],[239,-61,8,1372],[241,-183,7,587],[242,-40,12,549],[243,-194,8,711],[244,-113,11,577],[245,-140,7,575],[246,-135,11,418],[247,-132,11,519],[248,-109,11,477],[249,-128,10,541],[250,-153,7,491],[251,-204,8,487],[252,-129,11,511],[253,-120,8,468],[254,-152,10,513],[255,-185,8,572],[257,-190,7,381],[258,-64,12,950],[259,-166,8,1293],[260,-120,11,247],[261,-143,7,395],[262,-135,11,669],[263,-120,11,367],[264,-110,11,253],[265,-151,10,964],[266,-158,7,459],[267,-165,8,337],[268,-119,11,303],[269,-111,8,233],[270,-162,10,333],[271,-161,8,307],[272,-100,10,344],[273,-20,7,72],[274,-119,12,608],[275,-14,7,98],[276,-170,11,813],[277,-18,7,99],[278,-121,11,501],[279,-106,11,555],[280,-133,11,746],[281,-57,9,222],[282,-10,6,96],[283,-159,14,622],[284,-139,11,422],[285,-44,9,481],[286,-156,11,300],[287,-112,10,259],[288,-94,10,281],[289,-20,7,72],[290,-106,12,320],[291,-14,7,98],[292,-176,11,407],[293,-18,7,99],[294,-120,11,423],[295,-106,11,369],[296,-129,11,516],[297,-63,9,253],[298,-10,6,96],[299,-142,12,472],[300,-132,11,282],[301,-35,9,336],[302,-163,11,495],[303,-107,10,422],[304,-91,10,261],[305,-20,7,72],[306,-107,10,208],[307,-14,7,98],[308,-166,9,445],[309,-18,7,99],[310,-108,9,282],[311,-4,7,91],[312,-161,11,383],[313,-59,9,447],[314,-10,6,96],[315,-144,14,674],[316,-100,11,495],[317,-24,9,468],[318,-151,11,290],[319,-107,10,231],[320,-112,9,286],[321,-22,7,70],[322,-100,9,247],[323,-14,7,102],[324,-162,9,295],[325,-16,7,102],[326,-114,9,240],[327,-4,9,88],[328,-47,11,146],[329,-57,9,172],[330,-11,6,96],[331,-148,12,334],[332,-101,11,213],[333,-29,9,137],[334,-154,11,285],[335,-142,9,364],[336,-163,9,386],[337,-22,7,70],[338,-127,11,1031],[339,-14,7,102],[340,-160,11,322],[341,-16,7,102],[342,-129,11,630],[343,-144,11,540],[344,-50,11,208],[345,-60,9,231],[346,-11,6,96],[347,-154,14,792],[348,-184,11,743],[349,-27,9,239],[350,-163,11,333],[351,-145,12,441],[352,-119,9,258],[353,-22,7,70],[354,-143,11,1097],[355,-14,7,102],[356,-161,11,322],[357,-16,7,102],[358,-112,11,290],[359,-259,11,1121],[360,-61,11,255],[361,-55,9,271],[362,-11,6,96],[363,-142,12,328],[364,-107,11,391],[365,-34,9,158],[366,-151,11,297],[367,-147,10,346],[368,-146,9,399],[369,-22,7,70],[370,-99,8,215],[371,-14,7,102],[372,-138,8,346],[373,-16,7,102],[374,-106,8,290],[375,-108,8,239],[376,-44,11,136],[377,-55,9,203],[378,-11,6,96],[379,-171,14,483],[380,-101,11,238],[381,-35,9,190],[382,-158,11,340],[383,-132,12,361],[384,-112,9,255],[385,-22,7,70],[386,-106,8,203],[387,-14,7,102],[388,-158,8,330],[389,-16,7,102],[390,-105,8,236],[391,-142,8,418],[392,-51,11,204],[393,-50,9,153],[394,-11,6,96],[395,-150,12,407],[396,-99,11,239],[397,-33,9,206],[398,-152,11,269],[399,-141,12,342],[400,-38,9,187],[401,-199,7,389],[402,-178,7,333],[403,-197,7,435],[404,-106,7,186],[405,-144,7,269],[406,-102,7,204],[407,-130,7,325],[408,-96,8,165],[409,-110,9,354],[410,-139,6,339],[411,-188,8,325],[412,-104,8,159],[413,-102,8,152],[414,-141,8,303],[415,-148,8,289],[416,-35,9,195],[417,-179,7,293],[418,-159,7,406],[419,-183,7,477],[420,-104,7,177],[421,-153,7,395],[422,-128,7,417],[423,-108,7,250],[424,-95,8,185],[425,-109,9,334],[426,-134,6,245],[427,-261,8,517],[428,-94,8,225],[429,-99,8,155],[430,-186,8,500],[431,-149,8,252],[432,-63,8,194],[433,-45,7,163],[434,-32,9,174],[435,-53,7,215],[436,-18,9,52],[437,-35,7,161],[438,-58,9,156],[439,-16,9,92],[440,-14,9,74],[441,-28,9,116],[442,-37,6,165],[443,-39,8,101],[444,-16,9,65],[445,-42,8,111],[446,-27,9,103],[447,-48,8,164],[448,0,7,10],[449,0,7,10],[450,0,7,10],[451,0,7,10],[452,0,7,9],[453,0,7,9],[454,0,7,9],[455,0,7,9],[456,-32,9,129],[457,-28,9,157],[458,-45,9,453],[459,-28,9,341],[460,-20,8,107],[461,-20,8,115],[462,-21,8,139],[463,-31,8,162],[464,-25,9,82],[465,-41,9,362],[466,-34,9,205],[467,-36,9,193],[468,-22,8,174],[469,-22,8,91],[470,-25,8,115],[471,-33,8,326],[472,-1,5,36],[473,0,5,11],[474,-1,4,80],[475,-6,4,68],[476,-6,4,15],[477,-11,4,159],[478,-18,8,69],[479,-17,8,401],[480,-18,8,145],[481,-15,8,61],[482,-26,9,63],[483,-22,9,69],[484,0,6,8],[485,0,6,8],[486,-6,4,78],[487,-2,4,24],[488,-19,4,75],[489,-8,4,71],[490,-12,8,57],[491,-14,8,89],[492,-19,8,97],[493,-15,8,185],[494,-28,9,73],[495,-29,9,167],[496,-7,5,171],[497,0,5,16],[498,-8,6,30],[499,-94,7,161],[500,0,4,9],[501,-2,4,9],[502,-7,9,67],[503,-8,9,94],[504,-14,9,60],[505,-14,9,63],[506,-5,11,27],[507,-24,9,69],[508,0,6,8],[509,0,6,8],[510,-2,4,9],[511,-158,7,266],[512,-2,4,9],[513,-4,4,11],[514,-12,9,47],[515,-8,9,67],[516,-14,9,57],[517,-15,9,122],[518,-6,11,31],[519,-26,9,61],[520,-4,5,142],[521,0,5,11],[522,-6,4,45],[523,-4,4,35],[524,-5,4,23],[525,-16,4,149],[526,0,4,5],[527,-1,4,195],[528,0,4,11],[529,0,4,48],[530,-30,6,63],[531,0,7,7],[532,0,6,10],[533,0,6,10],[534,-8,4,61],[535,-4,4,77],[536,-12,4,65],[537,-3,4,20],[538,-2,4,7],[539,-5,4,18],[540,-2,4,7],[541,0,4,9],[542,-28,6,58],[543,0,7,7],[544,-5,5,57],[545,0,5,11],[546,-38,6,174],[547,-33,6,110],[548,-27,7,81],[549,-23,6,87],[550,0,4,5],[551,-2,4,33],[552,0,4,11],[553,-3,4,53],[554,-4,6,22],[555,0,7,7],[556,0,6,10],[557,0,6,10],[558,-26,7,92],[559,-3,6,45],[560,-35,6,135],[561,-14,6,70],[562,-2,4,9],[563,-4,4,27],[564,0,4,11],[565,-1,4,18],[566,-4,7,13],[567,0,7,7],[568,-28,5,125],[569,-6,5,24],[570,-23,5,78],[571,-2,5,31],[572,0,4,6],[573,0,4,5],[574,0,4,6],[575,0,4,5],[576,-10,4,30],[577,-8,4,36],[578,-11,4,96],[579,-7,4,36],[580,0,4,6],[581,0,4,6],[582,0,4,6],[583,0,4,6],[584,0,7,12],[585,0,7,12],[586,-2,7,13],[587,0,7,12],[588,0,7,8],[589,0,6,6],[590,0,7,7],[591,0,7,7],[592,-4,11,112],[593,-8,8,44],[594,-21,7,367],[595,0,7,30],[596,-14,6,276],[597,0,6,23],[598,-1,5,57],[599,0,5,23],[600,-20,11,174],[601,-10,8,73],[602,-16,7,267],[603,-2,7,40],[604,-16,6,266],[605,-2,6,42],[606,-3,5,105],[607,-4,5,73],[608,-15,11,82],[609,-33,8,247],[610,-21,7,138],[611,-7,7,82],[612,-13,6,84],[613,-1,6,53],[614,0,5,33],[615,-6,5,165],[616,-16,10,206],[617,-18,8,59],[618,-19,9,334],[619,-2,7,204],[620,-16,6,308],[621,-8,6,222],[622,-8,5,33],[623,-8,5,36],[624,-34,8,146],[625,-15,8,50],[626,-22,7,176],[627,-1,7,36],[628,-31,6,159],[629,-11,6,41],[630,-10,5,95],[631,-10,5,159],[632,-17,9,92],[633,-13,8,44],[634,-17,7,106],[635,-5,7,57],[636,-17,6,104],[637,-8,6,62],[638,-8,5,36],[639,-8,5,36],[640,-21,9,78],[641,-19,8,50],[642,-22,7,131],[643,-6,7,45],[644,-17,6,130],[645,-10,6,54],[646,-8,5,36],[647,-9,5,60],[648,-15,9,212],[649,-8,8,93],[650,-34,7,446],[651,-9,7,42],[652,-36,6,421],[653,-9,6,78],[654,-9,5,154],[655,-2,5,37],[656,-5,9,209],[657,-11,8,81],[658,-18,7,401],[659,-3,7,45],[660,-22,6,434],[661,-5,6,78],[662,-2,5,145],[663,-2,5,37],[664,-2,12,39],[665,-6,8,29],[666,-9,9,87],[667,0,7,33],[668,-9,6,86],[669,0,6,24],[670,0,5,24],[671,0,5,24],[672,-2,10,39],[673,-6,8,29],[674,-8,7,65],[675,0,7,36],[676,-12,6,54],[677,0,6,26],[678,0,5,24],[679,0,5,24],[680,0,11,35],[681,-6,8,33],[682,-6,7,33],[683,0,7,23],[684,-6,6,26],[685,0,6,22],[686,0,5,22],[687,0,5,22],[688,0,11,35],[689,-6,8,33],[690,-6,7,33],[691,0,7,23],[692,-6,6,26],[693,0,6,22],[694,0,5,22],[695,0,5,22],[696,0,11,35],[697,-6,8,33],[698,-6,7,33],[699,0,7,23],[700,-6,6,26],[701,0,6,22],[702,0,5,22],[703,0,5,22]],"schedule":[{"bounds":[0,2],"delta":-142,"path":[1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,1,1,1,1,2,2,2,2,2,2,2,2,1,1,1,1,1,1,2,2,2,2,2,2,2,2],"run":1,"states":3,"terms":[[259,1,true],[332,1,true],[403,1,true],[470,1,true],[552,1,true],[625,1,true],[696,1,true],[763,1,true],[843,2,true],[912,2,true],[977,2,true],[1044,2,true],[1113,2,true],[1180,2,true],[1245,2,true],[1312,2,true],[1563,1,true],[1756,1,true],[2285,1,true],[2358,1,true],[2427,1,true],[2498,1,true],[2571,1,true],[2642,1,true],[2711,1,true],[2782,1,true],[2854,2,true],[2927,2,true],[2998,2,true],[3071,2,true],[3147,2,true],[3220,2,true],[3291,2,true],[3364,2,true],[3612,1,true],[3811,1,true],[4124,1,true],[4292,1,true],[4429,2,true],[4508,2,true],[4578,2,true],[4645,2,true],[4719,2,true],[4785,2,true],[4855,2,true],[4921,2,true],[5569,1,true],[5697,1,true],[5838,1,true],[5900,1,true],[5987,1,true],[6144,1,true],[6299,2,true],[6372,2,true],[6443,2,true],[6517,2,true],[6593,2,true],[6666,2,true],[6737,2,true],[6810,2,true]],"vertices":180},{"bounds":[-1,4],"delta":-119,"path":[0,1,1,2,2,2,2,2,1,2,2,2,2,2,2,1,3,4,4,4,2,2,2,2,2,1,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,2,2,2,2,2,2,2,2,2,0,0,0],"run":4833,"states":6,"terms":[[21671,0,true],[21741,1,true],[21752,1,true],[21799,2,true],[22558,2,true],[22559,2,true],[22560,2,true],[22561,2,true],[22562,1,true],[22563,3,false],[22564,3,false],[22565,2,true],[22566,3,false],[22567,4,false],[22568,2,false],[22569,1,true],[22570,3,true],[22571,4,false],[22572,4,false],[22573,4,false],[22574,2,false],[22575,4,false],[22576,2,true],[22577,2,true],[22578,4,false],[22579,1,true],[22580,2,true],[22581,2,true],[22582,2,false],[22583,2,false],[22584,3,false],[22585,2,true],[22586,2,false],[22587,3,false],[22588,3,true],[22589,3,true],[22590,2,false],[22591,3,true],[22592,3,true],[22593,3,true],[22594,3,true],[22595,3,true],[22596,1,false],[22597,2,false],[22598,3,false],[22599,3,false],[22600,2,true],[22601,2,true],[22602,3,false],[22603,2,true],[22604,2,true],[22617,0,true],[22657,-1,false],[22693,0,true]],"vertices":324}],"total_vertices":95490},"forward":{"after":{"charged_payload_bits":192,"complex_primitives":148480,"paid_profile":{"1":2412,"2":418,"3":432,"4":142,"5":82,"8":8},"prefix_bits":52,"prefix_l1":"2765345294379392599/1024","real_primitives":74240},"baseline_endpoint":{"all_restored":true,"centre_columns":8,"data_helper_columns":704,"dirty_helper_columns":480,"formal_input_columns":712},"before":{"charged_payload_bits":192,"complex_primitives":149002,"paid_profile":{"1":2412,"2":418,"3":432,"4":142,"5":82,"8":8},"prefix_bits":52,"prefix_l1":"2765345294379392599/1024","real_primitives":74501},"candidate_endpoint":{"all_restored":true,"centre_columns":8,"data_helper_columns":704,"dirty_helper_columns":480,"formal_input_columns":712},"candidate_sha256":"4e19f0d5fef1fb02f902d73b197f74e85849a00c6264a259b7ecc5828bcda7d1","delta":-261,"helper":427,"helpers":477,"inserted_scales":22,"rows":[[225,-75,7,551],[226,-56,9,527],[227,-72,7,727],[228,-16,9,48],[229,-62,7,809],[230,-88,9,869],[231,-34,9,482],[232,-54,9,524],[233,-67,9,743],[234,-58,6,483],[235,-80,8,685],[236,-43,9,1147],[237,-62,8,799],[238,-56,9,473],[239,-61,8,1372],[241,-183,7,587],[242,-40,12,549],[243,-194,8,711],[244,-113,11,577],[245,-140,7,575],[246,-135,11,418],[247,-132,11,519],[248,-109,11,477],[249,-128,10,541],[250,-153,7,491],[251,-204,8,487],[252,-129,11,511],[253,-120,8,468],[254,-152,10,513],[255,-185,8,572],[257,-190,7,381],[258,-64,12,950],[259,-166,8,1293],[260,-120,11,247],[261,-143,7,395],[262,-135,11,669],[263,-120,11,367],[264,-110,11,253],[265,-151,10,964],[266,-158,7,459],[267,-165,8,337],[268,-119,11,303],[269,-111,8,233],[270,-162,10,333],[271,-161,8,307],[272,-100,10,344],[273,-20,7,72],[274,-119,12,608],[275,-14,7,98],[276,-170,11,813],[277,-18,7,99],[278,-121,11,501],[279,-106,11,555],[280,-133,11,746],[281,-57,9,222],[282,-10,6,96],[283,-159,14,622],[284,-139,11,422],[285,-44,9,481],[286,-156,11,300],[287,-112,10,259],[288,-94,10,281],[289,-20,7,72],[290,-106,12,320],[291,-14,7,98],[292,-176,11,407],[293,-18,7,99],[294,-120,11,423],[295,-106,11,369],[296,-129,11,516],[297,-63,9,253],[298,-10,6,96],[299,-142,12,472],[300,-132,11,282],[301,-35,9,336],[302,-163,11,495],[303,-107,10,422],[304,-91,10,261],[305,-20,7,72],[306,-107,10,208],[307,-14,7,98],[308,-166,9,445],[309,-18,7,99],[310,-108,9,282],[311,-4,7,91],[312,-161,11,383],[313,-59,9,447],[314,-10,6,96],[315,-144,14,674],[316,-100,11,495],[317,-24,9,468],[318,-151,11,290],[319,-107,10,231],[320,-112,9,286],[321,-22,7,70],[322,-100,9,247],[323,-14,7,102],[324,-162,9,295],[325,-16,7,102],[326,-114,9,240],[327,-4,9,88],[328,-47,11,146],[329,-57,9,172],[330,-11,6,96],[331,-148,12,334],[332,-101,11,213],[333,-29,9,137],[334,-154,11,285],[335,-142,9,364],[336,-163,9,386],[337,-22,7,70],[338,-127,11,1031],[339,-14,7,102],[340,-160,11,322],[341,-16,7,102],[342,-129,11,630],[343,-144,11,540],[344,-50,11,208],[345,-60,9,231],[346,-11,6,96],[347,-154,14,792],[348,-184,11,743],[349,-27,9,239],[350,-163,11,333],[351,-145,12,441],[352,-119,9,258],[353,-22,7,70],[354,-143,11,1097],[355,-14,7,102],[356,-161,11,322],[357,-16,7,102],[358,-112,11,290],[359,-259,11,1121],[360,-61,11,255],[361,-55,9,271],[362,-11,6,96],[363,-142,12,328],[364,-107,11,391],[365,-34,9,158],[366,-151,11,297],[367,-147,10,346],[368,-146,9,399],[369,-22,7,70],[370,-99,8,215],[371,-14,7,102],[372,-138,8,346],[373,-16,7,102],[374,-106,8,290],[375,-108,8,239],[376,-44,11,136],[377,-55,9,203],[378,-11,6,96],[379,-171,14,483],[380,-101,11,238],[381,-35,9,190],[382,-158,11,340],[383,-132,12,361],[384,-112,9,255],[385,-22,7,70],[386,-106,8,203],[387,-14,7,102],[388,-158,8,330],[389,-16,7,102],[390,-105,8,236],[391,-142,8,418],[392,-51,11,204],[393,-50,9,153],[394,-11,6,96],[395,-150,12,407],[396,-99,11,239],[397,-33,9,206],[398,-152,11,269],[399,-141,12,342],[400,-38,9,187],[401,-199,7,389],[402,-178,7,333],[403,-197,7,435],[404,-106,7,186],[405,-144,7,269],[406,-102,7,204],[407,-130,7,325],[408,-96,8,165],[409,-110,9,354],[410,-139,6,339],[411,-188,8,325],[412,-104,8,159],[413,-102,8,152],[414,-141,8,303],[415,-148,8,289],[416,-35,9,195],[417,-179,7,293],[418,-159,7,406],[419,-183,7,477],[420,-104,7,177],[421,-153,7,395],[422,-128,7,417],[423,-108,7,250],[424,-95,8,185],[425,-109,9,334],[426,-134,6,245],[427,-261,8,517],[428,-94,8,225],[429,-99,8,155],[430,-186,8,500],[431,-149,8,252],[432,-63,8,194],[433,-45,7,163],[434,-32,9,174],[435,-53,7,215],[436,-18,9,52],[437,-35,7,161],[438,-58,9,156],[439,-16,9,92],[440,-14,9,74],[441,-28,9,116],[442,-37,6,165],[443,-39,8,101],[444,-16,9,65],[445,-42,8,111],[446,-27,9,103],[447,-48,8,164],[448,0,7,10],[449,0,7,10],[450,0,7,10],[451,0,7,10],[452,0,7,9],[453,0,7,9],[454,0,7,9],[455,0,7,9],[456,-32,9,129],[457,-28,9,157],[458,-45,9,453],[459,-28,9,341],[460,-20,8,107],[461,-20,8,115],[462,-21,8,139],[463,-31,8,162],[464,-25,9,82],[465,-41,9,362],[466,-34,9,205],[467,-36,9,193],[468,-22,8,174],[469,-22,8,91],[470,-25,8,115],[471,-33,8,326],[472,-1,5,36],[473,0,5,11],[474,-1,4,80],[475,-6,4,68],[476,-6,4,15],[477,-11,4,159],[478,-18,8,69],[479,-17,8,401],[480,-18,8,145],[481,-15,8,61],[482,-26,9,63],[483,-22,9,69],[484,0,6,8],[485,0,6,8],[486,-6,4,78],[487,-2,4,24],[488,-19,4,75],[489,-8,4,71],[490,-12,8,57],[491,-14,8,89],[492,-19,8,97],[493,-15,8,185],[494,-28,9,73],[495,-29,9,167],[496,-7,5,171],[497,0,5,16],[498,-8,6,30],[499,-94,7,161],[500,0,4,9],[501,-2,4,9],[502,-7,9,67],[503,-8,9,94],[504,-14,9,60],[505,-14,9,63],[506,-5,11,27],[507,-24,9,69],[508,0,6,8],[509,0,6,8],[510,-2,4,9],[511,-158,7,266],[512,-2,4,9],[513,-4,4,11],[514,-12,9,47],[515,-8,9,67],[516,-14,9,57],[517,-15,9,122],[518,-6,11,31],[519,-26,9,61],[520,-4,5,142],[521,0,5,11],[522,-6,4,45],[523,-4,4,35],[524,-5,4,23],[525,-16,4,149],[526,0,4,5],[527,-1,4,195],[528,0,4,11],[529,0,4,48],[530,-30,6,63],[531,0,7,7],[532,0,6,10],[533,0,6,10],[534,-8,4,61],[535,-4,4,77],[536,-12,4,65],[537,-3,4,20],[538,-2,4,7],[539,-5,4,18],[540,-2,4,7],[541,0,4,9],[542,-28,6,58],[543,0,7,7],[544,-5,5,57],[545,0,5,11],[546,-38,6,174],[547,-33,6,110],[548,-27,7,81],[549,-23,6,87],[550,0,4,5],[551,-2,4,33],[552,0,4,11],[553,-3,4,53],[554,-4,6,22],[555,0,7,7],[556,0,6,10],[557,0,6,10],[558,-26,7,92],[559,-3,6,45],[560,-35,6,135],[561,-14,6,70],[562,-2,4,9],[563,-4,4,27],[564,0,4,11],[565,-1,4,18],[566,-4,7,13],[567,0,7,7],[568,-28,5,125],[569,-6,5,24],[570,-23,5,78],[571,-2,5,31],[572,0,4,6],[573,0,4,5],[574,0,4,6],[575,0,4,5],[576,-10,4,30],[577,-8,4,36],[578,-11,4,96],[579,-7,4,36],[580,0,4,6],[581,0,4,6],[582,0,4,6],[583,0,4,6],[584,0,7,12],[585,0,7,12],[586,-2,7,13],[587,0,7,12],[588,0,7,8],[589,0,6,6],[590,0,7,7],[591,0,7,7],[592,-4,11,112],[593,-8,8,44],[594,-21,7,367],[595,0,7,30],[596,-14,6,276],[597,0,6,23],[598,-1,5,57],[599,0,5,23],[600,-20,11,174],[601,-10,8,73],[602,-16,7,267],[603,-2,7,40],[604,-16,6,266],[605,-2,6,42],[606,-3,5,105],[607,-4,5,73],[608,-15,11,82],[609,-33,8,247],[610,-21,7,138],[611,-7,7,82],[612,-13,6,84],[613,-1,6,53],[614,0,5,33],[615,-6,5,165],[616,-16,10,206],[617,-18,8,59],[618,-19,9,334],[619,-2,7,204],[620,-16,6,308],[621,-8,6,222],[622,-8,5,33],[623,-8,5,36],[624,-34,8,146],[625,-15,8,50],[626,-22,7,176],[627,-1,7,36],[628,-31,6,159],[629,-11,6,41],[630,-10,5,95],[631,-10,5,159],[632,-17,9,92],[633,-13,8,44],[634,-17,7,106],[635,-5,7,57],[636,-17,6,104],[637,-8,6,62],[638,-8,5,36],[639,-8,5,36],[640,-21,9,78],[641,-19,8,50],[642,-22,7,131],[643,-6,7,45],[644,-17,6,130],[645,-10,6,54],[646,-8,5,36],[647,-9,5,60],[648,-15,9,212],[649,-8,8,93],[650,-34,7,446],[651,-9,7,42],[652,-36,6,421],[653,-9,6,78],[654,-9,5,154],[655,-2,5,37],[656,-5,9,209],[657,-11,8,81],[658,-18,7,401],[659,-3,7,45],[660,-22,6,434],[661,-5,6,78],[662,-2,5,145],[663,-2,5,37],[664,-2,12,39],[665,-6,8,29],[666,-9,9,87],[667,0,7,33],[668,-9,6,86],[669,0,6,24],[670,0,5,24],[671,0,5,24],[672,-2,10,39],[673,-6,8,29],[674,-8,7,65],[675,0,7,36],[676,-12,6,54],[677,0,6,26],[678,0,5,24],[679,0,5,24],[680,0,11,35],[681,-6,8,33],[682,-6,7,33],[683,0,7,23],[684,-6,6,26],[685,0,6,22],[686,0,5,22],[687,0,5,22],[688,0,11,35],[689,-6,8,33],[690,-6,7,33],[691,0,7,23],[692,-6,6,26],[693,0,6,22],[694,0,5,22],[695,0,5,22],[696,0,11,35],[697,-6,8,33],[698,-6,7,33],[699,0,7,23],[700,-6,6,26],[701,0,6,22],[702,0,5,22],[703,0,5,22]],"schedule":[{"bounds":[-2,0],"delta":-142,"path":[-1,-1,-1,-1,-1,-1,-1,-1,-2,-2,-2,-2,-2,-2,-2,-2,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-2,-2,-2,-2,-2,-2,-2,-2,-1,-1,-1,-1,-2,-2,-2,-2,-2,-2,-2,-2,-1,-1,-1,-1,-1,-1,-2,-2,-2,-2,-2,-2,-2,-2],"run":1,"states":3,"terms":[[259,-1,true],[332,-1,true],[403,-1,true],[470,-1,true],[552,-1,true],[625,-1,true],[696,-1,true],[763,-1,true],[843,-2,true],[912,-2,true],[977,-2,true],[1044,-2,true],[1113,-2,true],[1180,-2,true],[1245,-2,true],[1312,-2,true],[1563,-1,true],[1756,-1,true],[2285,-1,true],[2358,-1,true],[2427,-1,true],[2498,-1,true],[2571,-1,true],[2642,-1,true],[2711,-1,true],[2782,-1,true],[2854,-2,true],[2927,-2,true],[2998,-2,true],[3071,-2,true],[3147,-2,true],[3220,-2,true],[3291,-2,true],[3364,-2,true],[3612,-1,true],[3811,-1,true],[4124,-1,true],[4292,-1,true],[4429,-2,true],[4508,-2,true],[4578,-2,true],[4645,-2,true],[4719,-2,true],[4785,-2,true],[4855,-2,true],[4921,-2,true],[5569,-1,true],[5697,-1,true],[5838,-1,true],[5900,-1,true],[5987,-1,true],[6144,-1,true],[6299,-2,true],[6372,-2,true],[6443,-2,true],[6517,-2,true],[6593,-2,true],[6666,-2,true],[6737,-2,true],[6810,-2,true]],"vertices":180},{"bounds":[-4,1],"delta":-119,"path":[0,-1,-1,-2,-2,-2,-2,-2,-1,-2,-2,-2,-2,-2,-2,-1,-3,-4,-4,-4,-2,-2,-2,-2,-2,-1,-2,-2,-2,-2,-2,-2,-2,-3,-3,-3,-3,-3,-3,-3,-3,-3,-2,-2,-2,-2,-2,-2,-2,-2,-2,0,0,0],"run":4833,"states":6,"terms":[[21671,0,true],[21741,-1,true],[21752,-1,true],[21799,-2,true],[22558,-2,true],[22559,-2,true],[22560,-2,true],[22561,-2,true],[22562,-1,true],[22563,-3,false],[22564,-3,false],[22565,-2,true],[22566,-3,false],[22567,-4,false],[22568,-2,false],[22569,-1,true],[22570,-3,true],[22571,-4,false],[22572,-4,false],[22573,-4,false],[22574,-2,false],[22575,-4,false],[22576,-2,true],[22577,-2,true],[22578,-4,false],[22579,-1,true],[22580,-2,true],[22581,-2,true],[22582,-2,false],[22583,-2,false],[22584,-3,false],[22585,-2,true],[22586,-2,false],[22587,-3,false],[22588,-3,true],[22589,-3,true],[22590,-2,false],[22591,-3,true],[22592,-3,true],[22593,-3,true],[22594,-3,true],[22595,-3,true],[22596,-1,false],[22597,-2,false],[22598,-3,false],[22599,-3,false],[22600,-2,true],[22601,-2,true],[22602,-3,false],[22603,-2,true],[22604,-2,true],[22617,0,true],[22657,1,false],[22693,0,true]],"vertices":324}],"total_vertices":95490}},"scope":"one helper, all integer exponents, reset at every non-scalar event","seed":26,"status":"PASS_K8_PHASE_LOCAL_GAUGES","wrapped_example":{"backward":{"after":{"charged_payload_bits":192,"complex_primitives":148946,"paid_profile":{"1":2412,"2":418,"3":432,"4":142,"5":82,"8":8},"prefix_bits":68,"prefix_l1":"14824960514781440791821/64","real_primitives":74473},"before":{"charged_payload_bits":192,"complex_primitives":149018,"paid_profile":{"1":2412,"2":418,"3":432,"4":142,"5":82,"8":8},"prefix_bits":68,"prefix_l1":"14824960514781440791821/64","real_primitives":74509},"candidate_endpoint":{"all_restored":true,"centre_columns":8,"data_helper_columns":704,"dirty_helper_columns":480,"formal_input_columns":712},"candidate_sha256":"e3f1f55379b7243c7cbc18b81f92a0208a428a37831b37bf4a63d812518781f1","delta":-36,"helper":652,"inserted_scales":10,"rows":[[652,-36,6,421]],"schedule":[{"bounds":[0,1],"delta":-6,"path":[1,1,1,1],"run":1767,"states":2,"terms":[[12999,1,true],[13000,1,true],[13001,1,true],[13002,1,true]],"vertices":8},{"bounds":[-2,10],"delta":-30,"path":[0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,0,-2,-2,-2,-1,-1,-1,-1,-1,-1,0,0,-1,-1,-1,-1,4,4],"run":4833,"states":13,"terms":[[17910,0,true],[18024,-1,true],[18219,0,true],[18223,0,true],[18227,0,true],[18443,0,true],[18678,-1,true],[18739,-1,true],[18785,-1,true],[18804,-1,true],[19705,-1,true],[19986,-1,true],[20197,-1,true],[20220,0,true],[20356,-2,true],[20573,-2,true],[21107,-2,true],[21128,-1,true],[21336,-1,false],[21370,-1,true],[21408,-1,true],[21505,0,false],[22331,-1,true],[22884,0,true],[22914,1,true],[23646,-1,true],[23722,-2,true],[23774,-1,true],[23976,-1,false],[24113,4,true],[24500,10,true]],"vertices":403}],"wrapped_helpers_checked":240},"forward":{"after":{"charged_payload_bits":192,"complex_primitives":148930,"paid_profile":{"1":2412,"2":418,"3":432,"4":142,"5":82,"8":8},"prefix_bits":52,"prefix_l1":"2765345294379392599/1024","real_primitives":74465},"before":{"charged_payload_bits":192,"complex_primitives":149002,"paid_profile":{"1":2412,"2":418,"3":432,"4":142,"5":82,"8":8},"prefix_bits":52,"prefix_l1":"2765345294379392599/1024","real_primitives":74501},"candidate_endpoint":{"all_restored":true,"centre_columns":8,"data_helper_columns":704,"dirty_helper_columns":480,"formal_input_columns":712},"candidate_sha256":"6d86e444a2a54e0b2b2e4f8ab518969eb811b27b59caadfa52e2f028d7372b06","delta":-36,"helper":652,"inserted_scales":10,"rows":[[652,-36,6,421]],"schedule":[{"bounds":[-1,0],"delta":-6,"path":[-1,-1,-1,-1],"run":1767,"states":2,"terms":[[12999,-1,true],[13000,-1,true],[13001,-1,true],[13002,-1,true]],"vertices":8},{"bounds":[-10,2],"delta":-30,"path":[0,0,0,0,0,0,1,1,1,1,1,1,1,0,2,2,2,1,1,1,1,1,1,0,0,1,1,1,1,-4,-4],"run":4833,"states":13,"terms":[[17910,0,true],[18024,1,true],[18219,0,true],[18223,0,true],[18227,0,true],[18443,0,true],[18678,1,true],[18739,1,true],[18785,1,true],[18804,1,true],[19705,1,true],[19986,1,true],[20197,1,true],[20220,0,true],[20356,2,true],[20573,2,true],[21107,2,true],[21128,1,true],[21336,1,false],[21370,1,true],[21408,1,true],[21505,0,false],[22331,1,true],[22884,0,true],[22914,-1,true],[23646,1,true],[23722,2,true],[23774,1,true],[23976,1,false],[24113,-4,true],[24500,-10,true]],"vertices":403}],"wrapped_helpers_checked":240}}} diff --git a/research/k8-phase-local-gauges/CLAIM.json b/research/k8-phase-local-gauges/CLAIM.json new file mode 100644 index 0000000000..f85dba5e15 --- /dev/null +++ b/research/k8-phase-local-gauges/CLAIM.json @@ -0,0 +1,21 @@ +{ + "worker": "astra_006", + "seed": 26, + "track": "complex supplier", + "base_commit": "dadfea6e8a78ff6ba901705f87532a71c6f5bbb8", + "branch": "codex/astra-006-phase-local-gauges", + "scope": "Exact optimal phase-local time-varying dyadic gauge on one selected k8 helper; reset before every non-scalar event, original ADD topology and SCALEs fixed.", + "candidates": [ + "All-helper coupled constant gauges: dense graph, nearest PR1161/1214", + "Two-sided cleanup refactorization: already PR1119", + "Phase-local dynamic single-helper gauges: selected distinct mechanism" + ], + "start_utc": "2026-10-13T21:14:22.616603+00:00", + "predecessors": { + "1161": "d210969d3158a1e6c505e41f67dd84e555c88564", + "1214": "26162c56ec9c50a80e49949f36d4dd9a137a76a6", + "1259": "61367611154266a982fe25e1a6243a8aad77227d" + }, + "stopping_rule": "Finish one contribution; exact finite DP and clipping proof; no profile/kappa claim; reserve final quarter for verification.", + "scope_refinement": "Concurrent PR1259 already has varying gauges and clipping DP. Final contribution centers on zero at every nonscalar boundary, its exact price versus PR1259, wrapped-helper coverage, local admission and fixed-PR1214 composition." +} diff --git a/research/k8-phase-local-gauges/PROOF.md b/research/k8-phase-local-gauges/PROOF.md new file mode 100644 index 0000000000..1abb375a7e --- /dev/null +++ b/research/k8-phase-local-gauges/PROOF.md @@ -0,0 +1,106 @@ +# Paid phase-local gauge schedules + +The varying-gauge identity, clipping lemma and chain DP also occur in Sagar +Thakrar's concurrent PR1259; they were independently derived during this work. +We credit that overlap explicitly. The new proof obligation here is exact identity +at **every** non-scalar boundary, including recursive and residual-wrapper events, +and the exact price of imposing it. No novelty is claimed for the common DP. + +Fix a helper h not occurring in any scalar COPY/CLEAR and not a private center. +Partition the emitted program at every non-scalar event, including phase markers, +climbs, adapters, residual wrappers and center events. Each resulting scalar run +begins and ends with gauge exponent zero. All other registers have gauge zero. + +## Exact arbitrary-input identity + +Let D(k) scale h by 2^k. Immediately before an original scalar gate A, change the +current gauge j to k by the paid scale D(k-j), and replace A by D(k) A D(-k). +For an ADD `t += q*s`, this changes only its coefficient, to +`q*2^(k*([t=h]-[s=h]))`. Original SCALEs commute with D and remain unchanged; +COPY/CLEAR has no incidence with h. Finish the run by D(-k). + +Telescoping shows that the new run has exactly the old linear map on every input, +including arbitrary helper and coefficient-work dirt (the latter is separately +handled by the retained literal lowerer). Since the gauge is zero at every +non-scalar boundary, no commutation through a recursive child, wrapper or phase +operation is needed. The entire non-scalar state and paid child stream are +unchanged. The original common frame of an incident ADD is also h's current +frame, so an adjacent scale on h uses exactly that frame. The unchanged emitted +frame/wrapper checker tests these conditions on the materialized winners. + +Gauges need change only immediately before incident ADDs, with restoration just +after the last such ADD in a run. They commute with disjoint scalar gates and +existing SCALEs; moving a scale to such an adjacent position changes neither +map nor price. Multiple successive changes collapse at no greater price by the +triangle inequality. Runs without incident ADDs optimally use no new scales. + +## Complete cost and finite exact optimization + +Write the absolute reduced dyadic ADD coefficient as p*2^e with p positive odd. +The retained PR696 one-component cost is + +``` +c(p,e) = 2 + floor(log2(p)) + popcount(p) + |e| - [p=1 and e=0]. +``` + +For the i-th incident ADD, set s_i=+1 for h as target and -1 as source, +b_i=-s_i e_i, and u_i=[p_i=1]. Its gauge-dependent cost, up to an unchanged +constant, is `f_i(k)=|k-b_i|-u_i[k=b_i]`. A positive dyadic scale costs the +absolute change of exponent. Thus the complete variable objective is + +``` +|k_1| + sum_i f_i(k_i) + sum_{i=2}^n |k_i-k_(i-1)| + |k_n|. +``` + +No entry, interior or exit scale is omitted. The unchanged scalar gates and all +COPY/CLEAR costs are added back by a complete literal invoice. The complex call +executes this one-component word on real and imaginary parts, doubling the count. + +**Clipping lemma.** Put L=min(0,b_1,...,b_n), U=max(0,b_1,...,b_n). Project every +integer k_i onto [L,U]. Projection is 1-Lipschitz and fixes zero, so all transition +and boundary costs weakly decrease. Each distance to b_i weakly decreases. A +discount previously attained is retained, and a new one may appear. Therefore +the objective cannot increase. There is an optimal schedule entirely in this +finite integer interval; this is not an empirical exponent cutoff. + +The exact DP starts at state 0 with cost zero. For each incident ADD, compute +`V_i(k)=f_i(k)+min_j(V_(i-1)(j)+|k-j|)` and finally minimize `V_n(k)+|k|`. +All costs and states are integers; backtracking supplies a witness. The intervals +include every integer, not merely coefficient breakpoints. The unit discount +makes a naive convex/median shortcut invalid. + +Different runs are independent because each boundary state is fixed at zero. +Sum the exact run minima for each helper, then compare all 477 admissible helpers. +This proves the declared one-helper optimum, conditional on the source-bound +finite input and retained primitive cost model. It does not prove an all-circuit +or all-helper bound. The same argument applies after fixing PR1214's fully priced +two-helper word; only one new phase-local helper is optimized in that comparison. +The identity boundary in that composition is relative to the fixed PR1214 word; +its existing two constant gauges and their transfer assumptions are inherited. +The wrapped L652 witness instead applies the zero-boundary rule directly to the +selected original word, including both residual-wrapper boundaries. + +## Separate checks and limits + +`comparison.py` removes the reset barriers only for pricing, joins each helper's +incident terms, and reproduces every one of PR1259's 32 saved minima. The barrier +objective is a restriction of that chain: it inserts a fixed-zero state at every +non-scalar boundary, so its optimum cannot be lower. Its one-component extra price +is 2 at L276, 2 at L427, and 0 at L359, in each orientation. The unrestricted L427 +comparison is scalar pricing only; we do not construct or admit that unrestricted +word. The reset L427 and fixed-PR1214-plus-reset-L359 words are the materialized +and locally admitted constructions in this package. This distinction avoids +assuming any new gauge commutation through the inherited recursive interface. + +The main implementation explicitly minimizes over all predecessor states. +`independent.py` instead uses forward/backward distance-transform sweeps, +evaluates costs by the actual PR696 lowerer rather than the formula, and enlarges +every exponent interval by two on each side. Its independently reconstructed +candidate streams match canonical hashes, and its literal primitive interpreter +tracks 713 arbitrary initial columns, including dirty coefficient work. + +The finite exact replays support the source-bound construction. The clipping and +telescoping arguments are written proofs, not proof-assistant certificates of +the multiplication theorem. The paid recursive profile is unchanged, so this +does not improve the selected moment root or kappa. Full compiler, native, hosting, +global precision/tape and analytic obligations remain as stated in the README. diff --git a/research/k8-phase-local-gauges/README.md b/research/k8-phase-local-gauges/README.md new file mode 100644 index 0000000000..249152d6cb --- /dev/null +++ b/research/k8-phase-local-gauges/README.md @@ -0,0 +1,169 @@ +# Exact zero-at-boundary gauges on the selected k8 word + +**Finite scalar construction, boundary-price comparison and scoped optimum; +no new kappa.** Concurrent Sagar Thakrar [PR1259](https://github.com/CrocSwap/integer-mult-bounds/pull/1259) +already supplies varying helper gauges and the integer-clipping/shortest-path +mechanism, independently rediscovered here. This package adds a stricter +interface: return the gauge to zero before **every non-scalar event**, including +recursive children and residual wrappers. It prices that restriction exactly, +checks all 477 eligible helpers including wrapped helpers, and admits the +materialized words to the retained local scalar/frame/wrapper checker. Original +SCALEs remain in place. No priority or novel shortest-path mechanism is claimed. + +The zero-boundary contract needs no commutation of a nonzero gauge through a +recursive child or wrapper. Replaying PR1259's 32 unrestricted helper minima +agrees exactly. For L276, imposing all boundary resets costs **4 primitives per +complex call**: its unrestricted saving 344 becomes 340. L427 likewise pays 4, +while L359 pays zero. [BOUNDARY-COMPARISON.json](BOUNDARY-COMPARISON.json) records +the full 16-helper comparison and four corruption/coverage controls. + +Among the **240 wrapped helpers**, the exact best reset schedule is L652, saving +**72 primitives per complex call**. Its complete forward/backward words are also +materialized, literally replayed and admitted by the retained local frame/wrapper +checker. This demonstrates a helper interface excluded by PR1259's unwrapped domain. + +On the source-bound PR1094/PR1042 k8 word, the exact best single-helper schedule +is L427, with 22 new SCALE macros in each orientation. It saves **522 real scalar +primitives per complex call** (261 per real/imaginary component), compared with +PR1161's 332 for one constant whole-word gauge. + +Adding one such schedule to the *fixed* PR1214 L251/L427 two-helper witness picks +L359, with 28 new SCALE macros. It saves another **518 primitives**, for a total +**1,094** against the selected word. Both the original and composed programs +restore arbitrary helper dirt, preserve every non-scalar event and the paid +recursive profile, and pass the retained emitted scalar/frame/wrapper checker. + +| Complete complex call, both components | Forward | Backward | +| --- | ---: | ---: | +| Selected original | 149,002 | 149,018 | +| One phase-local helper, L427 | 148,480 | 148,496 | +| PR1214's fixed two-helper baseline | 148,426 | 148,442 | +| PR1214 plus phase-local L359 | **147,908** | **147,924** | + +The inherited engine names the one-component count `real_primitives` and twice +that count `complex_primitives`; this table reports the latter, i.e. actual real +primitive operations for both components. Positive local prefix envelopes remain +52/68 bits under the unchanged 192-bit allowance. + +## Exact scope and evidence + +The domain is all 477 non-center helpers not incident with COPY/CLEAR, one helper +at a time, both orientations, arbitrary integer gauge exponents and arbitrary +changes within scalar runs, resetting to zero at every non-scalar event. Original +ADD topology, frames and SCALEs remain fixed. A clipping proof in [PROOF.md](PROOF.md) +reduces all integer exponents to a finite interval; the replay is not a finite +cutoff presented as an unbounded search. This class and the whole-word constant +gauge class differ: the latter may remain nonzero across non-scalar events. + +The composed claim fixes PR1214's two-helper witness and optimizes **one extra +phase-local helper**. It is not a global three-helper or all-helper optimum. +In this comparison, the added gauge is zero at each boundary **relative to the +fixed PR1214 word**; PR1214's two constant gauges and their inherited transfer +assumptions remain. It does not make those predecessor gauges zero at boundaries. +No native C++ compiler, complete hosting/invoice, outer moment, selected cold +replay, CI or Lean result is claimed. The unchanged emitted Python frame/wrapper +checker is a local check, distinct from those obligations. All-size/compiler, +realization, hosting, precision/tape, analytic and bit assumptions remain. + +- Main DP: 95,490 vertices per orientation on the selected word; 94,261 on PR1214. +- Separate distance-transform DP uses literal PR696 lowerer lengths on a padded + domain: all **1,908** census minima, plus both wrapped-witness minima, agree exactly. +- Independently reconstructed unrestricted minima agree with all **32** values + in the pinned PR1259 certificate; exact boundary premiums distinguish the classes. +- Literal lowered replay: **445,342 primitives** across six candidate words, + all **713** initial columns, including initially dirty coefficient work. +- Original macro replay separately checks all 712 data/helper/center columns. +- Unchanged source-pinned frame/wrapper checker: three versions, both orientations, + all **25 inherited mutation controls** rejected for each version. +- Ten package test groups include 258 exhaustive tiny shortest-path instances, + unit-discount, domain-expansion, missing-scale, wrong-orientation pricing, + nonzero-boundary and source-corruption controls. Checks also pass with `-O`. + +The new schedules and all per-helper minima are in `CERTIFICATE.json`; complete +programs are deterministically reconstructed and bound by canonical JSON hashes. +No compressed generated container hash is used as an equality oracle. + +## Reproduce + +Python standard library only, from the repository root: + +```sh +python3 -I -B research/k8-phase-local-gauges/reproduce.py +``` + +That bounded driver runs the five scoped checks below and ends with +`PASS_COMPLETE_K8_PHASE_LOCAL_GAUGES`: + +```sh +python3 -I -B research/k8-phase-local-gauges/verify.py +python3 -I -B research/k8-phase-local-gauges/independent.py +python3 -I -B research/k8-phase-local-gauges/comparison.py +python3 -I -O -B research/k8-phase-local-gauges/test_package.py +python3 -I -B research/k8-phase-local-gauges/frame_replay.py +``` + +Expected markers: `PASS_K8_PHASE_LOCAL_GAUGES`, +`PASS_INDEPENDENT_PHASE_GAUGES`, ten tests `OK`, and three +`PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY` receipts with 25 controls. +The source-pinned historical frame checker uses assertions; its subprocess always +runs without `-O`, even if the driver is invoked with `-O`. + +## Provenance, overlap and credit + +Base **dadfea6e8a78ff6ba901705f87532a71c6f5bbb8**; OS-random seed **26**, original +20–39 complex-supplier track. [CLAIM.json](CLAIM.json) records three candidates +and the stopping rule. This is a scalar side contribution; unchanged recursive +profiles cannot improve the binding moment or the selected kappa. + +PR1161 `d210969d3158a1e6c505e41f67dd84e555c88564` by @woklerx provides the retained +source loader, one-helper conjugation, exact macro replay, unit-discount pricing +and envelope engine, vendored unchanged with its notices. PR1214 +`26162c56ec9c50a80e49949f36d4dd9a137a76a6` by Hanson Sun (@bbMisk) supplies the fixed +two-helper comparator; its original certificate is pinned, and its complete +invoice is independently reconstructed. Their constant-gauge optima are credited, +not claimed as new proofs here. PR1170 consolidates existing stage SCALEs, whereas +this package retains them; no composition with that pending result is claimed. + +Sagar Thakrar's concurrent PR1259 at +`61367611154266a982fe25e1a6243a8aad77227d` (previous head +`10f4aaed33d79f76ebdebc974e201b1baad8b8aa`) is the closest mechanism overlap. +It checks 16 cold/FULL unwrapped helpers and permits nonzero gauges across +non-scalar events under the inherited homogeneous-transfer contract. Its original +certificate is pinned unchanged; this package replays its 32 minima before pricing +the added reset restriction. Philipp / @mightyOil's concurrent PR1263 at +`5fbaca13028846bddbb001e8e07addc2ab8e5816` uses many constant gauges and has the +larger scalar saving 13,000. This package does **not** claim a best scalar bill +across these classes, or composition with PR1263. Its specific contribution is +the zero-boundary contract, exact restriction price and local admission evidence. + +Sagar Thakrar's PR696 supplies the literal lowerer. The emitted frame checker is +the retained PR514/433 local replay, following icekylinx; source bytes are pinned. +The selected construction is Rohan Arun's PR1094 packing on Jeremy Kothe's k8/T16 +word and the retained Hao Yan/icekylinx, Chafik Boukhalfa, BRoute, NewBArch and +earlier supplier lineage, as documented in the frozen maintainer review. + +At selection, live open PR bodies (up to the 1,000-result request), current +discussions and the local ledger/negative-result descriptions were inspected. +Nearest initial scopes were PR1161, PR1214, PR1170, PR1119 and PR1186. The final +refresh and coordinator review identified overlapping PR1259; the contribution +was reframed around the distinct boundary contract and exact comparison above. +No pinned sprint issue was present; the local +claim was recorded. Existing source packages, selection and `upstream/` are unchanged. + +Prepared for **Philipp / @mightyOil**, with substantial **OpenAI Codex +(GPT-6 Astra)** assistance in mathematics, implementation and writing. The two +algorithms are separately implemented but both AI-assisted; no independent human +review or formal multiplication theorem is claimed. New work: Apache-2.0. + +## Open next questions + +1. **Admit the composed word to the full native/hosted compiler.** This would + determine whether the finite scalar saving translates to a complete invoice. + First step: replace only the emitted local streams in an isolated pinned k8 + replay and regenerate all downstream binds. Blocker: that complete admission + and its precision/global accounting are not supplied here. +2. **Joint phase-local schedules on two interacting helpers.** The present exact + DP is one-dimensional; two simultaneous gauges can interact on a shared ADD. + First step: choose one run containing L359/L427 and price the exact 2D transition + problem, including both helpers' scales. Blocker: a complete unbounded-domain + reduction and full-word reconstruction must precede any global-optimum claim. diff --git a/research/k8-phase-local-gauges/SOURCES.json b/research/k8-phase-local-gauges/SOURCES.json new file mode 100644 index 0000000000..0e56ee7655 --- /dev/null +++ b/research/k8-phase-local-gauges/SOURCES.json @@ -0,0 +1,20 @@ +{ + "base": "dadfea6e8a78ff6ba901705f87532a71c6f5bbb8", + "pr1161_head": "d210969d3158a1e6c505e41f67dd84e555c88564", + "pr1214_head": "26162c56ec9c50a80e49949f36d4dd9a137a76a6", + "vendor": { + "BASE-SELECTED.json": "c49e308d209dfbaba184a0d41dbc03cb424663f7ad8136d56aba088bba7f5723", + "PROOF.md": "89cbba31b4d95b9c7c69e3bbccd9858e45cd43e1968c39472af7e03fea0e3e54", + "PROVENANCE.md": "76dca2049e8c008da0398fd722745e421be92c66dac876cf8463295f6cb18518", + "SOURCES.json": "45f24dbd27239e499600e497e3d86cf812f3b45122088ad083a836e8d646b320", + "engine.py": "997b34533aea200c339263a96dd6f76facf21bf54b1627ab244e2ae72d348400" + }, + "pr1214_certificate_sha256": "8bfe759c365d87c7f9d0278fa9ee70734aee2cdcca34972de44ed3203f0103d2", + "frame_checker": { + "path": "research/complex-sw4-frame8/local/hpe_audit_local.py", + "sha256": "6bd9a1e279c9c9e4f3767d9f82e537b559292906feb2ddab02f380fb6523a810" + }, + "pr1259_head": "61367611154266a982fe25e1a6243a8aad77227d", + "pr1259_certificate_sha256": "3c5acedd505941f600124663c1bf53ddd4799573684b9da311e25a8c14780395", + "pr1263_head_context_only": "5fbaca13028846bddbb001e8e07addc2ab8e5816" +} diff --git a/research/k8-phase-local-gauges/VALIDATION.json b/research/k8-phase-local-gauges/VALIDATION.json new file mode 100644 index 0000000000..97fbdf7b80 --- /dev/null +++ b/research/k8-phase-local-gauges/VALIDATION.json @@ -0,0 +1,50 @@ +{ + "status": "PASS_COMPLETE_SCOPED_PACKAGE", + "base": "dadfea6e8a78ff6ba901705f87532a71c6f5bbb8", + "timestamp_utc": "2026-10-13T21:30:12.618897+00:00", + "platform": "macOS-27.0.1-arm64-arm-64bit-Mach-O", + "main_interpreter": "3.14.7", + "portable_interpreter": "CPython 3.12.13", + "checks": [ + "Complete reproduce.py on CPython3.12.13", + "Main and independent checks under isolated optimized default Python", + "Ten test groups under isolated optimized Python", + "25 selected-record source/inventory tests", + "verify_selected_result.py", + "research_baseline.py (source bindings only)", + "Complete offline relocated replay from path containing a space with exactly12 external pinned files", + "Exact pinned PR1259 comparison: all32 unrestricted minima; four corruption/domain controls", + "Wrapped L652 full literal and emitted frame/wrapper admission, both orientations" + ], + "overlap_refresh": { + "open_prs": 860, + "newest_pr": 1268, + "main": "dadfea6e8a78ff6ba901705f87532a71c6f5bbb8", + "closest": [ + 1161, + 1214, + 1170, + 1119, + 1186, + 1259, + 1263 + ], + "new_overlap_found": true, + "resolution": "Credit PR1259 varying-gauge/clipping mechanism; distinct zero-at-every-nonscalar contract, exact restriction-price comparison, wrapped-helper coverage and emitted local frame/wrapper admission. No composition with PR1263." + }, + "certificate_sha256": "072fd0970d6a7d5b06b1d2def082aa6e1b83800c1b3f6e05b889d6773c20d705", + "not_run": [ + "Native C++ compiler", + "Complete hosting/global invoice", + "Selected cold replay", + "Remote CI", + "Lean" + ], + "changes_kappa": false, + "independent_totals": { + "helper_minima": 1910, + "padded_vertices": 759448, + "literal_primitives": 445342, + "formal_columns": 713 + } +} diff --git a/research/k8-phase-local-gauges/comparison.py b/research/k8-phase-local-gauges/comparison.py new file mode 100644 index 0000000000..0148fcb1c0 --- /dev/null +++ b/research/k8-phase-local-gauges/comparison.py @@ -0,0 +1,70 @@ +"""Exact price of resetting at every non-scalar boundary versus PR1259.""" +import importlib.util +import json +from pathlib import Path +import sys + +HERE = Path(__file__).resolve().parent +spec = importlib.util.spec_from_file_location('v', HERE / 'verify.py') +v = importlib.util.module_from_spec(spec) +spec.loader.exec_module(v) + + +def check_predecessor(rows, actual): + v.need(set(actual) == {r['helper'] for r in rows}, 'complete predecessor helper coverage') + for row in rows: + v.need(actual[row['helper']] == row['delta_real'], 'PR1259 minimum mismatch') + + +def compute(): + lib = v.engine() + word, programs, _, _ = lib.load() + helpers, _ = lib.domain(word, programs) + predecessor = json.loads((HERE / 'vendor/pr1259/CERTIFICATE.json').read_text()) + cert = json.loads((HERE / 'CERTIFICATE.json').read_text()) + answer = {'status': 'PASS_ZERO_BOUNDARY_PRICE_COMPARISON', 'pr1259_head': + '61367611154266a982fe25e1a6243a8aad77227d', 'orientations': {}} + for orientation, events in programs.items(): + streams = v.terms(lib, events, helpers) + prior = predecessor['orientations'][orientation]['census'] + wanted_helpers = set(predecessor['helpers']) | {359, 427} + rows, actual = [], {} + for h in sorted(wanted_helpers): + runs = list(streams[h].values()) + relaxed = v.solve_run([term for run in runs for term in run])['delta'] + reset = sum(v.solve_run(run)['delta'] for run in runs) + v.need(reset >= relaxed, 'restriction cannot improve optimum') + v.need(reset == next(r[1] for r in cert['orientations'][orientation]['rows'] if r[0] == h), + 'reset census binding') + if h in predecessor['helpers']: + actual[h] = relaxed + rows.append({'helper': h, 'unrestricted_delta_per_component': relaxed, + 'reset_delta_per_component': reset, 'reset_price_per_component': reset - relaxed}) + check_predecessor(prior, actual) + for h, premium in ((276, 2), (359, 0), (427, 2)): + v.need(next(r['reset_price_per_component'] for r in rows if r['helper'] == h) == premium, + 'named boundary price') + # Actual certificate price corruption and missing-domain controls. + bad = dict(actual) + bad[276] += 1 + rejected = 0 + for corrupted in (bad, {h: d for h, d in actual.items() if h != 276}): + try: + check_predecessor(prior, corrupted) + except ValueError: + rejected += 1 + v.need(rejected == 2, 'comparison controls') + answer['orientations'][orientation] = {'predecessor_minima_checked': len(actual), + 'rows': rows, 'rejection_controls': rejected} + return answer + + +if __name__ == '__main__': + result = compute() + path = HERE / 'BOUNDARY-COMPARISON.json' + if '--write' in sys.argv: + path.write_text(json.dumps(result, indent=2) + '\n') + else: + v.need(result == json.loads(path.read_text()), 'saved boundary comparison') + print(result['status'], 'PR1259 minima 32', 'comparison controls 4', + 'complex reset price L276=4 L359=0 L427=4') diff --git a/research/k8-phase-local-gauges/frame_replay.py b/research/k8-phase-local-gauges/frame_replay.py new file mode 100644 index 0000000000..52b1ecaac6 --- /dev/null +++ b/research/k8-phase-local-gauges/frame_replay.py @@ -0,0 +1,43 @@ +"""Run the unchanged source-pinned emitted scalar/frame/wrapper checker.""" +import gzip +import importlib.util +import json +from pathlib import Path +import subprocess +import sys +import tarfile +import tempfile + +HERE = Path(__file__).resolve().parent +spec = importlib.util.spec_from_file_location('verify', HERE / 'verify.py') +v = importlib.util.module_from_spec(spec) +spec.loader.exec_module(v) + + +def main(): + receipt, witnesses = v.compute() + pins = json.loads((HERE / 'SOURCES.json').read_text()) + lib = v.engine() + with tarfile.open(v.ROOT / lib.ARCHIVE) as archive: + word = archive.extractfile('slots/local/CANONICAL-WORD.json.gz').read() + for prefix in ('', 'pr1214_', 'wrapped_'): + programs = {orientation: witnesses[prefix + orientation] + for orientation in ('forward', 'backward')} + with tempfile.TemporaryDirectory(prefix='k8-phase-gauges-') as directory: + out = Path(directory) + (out / 'CANONICAL-WORD.json.gz').write_bytes(word) + (out / 'LOCAL-PROGRAMS.json.gz').write_bytes(gzip.compress(v.canonical(programs), mtime=0)) + # The historical checker uses asserts. Deliberately do not inherit -O. + command = [sys.executable, '-I', '-B', str(v.ROOT / pins['frame_checker']['path']), str(out)] + run = subprocess.run(command, check=True, capture_output=True, text=True) + result = json.loads((out / 'INDEPENDENT-LOCAL-REPLAY.json').read_text()) + v.need(result['status'] == 'PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY', 'frame status') + v.need(len(result['negative_controls_rejected']) == 25, 'frame control coverage') + print(prefix or 'selected_', result['status'], len(result['negative_controls_rejected']), 'controls') + if '--write' in sys.argv: + # Container hashes are run metadata; stable payload digests live in CERTIFICATE. + (HERE / ((prefix or 'selected_') + 'FRAME-RECEIPT.json')).write_text(json.dumps(result, indent=2) + '\n') + + +if __name__ == '__main__': + main() diff --git a/research/k8-phase-local-gauges/independent.py b/research/k8-phase-local-gauges/independent.py new file mode 100644 index 0000000000..93233757a9 --- /dev/null +++ b/research/k8-phase-local-gauges/independent.py @@ -0,0 +1,179 @@ +"""Literal-lowerer oracle and distance-transform DP, independently implemented. + +Philipp with substantial OpenAI Codex assistance; Apache-2.0. +This is algorithmic independence, not independent human review. +""" +from collections import defaultdict +from fractions import Fraction +import importlib.util +import json +from pathlib import Path + +HERE = Path(__file__).resolve().parent + + +def module(name, path): + spec = importlib.util.spec_from_file_location(name, path) + obj = importlib.util.module_from_spec(spec) + spec.loader.exec_module(obj) + return obj + + +v = module('phase_verify', HERE / 'verify.py') +lower = module('credited_pr696', v.ROOT / 'research/complex-dyadic-lowering/lower.py').lower + + +def p2(k): + return Fraction(2**k) if k >= 0 else Fraction(1, 2**(-k)) + + +def oracle(events, helper): + """All runs, padded exponent domain, literal predecessor macro lengths. + + Unlike the main all-pairs transition recurrence, use two linear passes for + the exact distance transform min_j (old[j] + |k-j|). + """ + groups, current = [], [] + for event in events + [['stop']]: + if event[0] != 'scalar': + if current: + groups.append(current) + current = [] + else: + g = event[1] + if g[0] == 'add' and ['L', helper] in (g[1], g[2]): + q = Fraction(g[3], g[4]) + n, d = abs(q.numerator), q.denominator + e = 0 + while n % 2 == 0: + n //= 2 + e += 1 + while d > 1: + d //= 2 + e -= 1 + sign = 1 if g[1] == ['L', helper] else -1 + current.append((g, q, sign, -sign * e)) + answer, vertices = 0, 0 + for group in groups: + lo = min([0] + [x[3] for x in group]) - 2 + hi = max([0] + [x[3] for x in group]) + 2 + ks = range(lo, hi + 1) + costs = [abs(k) for k in ks] + oldprice = 0 + for gate, q, sign, _ in group: + oldprice += len(lower(gate)) + for i in range(1, len(costs)): + costs[i] = min(costs[i], costs[i - 1] + 1) + for i in range(len(costs) - 2, -1, -1): + costs[i] = min(costs[i], costs[i + 1] + 1) + for i, k in enumerate(ks): + r = q * p2(sign * k) + costs[i] += len(lower(['add', gate[1], gate[2], r.numerator, r.denominator])) + vertices += len(costs) + answer += min(costs[i] + abs(k) for i, k in enumerate(ks)) - oldprice + return answer, vertices + + +def reconstruct(events, helper, plan): + """Read the explicit schedule and build a separate literal gauge stream.""" + assignment, last = {}, set() + for segment in plan: + v.need(len(segment['terms']) == len(segment['path']), 'path cardinality') + for term, k in zip(segment['terms'], segment['path']): + v.need(term[0] not in assignment, 'duplicate event') + assignment[term[0]] = k + last.add(segment['terms'][-1][0]) + result, gauge = [], 0 + for index, event in enumerate(events): + if event[0] != 'scalar': + v.need(gauge == 0, 'non-scalar identity boundary') + result.append(event) + continue + gate = event[1][:] + if index in assignment: + v.need(gate[0] == 'add' and ['L', helper] in (gate[1], gate[2]), 'incident schedule event') + target = assignment[index] + if target != gauge: + q = p2(target - gauge) + result.append(['scalar', ['scale', ['L', helper], q.numerator, q.denominator], event[2]]) + gauge = target + if gate[0] == 'add': + exponent = gauge if gate[1] == ['L', helper] else -gauge if gate[2] == ['L', helper] else 0 + q = Fraction(gate[3], gate[4]) * p2(exponent) + gate[3:5] = [q.numerator, q.denominator] + result.append(['scalar', gate, event[2]]) + if index in last and gauge: + q = p2(-gauge) + result.append(['scalar', ['scale', ['L', helper], q.numerator, q.denominator], event[2]]) + gauge = 0 + v.need(gauge == 0, 'final identity') + return result + + +def primitive_replay(events, orientation): + """All 713 formal columns, including initially dirty coefficient work.""" + roles = [('L', i) for i in range(704)] + [('C', i) for i in range(8)] + [('W', 0)] + rows = {role: {i: Fraction(1)} for i, role in enumerate(roles)} + count = 0 + for event in events: + if event[0] != 'scalar': + continue + for op in lower(event[1]): + count += 1 + tag, target = op[0], op[1] + if tag == 'clear': + rows[target] = {} + elif tag == 'copy': + rows[target] = dict(rows[op[2]]) + elif tag in ('double', 'halve', 'negate'): + coefficient = {'double': 2, 'halve': Fraction(1, 2), 'negate': -1}[tag] + rows[target] = {i: q * coefficient for i, q in rows[target].items()} + else: + v.need(tag in ('add', 'subtract'), 'primitive opcode') + sign = 1 if tag == 'add' else -1 + for i, q in rows[op[2]].items(): + new = rows[target].get(i, 0) + sign * q + if new: + rows[target][i] = new + else: + rows[target].pop(i, None) + for i in range(704): + expected = {i: Fraction(1)} + if orientation == 'forward' and 112 <= i < 224: + expected[i - 112] = Fraction(1) + if orientation == 'backward' and i < 112: + expected[i + 112] = Fraction(-1) + v.need(rows['L', i] == expected, 'literal endpoint ' + str(i)) + v.need(all(not rows['C', i] for i in range(8)), 'literal centers') + v.need(not rows['W', 0], 'literal work restoration') + return count + + +def main(): + lib = v.engine() + word, programs, _, _ = lib.load() + cert = json.loads((HERE / 'CERTIFICATE.json').read_text()) + total_vertices, rows_checked, primitives = 0, 0, 0 + for scenario in ('orientations', 'on_pr1214', 'wrapped_example'): + for orientation, original in programs.items(): + events = original + if scenario == 'on_pr1214': + for h in (251, 427): + events = lib.transform(events, word, h, -2 if orientation == 'forward' else 2) + result = cert[scenario][orientation] + for helper, wanted, _, _ in result['rows']: + actual, vertices = oracle(events, helper) + v.need(actual == wanted, 'independent minimum ' + str(helper)) + total_vertices += vertices + rows_checked += 1 + candidate = reconstruct(events, result['helper'], result['schedule']) + v.need(v.sha(v.canonical(candidate)) == result['candidate_sha256'], 'independent candidate') + count = primitive_replay(candidate, orientation) + v.need(count == result['after']['real_primitives'], 'literal full invoice') + primitives += count + print('PASS_INDEPENDENT_PHASE_GAUGES', 'helper_minima', rows_checked, + 'padded_vertices', total_vertices, 'literal_primitives', primitives, 'columns', 713) + + +if __name__ == '__main__': + main() diff --git a/research/k8-phase-local-gauges/pr1214_FRAME-RECEIPT.json b/research/k8-phase-local-gauges/pr1214_FRAME-RECEIPT.json new file mode 100644 index 0000000000..c443b743fb --- /dev/null +++ b/research/k8-phase-local-gauges/pr1214_FRAME-RECEIPT.json @@ -0,0 +1,71 @@ +{ + "status": "PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY", + "canonical_word_sha256": "16bc0ebb04b4be6c0ade74badc6a0c0cdba4215eda86e4ff9f13abf8ecebd219", + "local_programs_sha256": "207c33828014bd1ec7c294ae6eb7008dd7ff536c57afc0f979d13b104e6f14b9", + "v": 112, + "helpers": 480, + "local": { + "forward": { + "all_exact_columns": 704, + "prefix_l1_upper": "2765345294379392599/1024", + "prefix_bits_upper": 52, + "charged_payload_bits": 192, + "private_work_erased": true + }, + "backward": { + "all_exact_columns": 704, + "prefix_l1_upper": "14824960514781440791821/64", + "prefix_bits_upper": 68, + "charged_payload_bits": 192, + "private_work_erased": true + } + }, + "paid_profiles": { + "forward": { + "1": 2412, + "4": 142, + "8": 8, + "3": 432, + "2": 418, + "5": 82 + }, + "backward": { + "1": 2412, + "4": 142, + "8": 8, + "3": 432, + "2": 418, + "5": 82 + } + }, + "entering_helpers": 192, + "cold_hyperplane_ended_helpers": 48, + "negative_controls_rejected": [ + "wrong_scale", + "missing_center", + "wrong_common_frame", + "wrong_child_rank", + "missing_pre_wrapper", + "missing_post_wrapper", + "wrapper_with_wrong_frame", + "wrapper_in_wrong_phase", + "wrapper_on_a_data_register", + "wrapper_on_a_target_register", + "wrapper_on_a_centre_register", + "hpe_pre_wrapper_resolved_to_full_recipe", + "hpe_post_wrapper_without_terminal_frame", + "hpe_post_wrapper_wrong_terminal_frame", + "hpe_tail_gate_at_full_frame", + "hpe_tail_climb_dropped", + "hpe_helper_exit_adapter_to_full", + "hpe_tail_gate_moved_into_full_cleanup", + "cold_hpe_pre_wrapper_replaced_by_identity_entry_adapter", + "cold_hpe_pre_wrapper_dropped", + "cold_hpe_post_wrapper_replaced_by_exit_adapter", + "cold_hpe_pre_wrapper_resolved_to_cold_full_convention", + "cold_hpe_wrapper_with_nonzero_entrance", + "cold_hpe_post_wrapper_wrong_terminal_frame", + "cold_hpe_premix_gate_before_pre_wrapper" + ], + "scope": "Literal forward and inverse-transpose replay on every arbitrary data/helper column, physical frame incidence, ordered paid wrappers, cleared private work and prefix coefficients. Global hosting and outer exponent are separate." +} diff --git a/research/k8-phase-local-gauges/reproduce.py b/research/k8-phase-local-gauges/reproduce.py new file mode 100644 index 0000000000..fa6b92cdb0 --- /dev/null +++ b/research/k8-phase-local-gauges/reproduce.py @@ -0,0 +1,13 @@ +"""One bounded standard-library replay of the complete scoped package.""" +from pathlib import Path +import subprocess +import sys + +here = Path(__file__).resolve().parent +for filename in ('verify.py', 'independent.py', 'comparison.py', 'test_package.py', 'frame_replay.py'): + command = [sys.executable, '-I', '-B'] + if filename == 'test_package.py': + command.append('-O') + command.append(str(here / filename)) + subprocess.run(command, check=True, timeout=120) +print('PASS_COMPLETE_K8_PHASE_LOCAL_GAUGES') diff --git a/research/k8-phase-local-gauges/selected_FRAME-RECEIPT.json b/research/k8-phase-local-gauges/selected_FRAME-RECEIPT.json new file mode 100644 index 0000000000..81c6a9c682 --- /dev/null +++ b/research/k8-phase-local-gauges/selected_FRAME-RECEIPT.json @@ -0,0 +1,71 @@ +{ + "status": "PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY", + "canonical_word_sha256": "16bc0ebb04b4be6c0ade74badc6a0c0cdba4215eda86e4ff9f13abf8ecebd219", + "local_programs_sha256": "b752783b1ebd69e14f124eeee07ead600944f6281f9cc52488bb61a73a2097b9", + "v": 112, + "helpers": 480, + "local": { + "forward": { + "all_exact_columns": 704, + "prefix_l1_upper": "2765345294379392599/1024", + "prefix_bits_upper": 52, + "charged_payload_bits": 192, + "private_work_erased": true + }, + "backward": { + "all_exact_columns": 704, + "prefix_l1_upper": "14824960514781440791821/64", + "prefix_bits_upper": 68, + "charged_payload_bits": 192, + "private_work_erased": true + } + }, + "paid_profiles": { + "forward": { + "1": 2412, + "4": 142, + "8": 8, + "3": 432, + "2": 418, + "5": 82 + }, + "backward": { + "1": 2412, + "4": 142, + "8": 8, + "3": 432, + "2": 418, + "5": 82 + } + }, + "entering_helpers": 192, + "cold_hyperplane_ended_helpers": 48, + "negative_controls_rejected": [ + "wrong_scale", + "missing_center", + "wrong_common_frame", + "wrong_child_rank", + "missing_pre_wrapper", + "missing_post_wrapper", + "wrapper_with_wrong_frame", + "wrapper_in_wrong_phase", + "wrapper_on_a_data_register", + "wrapper_on_a_target_register", + "wrapper_on_a_centre_register", + "hpe_pre_wrapper_resolved_to_full_recipe", + "hpe_post_wrapper_without_terminal_frame", + "hpe_post_wrapper_wrong_terminal_frame", + "hpe_tail_gate_at_full_frame", + "hpe_tail_climb_dropped", + "hpe_helper_exit_adapter_to_full", + "hpe_tail_gate_moved_into_full_cleanup", + "cold_hpe_pre_wrapper_replaced_by_identity_entry_adapter", + "cold_hpe_pre_wrapper_dropped", + "cold_hpe_post_wrapper_replaced_by_exit_adapter", + "cold_hpe_pre_wrapper_resolved_to_cold_full_convention", + "cold_hpe_wrapper_with_nonzero_entrance", + "cold_hpe_post_wrapper_wrong_terminal_frame", + "cold_hpe_premix_gate_before_pre_wrapper" + ], + "scope": "Literal forward and inverse-transpose replay on every arbitrary data/helper column, physical frame incidence, ordered paid wrappers, cleared private work and prefix coefficients. Global hosting and outer exponent are separate." +} diff --git a/research/k8-phase-local-gauges/test_package.py b/research/k8-phase-local-gauges/test_package.py new file mode 100644 index 0000000000..3c05049b92 --- /dev/null +++ b/research/k8-phase-local-gauges/test_package.py @@ -0,0 +1,128 @@ +"""Mathematical and corruption controls for phase-local dyadic gauges.""" +import copy +import importlib.util +import itertools +import json +from pathlib import Path +import tempfile +import unittest + +HERE = Path(__file__).resolve().parent +spec = importlib.util.spec_from_file_location('v', HERE / 'verify.py') +v = importlib.util.module_from_spec(spec) +spec.loader.exec_module(v) + + +class Controls(unittest.TestCase): + @classmethod + def setUpClass(cls): + cls.lib = v.engine() + cls.word, cls.programs, _, _ = cls.lib.load() + cls.receipt, cls.witnesses = v.compute() + + def test_01_exhaustive_tiny_path_oracle(self): + checked = 0 + symbols = list(itertools.product((-1, 0, 1), (False, True))) + for n in (1, 2, 3): + for seq in itertools.product(symbols, repeat=n): + rows = [[i, b, unit] for i, (b, unit) in enumerate(seq)] + base = sum(abs(b) - int(unit and b == 0) for b, unit in seq) + brute = min(abs(ks[0]) + abs(ks[-1]) + + sum(abs(a - b) for a, b in zip(ks, ks[1:])) + + sum(abs(k - b) - int(unit and k == b) + for k, (b, unit) in zip(ks, seq)) - base + for ks in itertools.product(range(-2, 3), repeat=n)) + self.assertEqual(v.solve_run(rows)['delta'], brute) + checked += 1 + self.assertEqual(checked, 258) + + def test_02_unit_discount_changes_optimum(self): + rows = [[0, 1, True], [1, 1, True]] + answer = v.solve_run(rows) + self.assertEqual((answer['delta'], answer['path']), (-2, [1, 1])) + self.assertEqual(v.solve_run([[0, 1, False], [1, 1, False]])['delta'], 0) + + def test_03_expanded_domain_agrees(self): + for scenario in ('orientations', 'on_pr1214'): + for result in self.receipt[scenario].values(): + for run in result['schedule']: + self.assertEqual(v.solve_run(run['terms'], extra=9)['delta'], run['delta']) + + def test_04_missing_entry_scale_rejected(self): + for orientation in self.programs: + events = copy.deepcopy(self.witnesses[orientation]) + i = next(i for i, e in enumerate(events) if e[0] == 'scalar' and + e[1][:2] == ['scale', ['L', 427]]) + events.pop(i) + with self.assertRaises(ValueError): + self.lib.replay(events, orientation) + + def test_05_missing_final_scale_rejected(self): + for orientation in self.programs: + events = copy.deepcopy(self.witnesses[orientation]) + i = max(i for i, e in enumerate(events) if e[0] == 'scalar' and + e[1][:2] == ['scale', ['L', 427]]) + events.pop(i) + with self.assertRaises(ValueError): + self.lib.replay(events, orientation) + + def test_06_wrong_inverse_orientation_rejected(self): + winner = self.receipt['orientations']['forward'] + candidate = v.construct(self.lib, self.programs['backward'], winner['helper'], winner['schedule']) + # Conjugation is still algebraically exact, but the inverse orientation + # cannot inherit forward pricing: its optimum has reflected exponents. + self.lib.replay(candidate, 'backward') + price = self.lib.invoice(candidate, 'copy-init')['real_primitives'] + self.assertNotEqual(price, self.receipt['orientations']['backward']['after']['real_primitives']) + + def test_07_nonzero_boundary_rejected(self): + result = copy.deepcopy(self.receipt['orientations']['forward']) + # Force two separate scalar runs into one schedule, carrying its gauge + # through an unchanged adapter/climb boundary. + a, b = result['schedule'] + a['terms'] += b['terms'] + a['path'] += b['path'] + a['path'][len(a['path']) - len(b['path']) - 1] = -1 + with self.assertRaises(ValueError): + v.construct(self.lib, self.programs['forward'], result['helper'], [a]) + + def test_08_vendor_tamper_and_missing_pin(self): + original = v.HERE + with tempfile.TemporaryDirectory() as name: + folder = Path(name) + (folder / 'vendor/pr1161').mkdir(parents=True) + sources = json.loads((HERE / 'SOURCES.json').read_text()) + del sources['vendor']['PROOF.md'] + (folder / 'SOURCES.json').write_text(json.dumps(sources)) + try: + v.HERE = folder + with self.assertRaisesRegex(ValueError, 'vendor inventory'): + v.engine() + sources['vendor']['PROOF.md'] = '0' * 64 + (folder / 'SOURCES.json').write_text(json.dumps(sources)) + for filename in sources['vendor']: + (folder / 'vendor/pr1161' / filename).write_bytes(b'corrupt') + with self.assertRaisesRegex(ValueError, 'vendor pin'): + v.engine() + finally: + v.HERE = original + + def test_09_profiles_and_full_cost(self): + for orientation in self.programs: + result = self.receipt['on_pr1214'][orientation] + self.assertEqual(result['after']['paid_profile'], result['original_before']['paid_profile']) + self.assertEqual(result['original_before']['complex_primitives'] - + result['after']['complex_primitives'], 1094) + self.assertLessEqual(result['after']['prefix_bits'], 68) + + def test_10_wrapped_witness_is_inside_wrapper_domain(self): + for orientation, events in self.programs.items(): + result = self.receipt['wrapped_example'][orientation] + self.assertEqual((result['helper'], result['delta'], result['wrapped_helpers_checked']), + (652, -36, 240)) + self.assertIn(652, {e[2] for e in events if e[0] == 'residual_adapter'}) + self.assertEqual(result['before']['paid_profile'], result['after']['paid_profile']) + + +if __name__ == '__main__': + unittest.main(verbosity=2) diff --git a/research/k8-phase-local-gauges/vendor/pr1161/BASE-SELECTED.json b/research/k8-phase-local-gauges/vendor/pr1161/BASE-SELECTED.json new file mode 100644 index 0000000000..74e4acfe73 --- /dev/null +++ b/research/k8-phase-local-gauges/vendor/pr1161/BASE-SELECTED.json @@ -0,0 +1 @@ +{"audited_source_head":"0fc329d0bec93ca7cd288eaea1295172e8789810","certificate":"research/community-frontier1094-audit/ASSEMBLY.json","certificate_sha256":"1122cb3a575f8c788345fc1bf4c108ac7c3250fb81a5988671f5eb04b3ab3045","decimal":"0.001672660197076918","kappa":"836330098538459/500000000000000000","previous_kappa":"1672188119205421/1000000000000000000","previous_record":"certificates/checkpoints/frontier1042.json","proof":"docs/research/community-batch1099-review.md","proof_supplements":{".github/workflows/t37-owners.yml":"c13acc2902c007237103072b7ec10caf5ca21c1b319d27934f194af2f7d87026","certificates/replay-coverage/pr741-sw4-v1.json":"7acd5033bc78e3f473718269edaa267c2785d84fbe95ccf6815a33dcf58c2756","docs/research/community-batch1047-review.md":"a6271faf5db0afe3ff7d24a34a3be7a959cdc33ee37784572fba014ee5358787","docs/research/community-batch1099-review.md":"7e76d2c38e5fce30587835b7251df1430488ae4dd372611ef69a3f03f476b6cb","docs/research/community-batch952-review.md":"04db59dfc2c31453229b6061bbf59547e71ce3abdc0ce0f6779144bb0dde127b","docs/research/community-cold617-review.md":"b3f2bcbae1249f1f651032022ce1e6e2bfb3f563ce580bf53671f50a074d7046","docs/research/community-frontier741-review.md":"4634694fa75ea9e749ecf19d3db3e4d82effe3b61a2efdf08ac5a97275fb676a","docs/research/community-frontier799-review.md":"bd91c10c67f2a873fd456b95cbb43f715a43dac0e0a66938737d591c6b754052","docs/research/community-frontier890-review.md":"cd03b7c2c6c09db2cfa89ae40133ae44e1deb6e32ec5ddd23aacecc9c50f2fea","docs/research/community-hyperplane599-review.md":"3298cd0d451541508af232cac72efbd7c10580e6c6ad493a855ab0faa01ade8c","docs/research/community-k492-review.md":"3b731d30e80010b15408a289b0b32192700885474c8b36d48ee3320a7a8c5c47","research/community-batch1099-audit/check_frontier1094.py":"2608ef213260a43d09a40b3429742f7a5f280861b54acae66400a7c29a123f51","research/complex-571-cold14-b3/PROOF-NOTE.md":"1cf592cbc8ab8e21d2dd8c1e945a5c64c6d5cde1216fb06e05a36c1c6ec6613d","research/complex-571-cold14-b3/README.md":"1945785785c153c7d0e8d4c071adabe626c1091b71721ff85d2d67191b376b96","research/complex-571-free4fc8/NOTICE.md":"a4c084abdc1c7a9ac683eeb11124335d51cff8a6deba6ee92ba5a12bceaa2c97","research/complex-571-hpeq5/README.md":"4000b37f6c07c09d971dc4010ceb137c13340f3a8809d3272046ccaf746c3e2b","research/complex-double-replica-owners/PROOF.md":"db99599e3966bec253c577c23915e2a2899c4c4e8568044efc11c7918b137bbc","research/complex-joint-prefix/proof/CONSTRUCTION.md":"a92e610e7a598d99c612d1b63d1a03a49c0cd1e15ddd29fa55c465ddd8c18105","research/complex-k492-owner-repair/PROOF-NOTE-R.md":"22312bb347bdf159e6a01a45c47675e6170d33b258e2fd9ed52aee88fb92c0ed","research/complex-k492-owner-repair/PROOF-NOTE.md":"337d70fe7abd9afca1d90954c23bde87f4dc27888cc1a6b4bb80506fd6fbf8c5","research/complex-k492-owner-repair/README.md":"ee5a1ace4828f7a073be97e95c2d931988774dd3a29a877e65abdf429aeec902","research/complex-multicold/proof/CONSTRUCTION.md":"27ece5e1c11b90d97a808b56eff897b998c10e61016db95867f84e6e6aef132f","research/complex-multicold/vendor/pr559/PROOF.md":"d5d498edc56fdef8c5798af7f5ec66948bd2f66c553b9efe366cdaab01bd3453","research/complex-sw4-frame8/PROVENANCE.md":"c7648719b01dd93af2c3a2c6e951a54711d13892dc4bd4339d16edb4c37c9bf0","research/complex-t21-owner-bound/PROOF.md":"2aa0aa6ec1d87402138564c38749b5ca0f058c16817efdf58a2685d2d90cb417","research/complex-t21-owners/PROOF.md":"78721b32fceb34b21b8e77c95381c38c60276e72e6d9c2e9c6262cb347457def","research/complex-t37-owners/ALL-T-PROOF.md":"4c0c71ccd0afb850538af1b467e5208b7eb3edd0260fded84e02a8c01dfc868b","research/complex-t37-owners/PROOF.md":"09b39ad0d5f1f59f54dcff15c16640f7a7acf27e6597660acaf957b95c7e8510","research/e8-bit-p111-tuned/tune/README.md":"46c7917fb252949f38b7bcd88cf568efc282e3ea065b61d11e457e41673d0b2d","research/e8-bit-r420/README.md":"9807be57c6adf26b30e4f54e2f8160075bbc05091f1a6d157e43d2a4620c1c9f","research/gauge44-barch/PROOF-NOTE-BARCH.md":"c24f211b09358b25d6cf47dd18e4bbd8bcf4ecf279e6f1c6c90613cfa230818d","research/gauge44-frames-x/PROOF-NOTE-FRAMES-X4.md":"39c50420ebb6e8813706a49b2cf759f277c4afac9f6780fc0a7ac6a5fb86e036","research/hyperplane-end-lean/HyperplaneEnd/Exact.lean":"eebf3a3982af7ab9be45777b272a6aaa523206fa7667ceb6df63ad6589fd8183","research/hyperplane-end-lean/PROOF.md":"1cbce5cf0ff0152f71e8ae7bef25841d1ce13010af248ff7209182d2328c21c9","research/kernel-frame-coalescing/PROOF.md":"fa8b2f36b9590ee80ff45d3f7724f8c7de8ad29a29f366d5133010c77e41fe1b","research/structural-gain/frontier-composition/README.md":"70f0f791cbe3b2603f85d85bb9055aa0ee1df6dc06ba82fc1921356948312887","scripts/verify_cold617_interface.py":"95d7a9094c05ad975fb72f5ab7605593003245a503c8456764987e512028fa6a","scripts/verify_frontier1042.py":"700fdcaeb6e8f57f6e63c71c2dd1652fc5b183e8d706cd092779bdc0d271e854","scripts/verify_frontier1094.py":"c7e20f59968ed5736fb859735de4de207de3418083e37012310ebcded946b949","scripts/verify_frontier588_bindings.py":"6d1932eea7b1936598118ea8e607b09c29b6e31b749ec41bbe0744ea4f0b606d","scripts/verify_frontier626.py":"2207bd0ef04a19ef276869085afdedad80a0938fa75db5e1aa7ab73fd3429444","scripts/verify_frontier626_bindings.py":"cda63ff41c6d6e2e352c7bf75b84e690c0ce57e4ec6c0355573bb5d9b1f98280","scripts/verify_frontier741.py":"215ee6a12de8dc2392e6811a1b8f2140035f6b2d2a0d2100ff4bd2fdcb8bb39b","scripts/verify_frontier741_bindings.py":"eff455167e2fd0bc9a67d35241d0e69d8edc58f3a23e776dcfe8f500ca8e8d67","scripts/verify_frontier741_bridge_coverage.py":"9a14f26762b6126eb54ed43db90371773374fe98733ada80ee871a74afa3b836","scripts/verify_frontier799.py":"19fe1b32079095160dc00fe2f7df75e0fcbc82cff37f7159b755c8a63bd5ce99","scripts/verify_frontier799_bindings.py":"43897b3c99212d6134870898a1840f32898aa1b3679b299e654901568ad7e19b","scripts/verify_frontier890.py":"88ea38dbef62dd7c0dd46e212618520cc89213edddb2032800e5509993958175","scripts/verify_frontier942.py":"27c6713532d9f53f55dfff4884d55a2d9ae74b68156e37a44596c0418fbed5b7","scripts/verify_hpe_lean_binding.py":"52aa1d23641e4c716b43c98f6b883ad042087dd03a9d01369e8e6a735b07aa03","scripts/verify_replay_coverage.py":"babe5941d7e6dac4248613ef01f950ee7bb6199e7355021aea4cf854fd1b91c5"},"reproduce":"make frontier1094-verify","review":"docs/research/community-batch1099-review.md","reviewed_dependency_heads":{"1004":"1974578f82a30158dd5fcdcdf226b83df8e7196f","1005":"779e80aef469bc3a28b19f1adde199871a9a22e3","1018":"eac7547cb191f875d5f5ea5f9bbb1d2b8c51c4ef","1022":"58618bcbfe88a252467755fc283c04c3db5ca4fd","1028":"be4bd89cb4483dcee43257200cd27601f938f13d","1031":"e900534f0beda892c726723524203b97471fb9a3","1042":"7e8ef087c02a77038a28a337a7ee3a77039cac0d","1050":"c87242f846cfab8c0b97fd889b5fecb0eacef939","1053":"6f92ce8884929c9fd4730c86a28e2e3735de02af","1055":"a8ea308976f1709eef0a328463f010cf51469277","1056":"d0201efbd68c4acc9832b84bcc986c8781b83c4f","1061":"223f581afb1d63d5f8476a69040617e11bcd50e4","1063":"d9377d32e0c97e41338e704c3960fd6f2fa73806","1065":"387d935e354a931d636e2c5e6ee63a6910f78a1b","1068":"cc71375eae4e8754da0f5d940cb519d66625fb2e","1074":"052afc128954f7b6a2b3c409eb4d72248e4020f2","1082":"0c2e294ec204e83846d27344f829d15ed9ee7cc6","1087":"589d1cedf5ef5f231182f4ec86408616311a8af0","1094":"0fc329d0bec93ca7cd288eaea1295172e8789810","543":"2065fe4f72a914d907f1046603f5a36f17018535","568":"71c99ac935a33bb7b59a1b4a7af8725a939b0b90","569":"1424da81263a5305b35e4cf74ef686c275f03f3f","571":"b7bdc5a8de18fcf418cfb9c7d83a2b1097a5e4a3","575":"eac6f7e378ab622dac50a2fd4b7ef6eab014de44","583":"89be768f0157f5a3d8e4db69cf1748768605eac9","586":"4846fee5b06af770e9b3a10c36200f673d656725","588":"6d0e53b66c29abd17981881a09eaff41ac862d85","589":"a5afc8c6169ea61ba7c51dfd3cade02cc7b13b46","591":"f622547244bf6d895a571a7b035142ba66279806","592":"1f471c445c06a45a32e2c47e8d74c8264b68356b","593":"fdb6dcc6d7bc29764c5b6b4d32b7fa050acf74a4","596":"7732dd5e46863ff294b5e443661cb9d99abf4e01","599":"bc13c8a3e000442606bd2dbe8583a17649ba6c32","601":"529ab7dcb59d5ea7a5798e9e06cf5b3aee8a1550","604":"1b795c5d7dea746ba310572585c0ef067574b4a6","615":"bf8a49a34350599763cced8592db81dc62c2c1c0","617":"904d62855723c00f8acef9a287a10768598fdeb2","622":"f69477f4f6d3c7eb1f740b166881bffed4ffa9f6","623":"e39a615ca601ce5d62abeb24f3fcdb8644ca1005","626":"660de893d27bb7abd1d5b01b1640207528a5c851","741":"e516b1463606840a15f80aac1995d64ce0092e89","799":"80e6463157cfc80b85af09e7e2f14748fe2dac60","858":"ae2e25fee91540c83ceee5a60e3b07422ce21c7d","869":"73e86f69bf9a391e3c334999f7bbe3825dc42759","870":"b734850dc348800942f0ffd1f0723fdec7539b2b","890":"4b3bd8cbe8e3e81c44161017c9b72c905a8040a8","942":"1960cfa919a0945d0ca4cb14ea96237000037903","987":"5142511af0437572aca71b35d1987cd2b47bb5e3"},"scope":"Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem.","source_manifest":"research/community-frontier1094-audit/SELECTED-SOURCE.json","source_prs":[1094,1087,1082,1074,1068,1065,1063,1061,1056,1055,1053,1050,1042,1031,1028,1022,1018,1005,1004,987,942,890,870,869,858,799,741,699,685,676,664,660,659,656,655,653,658,649,645,635,589,555,545,626,623,622,620,617,615,604,601,596,592,591,593,599,588,543,584,586,583,582,579,576,575,574,571,569,568,567,564,562,561,559,558,552,550,548,541,535,510,503,531,523,493,514,507,484,496,505,522,520,472,458,445,442,425,433,370,361,315],"status":"Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status","validation":"docs/research/community-batch1099-integration.json"} diff --git a/research/k8-phase-local-gauges/vendor/pr1161/PROOF.md b/research/k8-phase-local-gauges/vendor/pr1161/PROOF.md new file mode 100644 index 0000000000..d2925051c5 --- /dev/null +++ b/research/k8-phase-local-gauges/vendor/pr1161/PROOF.md @@ -0,0 +1,106 @@ +# Scope and exact algebra + +Fix one non-center helper h and k in Z. Let D multiply its entire scalar register +by2^k and leave every other data, helper and center coordinate fixed. An ADD +`t += q*s` becomes `t += (q*2^(k_t-k_s))*s`, where k_h=k and all other k_i=0. +Each existing SCALE commutes with D and is left literally unchanged. Clear/COPY +events have no incidence with h by the definition of the477-helper domain. + +For chronological original operations A1,...,Am, the new chronological word is +D, DA1D^-1,...,DAmD^-1,D^-1. Its matrix is + +```text +D^-1 (DAmD^-1) ... (DA1D^-1) D = Am ... A1. +``` + +This equality holds on all input vectors, including arbitrary helper dirt. It +does not assume a helper is initially zero. The stored backward program is +checked independently; the inverse-transpose coefficient rule changes the +chosen basis to D^-1 (k=+2), in the same chronological direction, rather than +naively reusing k=-2. Both candidate and original forward transfer are +`Y += X`, and both backward transfers are `X -= Y`, preserving480 helpers and +clearing8 centers. The sparse rational replay includes each center's initial +dirty column, not merely zero center initialization. + +All unchanged non-scalar operations act linearly on an individual register; +uniform scalar multiplication commutes with them. Center operations act on the +separate C registers. Excluding helper COPY sources ensures they commute too. +The selected candidate h427 starts in frame0 and ends in FULL frame1, and has +no residual wrapper. Its entry scale is after the zero-precondition phase +marker; the exit is after full-frame cleanup, before the done marker. This is +why the concrete stream requires no new frame climb or wrapper. Coefficient +changes use the original operands and frame labels. Native type/admission +replay and the complete hosted/compiler invoice remain separate obligations. + +# Actual retained cost, including the unit discontinuity + +For reduced q with |q|=p*2^e and positive odd p, Sagar Thakrar's retained +copy-init lowerer emits + +```text +c(p,e) = 2 + floor(log2(p)) + popcount(p) + |e| - 1[p=1 and e=0]. +``` + +The shortcut at q=+1 or-1 costs2: signed direct ADD followed by work clear. +Otherwise COPY initializes work from the source; numerator Horner steps, any +denominator halvings, signed accumulation and final clear are all charged. +The old Horner formula is `3+floor(log2(p))+popcount(p)+|e|`. +SCALE by a signed power of two costs `|e|+1[q<0]`. New boundary scales are +positive and cost2|k| in total, per real component. Real and imaginary words +each incur this complete cost. + +For each ADD incident with h, set s=+1 when h is its target and s=-1 when h is +its source. The exact change is + +```text +Delta_h(k) = 2|k| + sum_g ( c(p_g,e_g+s_g*k) - c(p_g,e_g) ). +``` + +No unchanged SCALE or disjoint ADD contributes a delta. Complete invoices +nevertheless recount them, and also count all clears/COPYs. The coefficient +work is arbitrary on entry: non-unit COPY overwrites it; unit direct ADD does +not read it; every macro clears it on exit. The independent checker executes +the predecessor's literal primitive words, including that work register. + +# Why finitely many exponents certify an unbounded optimum + +Let B={0} union {-s_g*e_g}. All absolute-value slope changes and all negative +unit discounts occur at integer points of B. Between consecutive points the +undiscounted objective is affine and there are no discounts. An affine function +attains its minimum at an endpoint (or is constant); the possible negative +discounts at endpoints only strengthen this conclusion. Outside the extreme +points every absolute-value term has the same outward slope, so the objective +increases with slope `2 + number_of_incident_ADDs`. Therefore at least one global +integer minimizer is in B. The method does not assume convexity of the discounted +function and is not simply a weighted-median argument. + +The certificate prices every B point for all477 helpers, including k=0, in both +orientations. It uses (cost,|k|,k) to resolve per-helper ties and then helper index +for global ties. The independent method enumerates *every* integer from two +below to two above the extreme valuations and derives the outward slope using +the actual lowerer's lengths. It agrees with every per-helper certificate row. +The unique global winner in each orientation is h427, with123 incident ADDs; +forward costs at k=-4,-3,-2,-1,0,1 are75,-46,-166,-128,0,132 relative to baseline. +The backward list is reflected. No exponent cutoff assumption is used. + +The pure unit-discount control has two incident coefficients1/2: the continuous +absolute-value objective is constant between k=0 and1, so the lower weighted +median is0; the correct discounted price strictly prefers1 by2 primitives. + +# Prefix and admission boundary + +For the source-bound positive scalar envelope, each original L/C register starts +with majorant1, clears set it to0, COPY copies it, SCALE multiplies by|q|, and +ADD replaces the target majorant by target+|q|*source. During non-unit numerator +Horner construction, the work majorant is at most |numerator(q)|*source before +denominator halvings. Unit direct ADD does not touch work until it clears. +Starting coefficient work at arbitrary unit majorant1 covers its dirty entry. +This exact rational recurrence accounts for every emitted primitive's absolute +coefficient majorant. Its complete maximum is unchanged at52/68bits, below192. + +These are scalar-majorant and exact map certificates for one finite provider +word, with actual retained lowering. They are not a rerun of the native checker, +global512-bit accounting, row inventory/packing admission, or the outer root. +The477-helper cost optimum fixes all other coordinate scales; joint scaling, +center normalization, phase-varying diagonals, stage retiming and coefficient +work persistence lie outside the class. The current selected result is retained. diff --git a/research/k8-phase-local-gauges/vendor/pr1161/PROVENANCE.md b/research/k8-phase-local-gauges/vendor/pr1161/PROVENANCE.md new file mode 100644 index 0000000000..6ee8cde472 --- /dev/null +++ b/research/k8-phase-local-gauges/vendor/pr1161/PROVENANCE.md @@ -0,0 +1,46 @@ +# Attribution and scope selection + +Prepared by @woklerx with substantial OpenAI Codex assistance, Apache-2.0. +No independent human review is claimed. Original source notices are retained. + +The current frozen construction is Rohan Arun's PR1094 rare-pattern exchange +placement on Jeremy Kothe's checked k8/T16 supplier, following PR1042. Its actual +archived gauge44 provider is byte-identical to the pinned slots/local provider +in the PR1042 archive. Douglas Colkitt's review, selected-source and complete +assembly receipts establish the inherited lineage; this package does not claim +to authenticate or repeat those native/global executions. The scalar program +and exact local invoice are from the credited icekylinx/PR425/433/531, +Jeremy Kothe/PR622 and gauge44-slots construction lineage. The stronger lowering +is Sagar Thakrar's `research/complex-dyadic-lowering/lower.py`, whose retained +source is imported by the independent checker. The optimum accounts for its +unit shortcut and does not claim an old-Horner gain that disappears there. + +Seed32 is the assigned complex-supplier track at fixed base +`ce7ad1b6ab09452c3478723a2e96ed5ff212dc08`. Three candidates considered: + +1. Uniform dyadic basis change on one complete-program helper (chosen). +2. Further coefficient-work sharing/rescaling (rejected as close to PR739/811, + PR984 and previous sprint round7/PR1032). +3. Frame-transition retiming (rejected as close to rounds26/29). + +Targeted live Curiosity Bot GitHub provider queries covered dyadic conjugation, +diagonal gauge, rescaling, scalar and helper work. PR739 was inspected directly: +it keeps private coefficient work across successive magnitude blocks, not a +uniform helper coordinate change through the full scalar word. PR836 concerns +unitary register mixing; PR426/401 concern other chronological/response gauges. +PR947 prices constant-row center shears; PR1081 fixes CK helper matching. +None supplies this one-helper unbounded valuation/discount certificate. + +Concurrent round31 was coordinated explicitly: it carries *existing* SCALEs +through stage A/B with a time-varying diagonal and consolidates them at stage +boundaries. This package fixes every existing SCALE and inserts two new inverse +boundary scales for one helper across all phases. Neither result asserts that +the two savings compose. Earlier rounds22 butterflies,23 cell minimum,25 dirt +span coverage,26 commuting frame barrier and29 Clifford transition rank have +different mechanisms and obligations. + +The exact mandatory source inventory uses LF-normalized text hashes and exact +binary/archive bytes. Archive member hashes bind original gzip containers, not +recompressed equivalents. Candidate hashes use sorted-key canonical JSON with +integer/list schema. Frozen selection and exact base are context; verification +does not require the mutable selected-result pointer still to select PR1094. diff --git a/research/k8-phase-local-gauges/vendor/pr1161/SOURCES.json b/research/k8-phase-local-gauges/vendor/pr1161/SOURCES.json new file mode 100644 index 0000000000..841bf21533 --- /dev/null +++ b/research/k8-phase-local-gauges/vendor/pr1161/SOURCES.json @@ -0,0 +1 @@ +{"archive_members":{"slots/local/CANONICAL-WORD.json.gz":"16bc0ebb04b4be6c0ade74badc6a0c0cdba4215eda86e4ff9f13abf8ecebd219","slots/local/INDEPENDENT-LOCAL-REPLAY.json":"13dd18297162569532983db1a2ab67926b064330cd7edd3587e7b546b2dedf17","slots/local/LOCAL-CHECKS.json":"2b8b1891a736598010232bfb26abc31973b265a53a2009a3fcfd9138b5ecadb4","slots/local/LOCAL-PROGRAMS.json.gz":"241fde27d4e43f5a9cb6b128f9f76c5131a53d09f0371676163f914d0b0fef3a"},"base":"ce7ad1b6ab09452c3478723a2e96ed5ff212dc08","files":{"docs/research/community-batch1099-review.md":"7e76d2c38e5fce30587835b7251df1430488ae4dd372611ef69a3f03f476b6cb","research/community-frontier1042-audit/RESULT.json":"bf12c6ed3b412539638b76addb40591a631609b2ab9e5ee0db1f6bbe067d0ec0","research/community-frontier1042-audit/selected-replay.tar.gz":"22c3f4dce4b897a1d423d1388801933e288b6a6b1906cb15e1b16a5eb68db754","research/community-frontier1094-audit/ASSEMBLY.json":"1122cb3a575f8c788345fc1bf4c108ac7c3250fb81a5988671f5eb04b3ab3045","research/community-frontier1094-audit/RESULT.json":"1e3e47e9ec24bcb6fb5f703b7fce0aab658d84ff72bfae5da3ae429d17b6e752","research/community-frontier1094-audit/selected-replay.tar.gz":"f1da80610bf33c58527f18ad63b4350d0b864e1d4486141ee17ac9bed4d529d6","research/complex-dyadic-lowering/README.md":"798209e9869d1612a2c34412ef2eb87c0eb0dcebcbed9963a45e0fe248326c2f","research/complex-dyadic-lowering/lower.py":"eb37d00063dc09323e9aca041d23da749ce17fbd71dade9aaf1c059cab0b9753","research/gauge44-slots/code/invoice_allcold.py":"141bd2fd58bbfb5b8d0fc8f56f61c45586d5608a5af3487c6b883dd987f998ec","research/gauge44-slots/independent/audit_local.py":"03afcfc9da428b3f6edac81c1fee7f277ab81b64998efae78380b63498dec6cd","scripts/verify_frontier1094.py":"c7e20f59968ed5736fb859735de4de207de3418083e37012310ebcded946b949"},"format":"exact-inventory-text-lf-binary-exact-sha256-v1","selected_snapshot_sha256":"cba7a81945a737a475251e77c6a1da21ffbc22d56ea835f4ee7dfbb813ae796e"} diff --git a/research/k8-phase-local-gauges/vendor/pr1161/engine.py b/research/k8-phase-local-gauges/vendor/pr1161/engine.py new file mode 100644 index 0000000000..33c0db7fe7 --- /dev/null +++ b/research/k8-phase-local-gauges/vendor/pr1161/engine.py @@ -0,0 +1,209 @@ +"""One-helper dyadic basis search. @woklerx with OpenAI Codex, Apache-2.0. + +Retained copy-init lowering: Sagar Thakrar's complex-dyadic-lowering/lower.py; +original Horner vocabulary: icekylinx PR425/433/531, Jeremy Kothe PR622. +""" +from collections import Counter, defaultdict +from fractions import Fraction as Q +import copy, gzip, hashlib, json, tarfile +from pathlib import Path + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +BASE = 'ce7ad1b6ab09452c3478723a2e96ed5ff212dc08' +ARCHIVE = 'research/community-frontier1042-audit/selected-replay.tar.gz' +REQUIRED = frozenset([ + ARCHIVE, 'research/community-frontier1042-audit/RESULT.json', + 'research/community-frontier1094-audit/selected-replay.tar.gz', + 'research/community-frontier1094-audit/RESULT.json', + 'research/community-frontier1094-audit/ASSEMBLY.json', + 'docs/research/community-batch1099-review.md', + 'scripts/verify_frontier1094.py', + 'research/complex-dyadic-lowering/lower.py', + 'research/complex-dyadic-lowering/README.md', + 'research/gauge44-slots/code/invoice_allcold.py', + 'research/gauge44-slots/independent/audit_local.py']) +MEMBERS = ('CANONICAL-WORD.json.gz','LOCAL-PROGRAMS.json.gz', + 'INDEPENDENT-LOCAL-REPLAY.json','LOCAL-CHECKS.json') + +def require(value, message): + if not value: raise ValueError(message) + +def canonical(value): + return json.dumps(json.loads(json.dumps(value)), sort_keys=True, + separators=(',', ':'), allow_nan=False).encode() + +def digest(data): return hashlib.sha256(data).hexdigest() +def pin(path): + b = path.read_bytes() + return digest(b if path.name.endswith('.gz') else b.replace(b'\r\n',b'\n')) + +def check_sources(manifest=None): + m = manifest if manifest is not None else json.loads((HERE/'SOURCES.json').read_bytes()) + require(m['base'] == BASE and set(m['files']) == REQUIRED, 'source inventory') + require(set(m['archive_members'])=={'slots/local/'+n for n in MEMBERS},'archive member inventory') + for p,d in m['files'].items(): require(pin(ROOT/p)==d, 'source pin '+p) + selected=json.loads((HERE/'BASE-SELECTED.json').read_bytes()) + require(digest(canonical(selected))==m['selected_snapshot_sha256'],'selected snapshot') + require(selected['kappa']=='836330098538459/500000000000000000','selected kappa') + old=json.loads((ROOT/'research/community-frontier1042-audit/RESULT.json').read_bytes()) + current=json.loads((ROOT/'research/community-frontier1094-audit/RESULT.json').read_bytes()) + require(current['baseline_receipt_sha256']==digest((ROOT/'research/community-frontier1042-audit/RESULT.json').read_bytes()),'selected baseline receipt') + require(old['status']=='PASS_COMPLETE_PR1042_COMPOSITION' and current['status']=='PASS_COMPLETE_PR1094_COMPOSITION','selected receipt statuses') + return m + +def load(): + m=check_sources(); objs={} + with tarfile.open(ROOT/ARCHIVE) as t: + for n in MEMBERS: + name='slots/local/'+n; raw=t.extractfile(name).read() + require(digest(raw)==m['archive_members'][name], 'archive member '+name) + objs[n]=json.loads(gzip.decompress(raw) if n.endswith('.gz') else raw) + w=objs[MEMBERS[0]]; programs=objs[MEMBERS[1]]; receipt=objs[MEMBERS[2]] + require(set(m['archive_members'])=={'slots/local/'+n for n in MEMBERS},'archive member inventory') + with tarfile.open(ROOT/'research/community-frontier1094-audit/selected-replay.tar.gz') as t: + for n in MEMBERS: + raw=t.extractfile('candidate/strict/global8/base/providers/gauge44/'+n).read() + require(digest(raw)==m['archive_members']['slots/local/'+n],'selected1094 provider alias '+n) + require((w['v'],w['h'],w['R'])==(112,9,480),'source dimensions') + require(receipt['canonical_word_sha256']==m['archive_members']['slots/local/'+MEMBERS[0]] and receipt['local_programs_sha256']==m['archive_members']['slots/local/'+MEMBERS[1]],'native receipt artifact binding') + require(set(programs)=={'forward','backward'},'orientations') + return w,programs,receipt,objs[MEMBERS[3]] + +def power(k): return Q(2**k) if k>=0 else Q(1,2**-k) + +def parts(q): + a=abs(q.numerator);d=q.denominator + require(a and d&(d-1)==0,'nonzero dyadic') + v=(a&-a).bit_length()-1 + return a>>v, v-(d.bit_length()-1) + +def price(q, mode='copy-init'): + p,e=parts(q) + return 3+(p.bit_length()-1)+p.bit_count()+abs(e) if mode=='horner' else 2+(p.bit_length()-1)+p.bit_count()+abs(e)-int(p==1 and e==0) + +def cost(g,mode='copy-init'): + if g[0]=='add':return price(Q(g[3],g[4]),mode) + if g[0] in ('copy','clear'):return 1 + require(g[0]=='scale','scalar opcode') + q=Q(g[2],g[3]);p,e=parts(q);require(p==1,'power of two scale') + return abs(e)+int(q<0) + +def domain(w,programs): + excluded=set(w['centers']) & set(range(224,704)) + for events in programs.values(): + for ev in events: + if ev[0]=='scalar' and ev[1][0] in ('copy','clear'): + for r in ev[1][1:]: + if isinstance(r,list) and r[0]=='L' and 224<=r[1]<704:excluded.add(r[1]) + return sorted(set(range(224,704))-excluded),sorted(excluded) + +def search(events,helpers,mode='copy-init'): + terms=defaultdict(list) + for ev in events: + if ev[0]=='scalar' and ev[1][0]=='add': + g=ev[1];p,e=parts(Q(g[3],g[4])) + for r,s in ((g[1],1),(g[2],-1)): + if r[0]=='L':terms[r[1]].append((p,e,s)) + rows=[] + for h in helpers: + ts=terms[h]; points=sorted({0}|{-s*e for p,e,s in ts}) + def delta(k): + return 2*abs(k)+sum(abs(e+s*k)-abs(e) - (int(p==1 and e+s*k==0)-int(p==1 and e==0) if mode=='copy-init' else 0) for p,e,s in ts) + values=[[k,delta(k)] for k in points] + best=min(values,key=lambda kv:(kv[1],abs(kv[0]),kv[0])) + rows.append(dict(helper=h,incident_adds=len(ts),candidates=values,best_k=best[0],delta=best[1],tail_slope=2+len(ts))) + return rows + +def transform(events,w,h,k): + require(224<=h<704 and h not in w['centers'],'non-center helper only') + result=copy.deepcopy(events) + for ev in result: + if ev[0]!='scalar':continue + g=ev[1] + if g[0]=='add': + shift=k*(int(g[1]==['L',h])-int(g[2]==['L',h])) + q=Q(g[3],g[4])*power(shift);g[3:5]=[q.numerator,q.denominator] + elif g[0] in ('copy','clear'): + require(['L',h] not in g[1:],'copy/clear carrier excluded') + q=power(k); entry=['scalar',['scale',['L',h],q.numerator,q.denominator],w['start'][h]] + q=1/q; leave=['scalar',['scale',['L',h],q.numerator,q.denominator],w['final'][h]] + # The materialized winner is cold/FULL and has no residual wrapper. The + # exit scale follows full-frame cleanup, in the retained FULL coordinate. + require(w['start'][h]==0 and w['final'][h]==1,'materialized cold/FULL helper') + require(not any(e[0]=='residual_adapter' and e[2]==h for e in result),'unwrapped helper') + require(result[0]==['phase','zero_frame_precondition'] and result[-1]==['phase','done'],'boundary phases') + result.insert(len(result)-1,leave);result.insert(1,entry) + require([e for e in result if e[0]!='scalar']==[e for e in events if e[0]!='scalar'],'nonscalar stream preserved') + return result + +def replay(events,orientation): + # Independent formal variables for all 704 data/helper and 8 centre registers. + rows={('L',i):{i:Q(1)} for i in range(704)} + rows.update({('C',i):{704+i:Q(1)} for i in range(8)}) + for ev in events: + if ev[0]!='scalar':continue + g=ev[1];t=tuple(g[1]);tag=g[0] + if tag=='clear':rows[t]={} + elif tag=='copy':rows[t]=dict(rows[tuple(g[2])]) + elif tag=='scale':rows[t]={i:a*Q(g[2],g[3]) for i,a in rows[t].items()} + elif tag=='add': + s=tuple(g[2]);q=Q(g[3],g[4]);require(t!=s,'distinct add operands') + for i,a in rows[s].items(): + v=rows[t].get(i,Q(0))+q*a + if v:rows[t][i]=v + else:rows[t].pop(i,None) + else:raise ValueError('scalar opcode') + for i in range(704): + expected={i:Q(1)} + if orientation=='forward' and 112<=i<224:expected[i-112]=Q(1) + if orientation=='backward' and i<112:expected[i+112]=Q(-1) + require(rows['L',i]==expected,'all-column endpoint '+str((orientation,i))) + require(all(not rows['C',i] for i in range(8)),'private centre erased') + return dict(formal_input_columns=712,data_helper_columns=704,dirty_helper_columns=480,centre_columns=8,all_restored=True) + +def invoice(events,mode): + env={('L',i):Q(1) for i in range(704)} + env.update({('C',i):Q(1) for i in range(8)}) + peak=Q(1);count=0;paid=Counter() + for ev in events: + if ev[0]=='climb':paid[ev[5]]+=1 + elif ev[0]=='center':paid[ev[4]]+=1 + if ev[0]!='scalar':continue + g=ev[1];tag=g[0];t=tuple(g[1]);count+=cost(g,mode) + if tag=='clear':env[t]=Q(0) + elif tag=='copy':env[t]=env[tuple(g[2])] + elif tag=='scale': + q=Q(g[2],g[3]);env[t]*=abs(q) + else: + s=tuple(g[2]);q=Q(g[3],g[4]);a=abs(q.numerator) + # Integer Horner work grows to |numerator| times source before halving. + # Copy-init has the same bound; unit direct-add does not touch W until clear. + if mode=='horner' or abs(q)!=1:peak=max(peak,a*env[s]) + env[t]+=abs(q)*env[s] + peak=max(peak,env[t]) + bits=peak.numerator.bit_length()-peak.denominator.bit_length()+1 + require(peak<2**192,'local 192-bit payload cap') + return dict(real_primitives=count,complex_primitives=2*count,prefix_l1=str(peak),prefix_bits=bits,charged_payload_bits=192,paid_profile=dict(sorted(paid.items()))) + +def compute(): + w,programs,receipt,checks=load();helpers,excluded=domain(w,programs) + result=dict(base=BASE,geometry=dict(v=112,h=9,R=480),helpers=helpers,excluded_center_or_copy_helpers=excluded,orientations={}) + candidates={} + for orientation in ('forward','backward'): + events=programs[orientation];rows=search(events,helpers) + winner=min(rows,key=lambda row:(row['delta'],row['helper'],abs(row['best_k']),row['best_k'])) + h,k=winner['helper'],winner['best_k'];candidate=transform(events,w,h,k);candidates[orientation]=candidate + entry={ 'optima':rows,'winner':winner,'candidate_sha256':digest(canonical(candidate)), + 'boundary_frames':[w['start'][h],w['final'][h]],'baseline_endpoint':replay(events,orientation),'candidate_endpoint':replay(candidate,orientation),'prices':{}} + for mode in ('horner','copy-init'): + before=invoice(events,mode);after=invoice(candidate,mode) + require(before['paid_profile']==after['paid_profile'],'paid children unchanged') + if mode=='horner': + require(before['prefix_l1']==receipt['local'][orientation]['prefix_l1_upper'],'source prefix invoice') + require(before['complex_primitives']==checks[orientation]['real_component_primitive_bound'],'source primitive invoice') + else:require(after['real_primitives']-before['real_primitives']==winner['delta'],'search vs whole stream cost') + entry['prices'][mode]=dict(before=before,after=after,saving_real=before['real_primitives']-after['real_primitives'],saving_complex=before['complex_primitives']-after['complex_primitives']) + result['orientations'][orientation]=entry + result['status']='PASS_EXACT_UNBOUNDED_SINGLE_NONCENTER_HELPER_DYADIC_GAUGE' + return result,candidates diff --git a/research/k8-phase-local-gauges/vendor/pr1214/CERTIFICATE.json b/research/k8-phase-local-gauges/vendor/pr1214/CERTIFICATE.json new file mode 100644 index 0000000000..d44d7d0a25 --- /dev/null +++ b/research/k8-phase-local-gauges/vendor/pr1214/CERTIFICATE.json @@ -0,0 +1 @@ +{"base":"1b59b624d21924f8e3537cdc1ac52d3be6eda2fe","orientations":{"backward":{"baseline_endpoint":{"all_restored":true,"centre_columns":8,"data_helper_columns":704,"dirty_helper_columns":480,"formal_input_columns":712},"bounded_pilot":{"assignments":38624,"delta_histogram":[[-256,1],[-240,1],[-235,1],[-218,1],[-216,2],[-204,1],[-202,1],[-200,1],[-199,1],[-197,2],[-196,3],[-195,3],[-194,3],[-193,1],[-192,1],[-191,2],[-190,1],[-189,1],[-188,1],[-186,1],[-182,3],[-180,3],[-178,5],[-176,4],[-175,2],[-173,1],[-172,2],[-171,3],[-170,1],[-169,2],[-166,3],[-165,2],[-164,1],[-163,1],[-162,1],[-161,1],[-160,1],[-159,1],[-158,9],[-157,3],[-156,2],[-155,3],[-154,5],[-153,1],[-152,2],[-151,1],[-150,2],[-149,3],[-147,2],[-146,1],[-145,2],[-144,3],[-143,2],[-142,6],[-141,5],[-140,2],[-139,5],[-138,3],[-137,5],[-136,1],[-135,4],[-134,1],[-133,1],[-132,2],[-131,4],[-130,4],[-129,2],[-128,1],[-127,5],[-126,4],[-125,3],[-124,1],[-123,1],[-122,3],[-121,4],[-120,5],[-119,4],[-118,1],[-117,5],[-116,7],[-115,7],[-114,6],[-113,9],[-112,3],[-111,5],[-110,4],[-109,3],[-108,4],[-107,3],[-106,3],[-105,7],[-104,4],[-103,9],[-102,11],[-101,6],[-100,6],[-99,10],[-98,7],[-97,5],[-96,6],[-95,3],[-94,11],[-93,4],[-92,3],[-91,5],[-90,11],[-89,8],[-88,6],[-87,3],[-86,7],[-85,8],[-84,4],[-83,12],[-82,13],[-81,15],[-80,7],[-79,11],[-78,15],[-77,9],[-76,11],[-75,5],[-74,10],[-73,12],[-72,12],[-71,11],[-70,9],[-69,9],[-68,10],[-67,12],[-66,17],[-65,20],[-64,11],[-63,22],[-62,17],[-61,13],[-60,17],[-59,14],[-58,23],[-57,10],[-56,19],[-55,16],[-54,13],[-53,17],[-52,24],[-51,17],[-50,17],[-49,12],[-48,23],[-47,23],[-46,22],[-45,37],[-44,27],[-43,27],[-42,30],[-41,25],[-40,35],[-39,33],[-38,36],[-37,36],[-36,31],[-35,36],[-34,28],[-33,36],[-32,32],[-31,27],[-30,32],[-29,30],[-28,41],[-27,42],[-26,38],[-25,38],[-24,42],[-23,32],[-22,40],[-21,48],[-20,51],[-19,40],[-18,46],[-17,55],[-16,56],[-15,30],[-14,41],[-13,50],[-12,47],[-11,44],[-10,51],[-9,37],[-8,61],[-7,49],[-6,56],[-5,43],[-4,90],[-3,57],[-2,70],[-1,68],[0,67],[1,69],[2,57],[3,53],[4,76],[5,70],[6,83],[7,60],[8,58],[9,63],[10,78],[11,83],[12,71],[13,80],[14,80],[15,73],[16,75],[17,66],[18,75],[19,88],[20,92],[21,91],[22,84],[23,70],[24,104],[25,80],[26,86],[27,97],[28,97],[29,76],[30,103],[31,105],[32,110],[33,97],[34,96],[35,81],[36,91],[37,88],[38,77],[39,87],[40,96],[41,117],[42,99],[43,113],[44,100],[45,95],[46,100],[47,97],[48,91],[49,107],[50,91],[51,117],[52,115],[53,94],[54,116],[55,100],[56,122],[57,103],[58,122],[59,110],[60,113],[61,116],[62,122],[63,100],[64,117],[65,106],[66,125],[67,110],[68,121],[69,118],[70,113],[71,108],[72,127],[73,114],[74,114],[75,110],[76,125],[77,115],[78,123],[79,129],[80,106],[81,113],[82,117],[83,110],[84,117],[85,127],[86,103],[87,111],[88,128],[89,99],[90,122],[91,114],[92,113],[93,129],[94,124],[95,104],[96,119],[97,119],[98,139],[99,128],[100,101],[101,136],[102,147],[103,130],[104,107],[105,129],[106,117],[107,124],[108,109],[109,118],[110,128],[111,107],[112,107],[113,134],[114,130],[115,105],[116,117],[117,128],[118,130],[119,145],[120,139],[121,145],[122,159],[123,140],[124,134],[125,145],[126,143],[127,143],[128,112],[129,122],[130,125],[131,131],[132,127],[133,110],[134,123],[135,123],[136,130],[137,132],[138,139],[139,141],[140,134],[141,128],[142,120],[143,131],[144,121],[145,132],[146,109],[147,129],[148,130],[149,127],[150,122],[151,124],[152,121],[153,127],[154,123],[155,120],[156,124],[157,129],[158,132],[159,119],[160,134],[161,131],[162,145],[163,118],[164,118],[165,127],[166,124],[167,133],[168,142],[169,115],[170,101],[171,118],[172,113],[173,110],[174,105],[175,132],[176,130],[177,113],[178,106],[179,111],[180,119],[181,122],[182,112],[183,126],[184,118],[185,145],[186,113],[187,109],[188,123],[189,115],[190,107],[191,133],[192,117],[193,105],[194,95],[195,111],[196,104],[197,106],[198,98],[199,119],[200,127],[201,84],[202,127],[203,106],[204,120],[205,103],[206,110],[207,103],[208,109],[209,103],[210,87],[211,97],[212,108],[213,95],[214,81],[215,110],[216,98],[217,95],[218,93],[219,88],[220,80],[221,89],[222,95],[223,77],[224,94],[225,84],[226,78],[227,103],[228,84],[229,100],[230,92],[231,110],[232,95],[233,100],[234,106],[235,87],[236,86],[237,75],[238,109],[239,74],[240,96],[241,92],[242,94],[243,88],[244,86],[245,76],[246,89],[247,102],[248,84],[249,79],[250,81],[251,95],[252,94],[253,86],[254,86],[255,80],[256,94],[257,78],[258,73],[259,66],[260,68],[261,73],[262,78],[263,68],[264,65],[265,71],[266,86],[267,85],[268,87],[269,72],[270,78],[271,77],[272,66],[273,73],[274,75],[275,73],[276,71],[277,75],[278,65],[279,83],[280,67],[281,78],[282,60],[283,78],[284,92],[285,58],[286,77],[287,61],[288,60],[289,61],[290,66],[291,55],[292,81],[293,68],[294,67],[295,68],[296,79],[297,44],[298,64],[299,58],[300,64],[301,73],[302,65],[303,62],[304,60],[305,52],[306,46],[307,52],[308,53],[309,69],[310,59],[311,61],[312,49],[313,58],[314,57],[315,52],[316,43],[317,44],[318,53],[319,53],[320,64],[321,56],[322,48],[323,53],[324,45],[325,59],[326,52],[327,52],[328,39],[329,38],[330,29],[331,39],[332,51],[333,49],[334,38],[335,38],[336,53],[337,38],[338,50],[339,43],[340,46],[341,42],[342,43],[343,48],[344,32],[345,36],[346,37],[347,34],[348,39],[349,30],[350,32],[351,39],[352,36],[353,35],[354,38],[355,49],[356,34],[357,37],[358,24],[359,28],[360,23],[361,32],[362,24],[363,39],[364,34],[365,32],[366,33],[367,19],[368,30],[369,39],[370,34],[371,26],[372,22],[373,26],[374,24],[375,25],[376,22],[377,32],[378,31],[379,12],[380,20],[381,24],[382,25],[383,29],[384,25],[385,32],[386,25],[387,22],[388,29],[389,16],[390,21],[391,19],[392,23],[393,19],[394,20],[395,22],[396,18],[397,22],[398,17],[399,23],[400,22],[401,12],[402,16],[403,26],[404,18],[405,13],[406,24],[407,17],[408,22],[409,15],[410,21],[411,13],[412,16],[413,15],[414,17],[415,16],[416,23],[417,22],[418,19],[419,13],[420,22],[421,21],[422,17],[423,12],[424,16],[425,15],[426,12],[427,11],[428,12],[429,17],[430,13],[431,14],[432,14],[433,8],[434,12],[435,16],[436,10],[437,23],[438,12],[439,11],[440,13],[441,14],[442,9],[443,16],[444,11],[445,10],[446,16],[447,14],[448,6],[449,3],[450,8],[451,6],[452,8],[453,6],[454,8],[455,7],[456,11],[457,12],[458,11],[459,8],[460,11],[461,12],[462,9],[463,13],[464,10],[465,10],[466,7],[467,5],[468,5],[469,6],[470,10],[471,8],[472,10],[473,8],[474,8],[475,11],[476,10],[477,3],[478,7],[479,7],[480,7],[481,3],[482,9],[483,4],[484,5],[485,4],[486,2],[487,8],[488,2],[489,5],[490,5],[491,1],[492,3],[493,2],[494,8],[495,3],[496,5],[497,1],[498,3],[499,3],[500,3],[501,4],[502,1],[503,4],[504,3],[505,1],[506,3],[507,3],[508,4],[510,1],[511,2],[512,2],[513,2],[514,1],[515,4],[516,6],[517,5],[518,1],[519,1],[520,2],[521,1],[522,2],[523,1],[524,4],[525,4],[526,2],[527,1],[529,4],[530,1],[532,3],[533,1],[534,3],[535,3],[536,1],[538,1],[539,2],[541,1],[542,1],[544,3],[548,3],[549,1],[550,1],[551,1],[552,2],[553,3],[554,1],[556,2],[557,4],[558,1],[559,2],[564,1],[566,1],[568,1],[570,2],[575,1],[576,1],[577,1]],"exponents":[-2,-1,1,2],"helpers":[225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,274,276,278,279,280,281,283,284,285,286,287,288,290,292,294,295,296,297,299,300,301,302,303,304,306,308,310,312,313,315,316,317,318,319,320,322,324,326,328,329,331,332,333,334,335,336,338,340,342,343,344,345,347,348,349,350,351,352,354,356,358,359,360,361,363,364,365,366,367,368,370,372,374,375,376,377,379,380,381,382,383,384,386,388,390,391,392,393,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,478,479,480,481,482,483,490,491,492,493,494,495,499,502,503,504,505,507,511,514,515,516,517,519,530,542,546,547,548,549,558,560,568,570],"pairs":2414,"winner":{"delta_real":-256,"exponents":[2,1],"helpers":[427,430],"interaction_delta_real":0,"separate_single_delta_real":-256}},"candidate_endpoint":{"all_restored":true,"centre_columns":8,"data_helper_columns":704,"dirty_helper_columns":480,"formal_input_columns":712},"candidate_sha256":"d8bac18a43eb36e708d904675776f2f488b8894de3830425e9a5bd14e06dee3b","domain":"all integer exponent pairs, including zero","helpers":[225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,274,276,278,279,280,281,283,284,285,286,287,288,290,292,294,295,296,297,299,300,301,302,303,304,306,308,310,312,313,315,316,317,318,319,320,322,324,326,328,329,331,332,333,334,335,336,338,340,342,343,344,345,347,348,349,350,351,352,354,356,358,359,360,361,363,364,365,366,367,368,370,372,374,375,376,377,379,380,381,382,383,384,386,388,390,391,392,393,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,478,479,480,481,482,483,490,491,492,493,494,495,499,502,503,504,505,507,511,514,515,516,517,519,530,542,546,547,548,549,558,560,568,570],"interacting_pairs":2414,"pair_rows_sha256":"417edb391940dc21e50cb80a8059b4d4ab458b520a61661e78ea98f33d1f4f08","pairs":27966,"prices":{"copy-init":{"after":{"charged_payload_bits":192,"complex_primitives":148442,"paid_profile":{"1":2412,"2":418,"3":432,"4":142,"5":82,"8":8},"prefix_bits":68,"prefix_l1":"14824960514781440791821/64","real_primitives":74221},"before":{"charged_payload_bits":192,"complex_primitives":149018,"paid_profile":{"1":2412,"2":418,"3":432,"4":142,"5":82,"8":8},"prefix_bits":68,"prefix_l1":"14824960514781440791821/64","real_primitives":74509},"saving_complex":576},"horner":{"after":{"charged_payload_bits":192,"complex_primitives":198398,"paid_profile":{"1":2412,"2":418,"3":432,"4":142,"5":82,"8":8},"prefix_bits":68,"prefix_l1":"14824960514781440791821/64","real_primitives":99199},"before":{"charged_payload_bits":192,"complex_primitives":198814,"paid_profile":{"1":2412,"2":418,"3":432,"4":142,"5":82,"8":8},"prefix_bits":68,"prefix_l1":"14824960514781440791821/64","real_primitives":99407},"saving_complex":416}},"separable_pairs":25552,"vertices":735975,"winner":{"delta_real":-288,"exponents":[2,2],"helpers":[251,427],"interaction_delta_real":0,"separate_single_delta_real":-288}},"forward":{"baseline_endpoint":{"all_restored":true,"centre_columns":8,"data_helper_columns":704,"dirty_helper_columns":480,"formal_input_columns":712},"bounded_pilot":{"assignments":38624,"delta_histogram":[[-256,1],[-240,1],[-235,1],[-218,1],[-216,2],[-204,1],[-202,1],[-200,1],[-199,1],[-197,2],[-196,3],[-195,3],[-194,3],[-193,1],[-192,1],[-191,2],[-190,1],[-189,1],[-188,1],[-186,1],[-182,3],[-180,3],[-178,5],[-176,4],[-175,2],[-173,1],[-172,2],[-171,3],[-170,1],[-169,2],[-166,3],[-165,2],[-164,1],[-163,1],[-162,1],[-161,1],[-160,1],[-159,1],[-158,9],[-157,3],[-156,2],[-155,3],[-154,5],[-153,1],[-152,2],[-151,1],[-150,2],[-149,3],[-147,2],[-146,1],[-145,2],[-144,3],[-143,2],[-142,6],[-141,5],[-140,2],[-139,5],[-138,3],[-137,5],[-136,1],[-135,4],[-134,1],[-133,1],[-132,2],[-131,4],[-130,4],[-129,2],[-128,1],[-127,5],[-126,4],[-125,3],[-124,1],[-123,1],[-122,3],[-121,4],[-120,5],[-119,4],[-118,1],[-117,5],[-116,7],[-115,7],[-114,6],[-113,9],[-112,3],[-111,5],[-110,4],[-109,3],[-108,4],[-107,3],[-106,3],[-105,7],[-104,4],[-103,9],[-102,11],[-101,6],[-100,6],[-99,10],[-98,7],[-97,5],[-96,6],[-95,3],[-94,11],[-93,4],[-92,3],[-91,5],[-90,11],[-89,8],[-88,6],[-87,3],[-86,7],[-85,8],[-84,4],[-83,12],[-82,13],[-81,15],[-80,7],[-79,11],[-78,15],[-77,9],[-76,11],[-75,5],[-74,10],[-73,12],[-72,12],[-71,11],[-70,9],[-69,9],[-68,10],[-67,12],[-66,17],[-65,20],[-64,11],[-63,22],[-62,17],[-61,13],[-60,17],[-59,14],[-58,23],[-57,10],[-56,19],[-55,16],[-54,13],[-53,17],[-52,24],[-51,17],[-50,17],[-49,12],[-48,23],[-47,23],[-46,22],[-45,37],[-44,27],[-43,27],[-42,30],[-41,25],[-40,35],[-39,33],[-38,36],[-37,36],[-36,31],[-35,36],[-34,28],[-33,36],[-32,32],[-31,27],[-30,32],[-29,30],[-28,41],[-27,42],[-26,38],[-25,38],[-24,42],[-23,32],[-22,40],[-21,48],[-20,51],[-19,40],[-18,46],[-17,55],[-16,56],[-15,30],[-14,41],[-13,50],[-12,47],[-11,44],[-10,51],[-9,37],[-8,61],[-7,49],[-6,56],[-5,43],[-4,90],[-3,57],[-2,70],[-1,68],[0,67],[1,69],[2,57],[3,53],[4,76],[5,70],[6,83],[7,60],[8,58],[9,63],[10,78],[11,83],[12,71],[13,80],[14,80],[15,73],[16,75],[17,66],[18,75],[19,88],[20,92],[21,91],[22,84],[23,70],[24,104],[25,80],[26,86],[27,97],[28,97],[29,76],[30,103],[31,105],[32,110],[33,97],[34,96],[35,81],[36,91],[37,88],[38,77],[39,87],[40,96],[41,117],[42,99],[43,113],[44,100],[45,95],[46,100],[47,97],[48,91],[49,107],[50,91],[51,117],[52,115],[53,94],[54,116],[55,100],[56,122],[57,103],[58,122],[59,110],[60,113],[61,116],[62,122],[63,100],[64,117],[65,106],[66,125],[67,110],[68,121],[69,118],[70,113],[71,108],[72,127],[73,114],[74,114],[75,110],[76,125],[77,115],[78,123],[79,129],[80,106],[81,113],[82,117],[83,110],[84,117],[85,127],[86,103],[87,111],[88,128],[89,99],[90,122],[91,114],[92,113],[93,129],[94,124],[95,104],[96,119],[97,119],[98,139],[99,128],[100,101],[101,136],[102,147],[103,130],[104,107],[105,129],[106,117],[107,124],[108,109],[109,118],[110,128],[111,107],[112,107],[113,134],[114,130],[115,105],[116,117],[117,128],[118,130],[119,145],[120,139],[121,145],[122,159],[123,140],[124,134],[125,145],[126,143],[127,143],[128,112],[129,122],[130,125],[131,131],[132,127],[133,110],[134,123],[135,123],[136,130],[137,132],[138,139],[139,141],[140,134],[141,128],[142,120],[143,131],[144,121],[145,132],[146,109],[147,129],[148,130],[149,127],[150,122],[151,124],[152,121],[153,127],[154,123],[155,120],[156,124],[157,129],[158,132],[159,119],[160,134],[161,131],[162,145],[163,118],[164,118],[165,127],[166,124],[167,133],[168,142],[169,115],[170,101],[171,118],[172,113],[173,110],[174,105],[175,132],[176,130],[177,113],[178,106],[179,111],[180,119],[181,122],[182,112],[183,126],[184,118],[185,145],[186,113],[187,109],[188,123],[189,115],[190,107],[191,133],[192,117],[193,105],[194,95],[195,111],[196,104],[197,106],[198,98],[199,119],[200,127],[201,84],[202,127],[203,106],[204,120],[205,103],[206,110],[207,103],[208,109],[209,103],[210,87],[211,97],[212,108],[213,95],[214,81],[215,110],[216,98],[217,95],[218,93],[219,88],[220,80],[221,89],[222,95],[223,77],[224,94],[225,84],[226,78],[227,103],[228,84],[229,100],[230,92],[231,110],[232,95],[233,100],[234,106],[235,87],[236,86],[237,75],[238,109],[239,74],[240,96],[241,92],[242,94],[243,88],[244,86],[245,76],[246,89],[247,102],[248,84],[249,79],[250,81],[251,95],[252,94],[253,86],[254,86],[255,80],[256,94],[257,78],[258,73],[259,66],[260,68],[261,73],[262,78],[263,68],[264,65],[265,71],[266,86],[267,85],[268,87],[269,72],[270,78],[271,77],[272,66],[273,73],[274,75],[275,73],[276,71],[277,75],[278,65],[279,83],[280,67],[281,78],[282,60],[283,78],[284,92],[285,58],[286,77],[287,61],[288,60],[289,61],[290,66],[291,55],[292,81],[293,68],[294,67],[295,68],[296,79],[297,44],[298,64],[299,58],[300,64],[301,73],[302,65],[303,62],[304,60],[305,52],[306,46],[307,52],[308,53],[309,69],[310,59],[311,61],[312,49],[313,58],[314,57],[315,52],[316,43],[317,44],[318,53],[319,53],[320,64],[321,56],[322,48],[323,53],[324,45],[325,59],[326,52],[327,52],[328,39],[329,38],[330,29],[331,39],[332,51],[333,49],[334,38],[335,38],[336,53],[337,38],[338,50],[339,43],[340,46],[341,42],[342,43],[343,48],[344,32],[345,36],[346,37],[347,34],[348,39],[349,30],[350,32],[351,39],[352,36],[353,35],[354,38],[355,49],[356,34],[357,37],[358,24],[359,28],[360,23],[361,32],[362,24],[363,39],[364,34],[365,32],[366,33],[367,19],[368,30],[369,39],[370,34],[371,26],[372,22],[373,26],[374,24],[375,25],[376,22],[377,32],[378,31],[379,12],[380,20],[381,24],[382,25],[383,29],[384,25],[385,32],[386,25],[387,22],[388,29],[389,16],[390,21],[391,19],[392,23],[393,19],[394,20],[395,22],[396,18],[397,22],[398,17],[399,23],[400,22],[401,12],[402,16],[403,26],[404,18],[405,13],[406,24],[407,17],[408,22],[409,15],[410,21],[411,13],[412,16],[413,15],[414,17],[415,16],[416,23],[417,22],[418,19],[419,13],[420,22],[421,21],[422,17],[423,12],[424,16],[425,15],[426,12],[427,11],[428,12],[429,17],[430,13],[431,14],[432,14],[433,8],[434,12],[435,16],[436,10],[437,23],[438,12],[439,11],[440,13],[441,14],[442,9],[443,16],[444,11],[445,10],[446,16],[447,14],[448,6],[449,3],[450,8],[451,6],[452,8],[453,6],[454,8],[455,7],[456,11],[457,12],[458,11],[459,8],[460,11],[461,12],[462,9],[463,13],[464,10],[465,10],[466,7],[467,5],[468,5],[469,6],[470,10],[471,8],[472,10],[473,8],[474,8],[475,11],[476,10],[477,3],[478,7],[479,7],[480,7],[481,3],[482,9],[483,4],[484,5],[485,4],[486,2],[487,8],[488,2],[489,5],[490,5],[491,1],[492,3],[493,2],[494,8],[495,3],[496,5],[497,1],[498,3],[499,3],[500,3],[501,4],[502,1],[503,4],[504,3],[505,1],[506,3],[507,3],[508,4],[510,1],[511,2],[512,2],[513,2],[514,1],[515,4],[516,6],[517,5],[518,1],[519,1],[520,2],[521,1],[522,2],[523,1],[524,4],[525,4],[526,2],[527,1],[529,4],[530,1],[532,3],[533,1],[534,3],[535,3],[536,1],[538,1],[539,2],[541,1],[542,1],[544,3],[548,3],[549,1],[550,1],[551,1],[552,2],[553,3],[554,1],[556,2],[557,4],[558,1],[559,2],[564,1],[566,1],[568,1],[570,2],[575,1],[576,1],[577,1]],"exponents":[-2,-1,1,2],"helpers":[225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,274,276,278,279,280,281,283,284,285,286,287,288,290,292,294,295,296,297,299,300,301,302,303,304,306,308,310,312,313,315,316,317,318,319,320,322,324,326,328,329,331,332,333,334,335,336,338,340,342,343,344,345,347,348,349,350,351,352,354,356,358,359,360,361,363,364,365,366,367,368,370,372,374,375,376,377,379,380,381,382,383,384,386,388,390,391,392,393,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,478,479,480,481,482,483,490,491,492,493,494,495,499,502,503,504,505,507,511,514,515,516,517,519,530,542,546,547,548,549,558,560,568,570],"pairs":2414,"winner":{"delta_real":-256,"exponents":[-2,-1],"helpers":[427,430],"interaction_delta_real":0,"separate_single_delta_real":-256}},"candidate_endpoint":{"all_restored":true,"centre_columns":8,"data_helper_columns":704,"dirty_helper_columns":480,"formal_input_columns":712},"candidate_sha256":"1d756480ebe954f304b717104954eee78d26d81f2b96de35e10da76e7bb511c2","domain":"all integer exponent pairs, including zero","helpers":[225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,274,276,278,279,280,281,283,284,285,286,287,288,290,292,294,295,296,297,299,300,301,302,303,304,306,308,310,312,313,315,316,317,318,319,320,322,324,326,328,329,331,332,333,334,335,336,338,340,342,343,344,345,347,348,349,350,351,352,354,356,358,359,360,361,363,364,365,366,367,368,370,372,374,375,376,377,379,380,381,382,383,384,386,388,390,391,392,393,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,478,479,480,481,482,483,490,491,492,493,494,495,499,502,503,504,505,507,511,514,515,516,517,519,530,542,546,547,548,549,558,560,568,570],"interacting_pairs":2414,"pair_rows_sha256":"2cb96e4cc5ce176816dab09312e080c2c3445088de06ce45baec922c56556454","pairs":27966,"prices":{"copy-init":{"after":{"charged_payload_bits":192,"complex_primitives":148426,"paid_profile":{"1":2412,"2":418,"3":432,"4":142,"5":82,"8":8},"prefix_bits":52,"prefix_l1":"2765345294379392599/1024","real_primitives":74213},"before":{"charged_payload_bits":192,"complex_primitives":149002,"paid_profile":{"1":2412,"2":418,"3":432,"4":142,"5":82,"8":8},"prefix_bits":52,"prefix_l1":"2765345294379392599/1024","real_primitives":74501},"saving_complex":576},"horner":{"after":{"charged_payload_bits":192,"complex_primitives":198350,"paid_profile":{"1":2412,"2":418,"3":432,"4":142,"5":82,"8":8},"prefix_bits":52,"prefix_l1":"2765345294379392599/1024","real_primitives":99175},"before":{"charged_payload_bits":192,"complex_primitives":198766,"paid_profile":{"1":2412,"2":418,"3":432,"4":142,"5":82,"8":8},"prefix_bits":52,"prefix_l1":"2765345294379392599/1024","real_primitives":99383},"saving_complex":416}},"separable_pairs":25552,"vertices":735975,"winner":{"delta_real":-288,"exponents":[-2,-2],"helpers":[251,427],"interaction_delta_real":0,"separate_single_delta_real":-288}}},"scope":"all integer gauges on at most two cold/FULL unwrapped helpers","seed":25,"status":"PASS_K8_PAIR_DYADIC_CENSUS"} diff --git a/research/k8-phase-local-gauges/vendor/pr1259/CERTIFICATE.json b/research/k8-phase-local-gauges/vendor/pr1259/CERTIFICATE.json new file mode 100644 index 0000000000..53248cb732 --- /dev/null +++ b/research/k8-phase-local-gauges/vendor/pr1259/CERTIFICATE.json @@ -0,0 +1,1478 @@ +{ + "base": "dd6403f774a0891093a006ae9716c02e371b1fdb", + "seed": 37, + "helpers": [ + 264, + 265, + 266, + 267, + 268, + 269, + 270, + 271, + 272, + 274, + 276, + 278, + 279, + 280, + 281, + 283 + ], + "formal_columns": 712, + "orientations": { + "forward": { + "census": [ + { + "helper": 264, + "domain": [ + -2, + 2 + ], + "incident_adds": 71, + "delta_real": -110, + "scale_macros": 10, + "constant_delta_real": -7, + "constant_exponent": -2 + }, + { + "helper": 265, + "domain": [ + -13, + 3 + ], + "incident_adds": 98, + "delta_real": -155, + "scale_macros": 17, + "constant_delta_real": -50, + "constant_exponent": -1 + }, + { + "helper": 266, + "domain": [ + -3, + 3 + ], + "incident_adds": 110, + "delta_real": -160, + "scale_macros": 12, + "constant_delta_real": -4, + "constant_exponent": -1 + }, + { + "helper": 267, + "domain": [ + -2, + 3 + ], + "incident_adds": 105, + "delta_real": -167, + "scale_macros": 11, + "constant_delta_real": -36, + "constant_exponent": -1 + }, + { + "helper": 268, + "domain": [ + -2, + 3 + ], + "incident_adds": 81, + "delta_real": -119, + "scale_macros": 8, + "constant_delta_real": 0, + "constant_exponent": 0 + }, + { + "helper": 269, + "domain": [ + -2, + 2 + ], + "incident_adds": 74, + "delta_real": -111, + "scale_macros": 11, + "constant_delta_real": -6, + "constant_exponent": -2 + }, + { + "helper": 270, + "domain": [ + -2, + 2 + ], + "incident_adds": 103, + "delta_real": -162, + "scale_macros": 14, + "constant_delta_real": -41, + "constant_exponent": -1 + }, + { + "helper": 271, + "domain": [ + -2, + 3 + ], + "incident_adds": 93, + "delta_real": -161, + "scale_macros": 12, + "constant_delta_real": -38, + "constant_exponent": -1 + }, + { + "helper": 272, + "domain": [ + -2, + 3 + ], + "incident_adds": 101, + "delta_real": -100, + "scale_macros": 14, + "constant_delta_real": 0, + "constant_exponent": 0 + }, + { + "helper": 274, + "domain": [ + -10, + 2 + ], + "incident_adds": 93, + "delta_real": -123, + "scale_macros": 8, + "constant_delta_real": 0, + "constant_exponent": 0 + }, + { + "helper": 276, + "domain": [ + -11, + 2 + ], + "incident_adds": 121, + "delta_real": -172, + "scale_macros": 18, + "constant_delta_real": -37, + "constant_exponent": -1 + }, + { + "helper": 278, + "domain": [ + -5, + 2 + ], + "incident_adds": 97, + "delta_real": -127, + "scale_macros": 19, + "constant_delta_real": -2, + "constant_exponent": -1 + }, + { + "helper": 279, + "domain": [ + -10, + 2 + ], + "incident_adds": 90, + "delta_real": -108, + "scale_macros": 12, + "constant_delta_real": 0, + "constant_exponent": 0 + }, + { + "helper": 280, + "domain": [ + -11, + 3 + ], + "incident_adds": 106, + "delta_real": -137, + "scale_macros": 13, + "constant_delta_real": 0, + "constant_exponent": 0 + }, + { + "helper": 281, + "domain": [ + -3, + 1 + ], + "incident_adds": 73, + "delta_real": -59, + "scale_macros": 12, + "constant_delta_real": 0, + "constant_exponent": 0 + }, + { + "helper": 283, + "domain": [ + -11, + 2 + ], + "incident_adds": 125, + "delta_real": -163, + "scale_macros": 21, + "constant_delta_real": -15, + "constant_exponent": -1 + } + ], + "winner": { + "helper": 276, + "domain": [ + -11, + 2 + ], + "incident_adds": 121, + "delta_real": -172, + "scale_macros": 18, + "constant_delta_real": -37, + "constant_exponent": -1, + "schedule": [ + [ + 213, + -2 + ], + [ + 286, + -2 + ], + [ + 357, + -2 + ], + [ + 430, + -2 + ], + [ + 512, + -2 + ], + [ + 585, + -2 + ], + [ + 650, + -2 + ], + [ + 723, + -2 + ], + [ + 797, + -1 + ], + [ + 866, + -1 + ], + [ + 933, + -1 + ], + [ + 1201, + -1 + ], + [ + 1345, + -2 + ], + [ + 1504, + -2 + ], + [ + 1636, + -2 + ], + [ + 1700, + -2 + ], + [ + 1893, + -2 + ], + [ + 2148, + -2 + ], + [ + 2237, + -1 + ], + [ + 2310, + -1 + ], + [ + 3381, + -2 + ], + [ + 3440, + -2 + ], + [ + 3572, + -2 + ], + [ + 3631, + -2 + ], + [ + 3708, + -2 + ], + [ + 3774, + -2 + ], + [ + 3914, + -2 + ], + [ + 3997, + -2 + ], + [ + 4069, + -2 + ], + [ + 4188, + -2 + ], + [ + 4239, + -2 + ], + [ + 4296, + -2 + ], + [ + 5097, + -1 + ], + [ + 5383, + -1 + ], + [ + 5581, + -2 + ], + [ + 5716, + -2 + ], + [ + 5929, + -2 + ], + [ + 6008, + -2 + ], + [ + 6088, + -2 + ], + [ + 6166, + -2 + ], + [ + 6848, + -2 + ], + [ + 6927, + -2 + ], + [ + 6998, + -2 + ], + [ + 7077, + -2 + ], + [ + 7145, + -2 + ], + [ + 7211, + -2 + ], + [ + 7275, + -2 + ], + [ + 7353, + -2 + ], + [ + 8189, + 0 + ], + [ + 8197, + 0 + ], + [ + 8220, + 0 + ], + [ + 8267, + 0 + ], + [ + 8268, + 0 + ], + [ + 8269, + 0 + ], + [ + 8270, + 0 + ], + [ + 8271, + 0 + ], + [ + 8272, + 0 + ], + [ + 8273, + 0 + ], + [ + 8274, + 0 + ], + [ + 8275, + 0 + ], + [ + 8278, + 0 + ], + [ + 8279, + 0 + ], + [ + 8280, + 0 + ], + [ + 8296, + 0 + ], + [ + 8297, + 0 + ], + [ + 8298, + 0 + ], + [ + 8302, + 0 + ], + [ + 10057, + 0 + ], + [ + 10122, + 0 + ], + [ + 10123, + 0 + ], + [ + 10155, + 0 + ], + [ + 14021, + 0 + ], + [ + 14587, + 0 + ], + [ + 14905, + 0 + ], + [ + 15610, + 0 + ], + [ + 15611, + -1 + ], + [ + 15614, + -1 + ], + [ + 18743, + -1 + ], + [ + 18752, + -1 + ], + [ + 19242, + -1 + ], + [ + 19256, + -1 + ], + [ + 20090, + -1 + ], + [ + 20091, + -1 + ], + [ + 20092, + 1 + ], + [ + 20093, + 1 + ], + [ + 20094, + -1 + ], + [ + 20095, + -1 + ], + [ + 20096, + -1 + ], + [ + 20097, + -1 + ], + [ + 20098, + -1 + ], + [ + 20099, + -1 + ], + [ + 20100, + -1 + ], + [ + 20101, + -1 + ], + [ + 20102, + -1 + ], + [ + 20103, + -1 + ], + [ + 20104, + -1 + ], + [ + 20105, + -1 + ], + [ + 20106, + -1 + ], + [ + 20107, + -1 + ], + [ + 20108, + -1 + ], + [ + 20109, + -1 + ], + [ + 20110, + -1 + ], + [ + 20111, + -1 + ], + [ + 20112, + -1 + ], + [ + 20113, + -1 + ], + [ + 20114, + -1 + ], + [ + 20115, + -1 + ], + [ + 20120, + 0 + ], + [ + 20123, + 0 + ], + [ + 20160, + 1 + ], + [ + 20176, + 1 + ], + [ + 20409, + 1 + ], + [ + 20564, + 1 + ], + [ + 22949, + 0 + ], + [ + 23095, + 0 + ], + [ + 23134, + -1 + ], + [ + 23958, + -4 + ], + [ + 24097, + -4 + ], + [ + 24282, + 1 + ], + [ + 24334, + 1 + ], + [ + 24440, + 0 + ] + ] + }, + "before": { + "complex_primitives": 149002, + "prefix_l1": "2765345294379392599/1024", + "prefix_bits": 52, + "coefficient_grid_depth_upper": 22, + "paid_profile": { + "1": 2412, + "2": 418, + "3": 432, + "4": 142, + "5": 82, + "8": 8 + } + }, + "after": { + "complex_primitives": 148658, + "prefix_l1": "2765345294379392599/1024", + "prefix_bits": 52, + "coefficient_grid_depth_upper": 22, + "paid_profile": { + "1": 2412, + "2": 418, + "3": 432, + "4": 142, + "5": 82, + "8": 8 + } + }, + "candidate_sha256": "11e9d6bb65b43f0e22be2e6a5bff0552cad0f844084be49c6da623f7d844496e", + "events": 24785 + }, + "backward": { + "census": [ + { + "helper": 264, + "domain": [ + -2, + 2 + ], + "incident_adds": 71, + "delta_real": -110, + "scale_macros": 10, + "constant_delta_real": -7, + "constant_exponent": 2 + }, + { + "helper": 265, + "domain": [ + -3, + 13 + ], + "incident_adds": 98, + "delta_real": -155, + "scale_macros": 17, + "constant_delta_real": -50, + "constant_exponent": 1 + }, + { + "helper": 266, + "domain": [ + -3, + 3 + ], + "incident_adds": 110, + "delta_real": -160, + "scale_macros": 12, + "constant_delta_real": -4, + "constant_exponent": 1 + }, + { + "helper": 267, + "domain": [ + -3, + 2 + ], + "incident_adds": 105, + "delta_real": -167, + "scale_macros": 11, + "constant_delta_real": -36, + "constant_exponent": 1 + }, + { + "helper": 268, + "domain": [ + -3, + 2 + ], + "incident_adds": 81, + "delta_real": -119, + "scale_macros": 8, + "constant_delta_real": 0, + "constant_exponent": 0 + }, + { + "helper": 269, + "domain": [ + -2, + 2 + ], + "incident_adds": 74, + "delta_real": -111, + "scale_macros": 11, + "constant_delta_real": -6, + "constant_exponent": 2 + }, + { + "helper": 270, + "domain": [ + -2, + 2 + ], + "incident_adds": 103, + "delta_real": -162, + "scale_macros": 14, + "constant_delta_real": -41, + "constant_exponent": 1 + }, + { + "helper": 271, + "domain": [ + -3, + 2 + ], + "incident_adds": 93, + "delta_real": -161, + "scale_macros": 12, + "constant_delta_real": -38, + "constant_exponent": 1 + }, + { + "helper": 272, + "domain": [ + -3, + 2 + ], + "incident_adds": 101, + "delta_real": -100, + "scale_macros": 14, + "constant_delta_real": 0, + "constant_exponent": 0 + }, + { + "helper": 274, + "domain": [ + -2, + 10 + ], + "incident_adds": 93, + "delta_real": -123, + "scale_macros": 8, + "constant_delta_real": 0, + "constant_exponent": 0 + }, + { + "helper": 276, + "domain": [ + -2, + 11 + ], + "incident_adds": 121, + "delta_real": -172, + "scale_macros": 18, + "constant_delta_real": -37, + "constant_exponent": 1 + }, + { + "helper": 278, + "domain": [ + -2, + 5 + ], + "incident_adds": 97, + "delta_real": -127, + "scale_macros": 19, + "constant_delta_real": -2, + "constant_exponent": 1 + }, + { + "helper": 279, + "domain": [ + -2, + 10 + ], + "incident_adds": 90, + "delta_real": -108, + "scale_macros": 12, + "constant_delta_real": 0, + "constant_exponent": 0 + }, + { + "helper": 280, + "domain": [ + -3, + 11 + ], + "incident_adds": 106, + "delta_real": -137, + "scale_macros": 13, + "constant_delta_real": 0, + "constant_exponent": 0 + }, + { + "helper": 281, + "domain": [ + -1, + 3 + ], + "incident_adds": 73, + "delta_real": -59, + "scale_macros": 12, + "constant_delta_real": 0, + "constant_exponent": 0 + }, + { + "helper": 283, + "domain": [ + -2, + 11 + ], + "incident_adds": 125, + "delta_real": -163, + "scale_macros": 21, + "constant_delta_real": -15, + "constant_exponent": 1 + } + ], + "winner": { + "helper": 276, + "domain": [ + -2, + 11 + ], + "incident_adds": 121, + "delta_real": -172, + "scale_macros": 18, + "constant_delta_real": -37, + "constant_exponent": 1, + "schedule": [ + [ + 213, + 2 + ], + [ + 286, + 2 + ], + [ + 357, + 2 + ], + [ + 430, + 2 + ], + [ + 512, + 2 + ], + [ + 585, + 2 + ], + [ + 650, + 2 + ], + [ + 723, + 2 + ], + [ + 797, + 1 + ], + [ + 866, + 1 + ], + [ + 933, + 1 + ], + [ + 1201, + 1 + ], + [ + 1345, + 2 + ], + [ + 1504, + 2 + ], + [ + 1636, + 2 + ], + [ + 1700, + 2 + ], + [ + 1893, + 2 + ], + [ + 2148, + 2 + ], + [ + 2237, + 1 + ], + [ + 2310, + 1 + ], + [ + 3381, + 2 + ], + [ + 3440, + 2 + ], + [ + 3572, + 2 + ], + [ + 3631, + 2 + ], + [ + 3708, + 2 + ], + [ + 3774, + 2 + ], + [ + 3914, + 2 + ], + [ + 3997, + 2 + ], + [ + 4069, + 2 + ], + [ + 4188, + 2 + ], + [ + 4239, + 2 + ], + [ + 4296, + 2 + ], + [ + 5097, + 1 + ], + [ + 5383, + 1 + ], + [ + 5581, + 2 + ], + [ + 5716, + 2 + ], + [ + 5929, + 2 + ], + [ + 6008, + 2 + ], + [ + 6088, + 2 + ], + [ + 6166, + 2 + ], + [ + 6848, + 2 + ], + [ + 6927, + 2 + ], + [ + 6998, + 2 + ], + [ + 7077, + 2 + ], + [ + 7145, + 2 + ], + [ + 7211, + 2 + ], + [ + 7275, + 2 + ], + [ + 7353, + 2 + ], + [ + 8189, + 0 + ], + [ + 8197, + 0 + ], + [ + 8220, + 0 + ], + [ + 8267, + 0 + ], + [ + 8268, + 0 + ], + [ + 8269, + 0 + ], + [ + 8270, + 0 + ], + [ + 8271, + 0 + ], + [ + 8272, + 0 + ], + [ + 8273, + 0 + ], + [ + 8274, + 0 + ], + [ + 8275, + 0 + ], + [ + 8278, + 0 + ], + [ + 8279, + 0 + ], + [ + 8280, + 0 + ], + [ + 8296, + 0 + ], + [ + 8297, + 0 + ], + [ + 8298, + 0 + ], + [ + 8302, + 0 + ], + [ + 10057, + 0 + ], + [ + 10122, + 0 + ], + [ + 10123, + 0 + ], + [ + 10155, + 0 + ], + [ + 14021, + 0 + ], + [ + 14587, + 0 + ], + [ + 14905, + 0 + ], + [ + 15610, + 0 + ], + [ + 15611, + 1 + ], + [ + 15614, + 1 + ], + [ + 18743, + 1 + ], + [ + 18752, + 1 + ], + [ + 19242, + 1 + ], + [ + 19256, + 1 + ], + [ + 20090, + -1 + ], + [ + 20091, + -1 + ], + [ + 20092, + -1 + ], + [ + 20093, + -1 + ], + [ + 20094, + 1 + ], + [ + 20095, + 1 + ], + [ + 20096, + 1 + ], + [ + 20097, + 1 + ], + [ + 20098, + 1 + ], + [ + 20099, + 1 + ], + [ + 20100, + 1 + ], + [ + 20101, + 1 + ], + [ + 20102, + 1 + ], + [ + 20103, + 1 + ], + [ + 20104, + 1 + ], + [ + 20105, + 1 + ], + [ + 20106, + 1 + ], + [ + 20107, + 1 + ], + [ + 20108, + 1 + ], + [ + 20109, + 1 + ], + [ + 20110, + 1 + ], + [ + 20111, + 1 + ], + [ + 20112, + 1 + ], + [ + 20113, + 1 + ], + [ + 20114, + 1 + ], + [ + 20115, + 1 + ], + [ + 20120, + 0 + ], + [ + 20123, + 0 + ], + [ + 20160, + -1 + ], + [ + 20176, + -1 + ], + [ + 20409, + -1 + ], + [ + 20564, + -1 + ], + [ + 22949, + 0 + ], + [ + 23095, + 0 + ], + [ + 23134, + 1 + ], + [ + 23958, + 4 + ], + [ + 24097, + 4 + ], + [ + 24282, + -1 + ], + [ + 24334, + -1 + ], + [ + 24440, + 0 + ] + ] + }, + "before": { + "complex_primitives": 149018, + "prefix_l1": "14824960514781440791821/64", + "prefix_bits": 68, + "coefficient_grid_depth_upper": 26, + "paid_profile": { + "1": 2412, + "2": 418, + "3": 432, + "4": 142, + "5": 82, + "8": 8 + } + }, + "after": { + "complex_primitives": 148674, + "prefix_l1": "14824960514781440791821/64", + "prefix_bits": 68, + "coefficient_grid_depth_upper": 26, + "paid_profile": { + "1": 2412, + "2": 418, + "3": 432, + "4": 142, + "5": 82, + "8": 8 + } + }, + "candidate_sha256": "1f535fb0fd54a86c3a3e987340ac8e6698fe47baf475b6293c249ff7f14e45e2", + "events": 24785 + } + }, + "lowerer_checks": { + "add_coefficients": 326, + "scale_coefficients": 23 + }, + "status": "PASS_K8_VARYING_GAUGE_16_HELPERS_NO_NEW_KAPPA" +} diff --git a/research/k8-phase-local-gauges/verify.py b/research/k8-phase-local-gauges/verify.py new file mode 100644 index 0000000000..0fbd10e3be --- /dev/null +++ b/research/k8-phase-local-gauges/verify.py @@ -0,0 +1,246 @@ +"""Phase-local one-helper dyadic gauges; Philipp / OpenAI Codex, Apache-2.0.""" +import argparse +from collections import defaultdict +import copy +import hashlib +import importlib.util +import json +from pathlib import Path + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +BASE = 'dadfea6e8a78ff6ba901705f87532a71c6f5bbb8' + + +def need(condition, message): + if not condition: + raise ValueError(message) + + +def canonical(x): + return json.dumps(x, sort_keys=True, separators=(',', ':')).encode() + + +def sha(x): + return hashlib.sha256(x).hexdigest() + + +def engine(): + pins = json.loads((HERE / 'SOURCES.json').read_text()) + need(pins['base'] == BASE, 'base pin') + need(set(pins['vendor']) == {'engine.py', 'SOURCES.json', 'BASE-SELECTED.json', + 'PROVENANCE.md', 'PROOF.md'}, 'vendor inventory') + frame_checker = pins['frame_checker'] + need(frame_checker['path'] == 'research/complex-sw4-frame8/local/hpe_audit_local.py', 'frame checker path') + need(sha((ROOT / frame_checker['path']).read_bytes()) == frame_checker['sha256'], 'frame checker pin') + for name, digest in pins['vendor'].items(): + need(sha((HERE / 'vendor/pr1161' / name).read_bytes()) == digest, 'vendor pin ' + name) + need(sha((HERE / 'vendor/pr1214/CERTIFICATE.json').read_bytes()) == + pins['pr1214_certificate_sha256'], 'PR1214 certificate pin') + need(sha((HERE / 'vendor/pr1259/CERTIFICATE.json').read_bytes()) == + pins['pr1259_certificate_sha256'], 'PR1259 certificate pin') + spec = importlib.util.spec_from_file_location('pr1161', HERE / 'vendor/pr1161/engine.py') + lib = importlib.util.module_from_spec(spec) + spec.loader.exec_module(lib) + lib.ROOT = ROOT + return lib + + +def terms(lib, events, helpers): + """Partition by *all* non-scalar events, including wraps and phase markers.""" + result = {h: defaultdict(list) for h in helpers} + run = 0 + for index, event in enumerate(events): + if event[0] != 'scalar': + run += 1 + continue + gate = event[1] + if gate[0] != 'add': + continue + p, e = lib.parts(lib.Q(gate[3], gate[4])) + for role, sign in ((gate[1], 1), (gate[2], -1)): + if role[0] == 'L' and role[1] in result: + result[role[1]][run].append([index, -sign * e, p == 1]) + return result + + +def solve_run(rows, extra=0): + """Integer shortest path; exact all-Z coverage follows the clipping lemma.""" + lo = min([0] + [r[1] for r in rows]) - extra + hi = max([0] + [r[1] for r in rows]) + extra + states = list(range(lo, hi + 1)) + dp = {0: 0} + links = [] + baseline = 0 + for _, b, unit in rows: + baseline += abs(b) - int(unit and b == 0) + new, prev = {}, {} + for k in states: + value, _, j = min((v + abs(k - j), abs(j), j) for j, v in dp.items()) + new[k] = value + abs(k - b) - int(unit and k == b) + prev[k] = j + links.append(prev) + dp = new + best, _, k = min((v + abs(k), abs(k), k) for k, v in dp.items()) + path = [] + for back in reversed(links): + path.append(k) + k = back[k] + path.reverse() + return {'delta': best - baseline, 'bounds': [lo, hi], 'states': len(states), + 'path': path, 'vertices': len(rows) * len(states)} + + +def census(lib, events, helpers): + all_terms = terms(lib, events, helpers) + rows, schedules = [], {} + for helper in helpers: + delta, vertices, runs, plan = 0, 0, 0, [] + for run, stream in sorted(all_terms[helper].items()): + answer = solve_run(stream) + need(answer['delta'] <= 0, 'zero path available') + delta += answer['delta'] + vertices += answer['vertices'] + runs += 1 + if any(answer['path']): + plan.append({'run': run, 'terms': stream, **answer}) + rows.append([helper, delta, runs, vertices]) + schedules[helper] = plan + winner = min(rows, key=lambda row: (row[1], row[0])) + return {'helpers': len(helpers), 'rows': rows, 'helper': winner[0], 'delta': winner[1], + 'total_vertices': sum(row[3] for row in rows), 'schedule': schedules[winner[0]]} + + +def construct(lib, events, helper, schedule): + before, after = {}, {} + for run in schedule: + previous = 0 + for term, exponent in zip(run['terms'], run['path']): + index = term[0] + if exponent != previous: + before[index] = exponent - previous + previous = exponent + if previous: + after[run['terms'][-1][0]] = -previous + answer, k = [], 0 + + def scale(exponent, frame): + q = lib.power(exponent) + return ['scalar', ['scale', ['L', helper], q.numerator, q.denominator], frame] + + for index, original in enumerate(events): + event = copy.deepcopy(original) + if event[0] != 'scalar': + need(k == 0, 'gauge reset at every non-scalar boundary') + if index in before: + answer.append(scale(before[index], event[2])) + k += before[index] + if event[0] == 'scalar' and event[1][0] == 'add': + g = event[1] + shift = k * (int(g[1] == ['L', helper]) - int(g[2] == ['L', helper])) + q = lib.Q(g[3], g[4]) * lib.power(shift) + g[3:5] = [q.numerator, q.denominator] + answer.append(event) + if index in after: + answer.append(scale(after[index], event[2])) + k += after[index] + need(k == 0, 'final gauge reset') + return answer + + +def compute(): + lib = engine() + word, programs, _, _ = lib.load() + helpers, excluded = lib.domain(word, programs) + receipt = {'base': BASE, 'seed': 26, 'status': 'PASS_K8_PHASE_LOCAL_GAUGES', + 'scope': 'one helper, all integer exponents, reset at every non-scalar event', + 'excluded_helpers': excluded, 'orientations': {}, 'on_pr1214': {}, 'wrapped_example': {}} + witnesses = {} + for orientation, events in programs.items(): + result = census(lib, events, helpers) + candidate = construct(lib, events, result['helper'], result['schedule']) + need([x for x in candidate if x[0] != 'scalar'] == + [x for x in events if x[0] != 'scalar'], 'non-scalar stream unchanged') + result['baseline_endpoint'] = lib.replay(events, orientation) + result['candidate_endpoint'] = lib.replay(candidate, orientation) + before, after = lib.invoice(events, 'copy-init'), lib.invoice(candidate, 'copy-init') + need(before['paid_profile'] == after['paid_profile'], 'recursive profile unchanged') + need(after['real_primitives'] - before['real_primitives'] == result['delta'], 'full price agrees with DP') + result['before'], result['after'] = before, after + result['candidate_sha256'] = sha(canonical(candidate)) + result['inserted_scales'] = len(candidate) - len(events) + receipt['orientations'][orientation] = result + witnesses[orientation] = candidate + wrapped = {event[2] for event in events if event[0] == 'residual_adapter'} + wrapped_rows = [row for row in result['rows'] if row[0] in wrapped] + need(len(wrapped_rows) == 240, 'wrapped helper domain') + best_wrapped = min(wrapped_rows, key=lambda row: (row[1], row[0])) + h = best_wrapped[0] + stream = terms(lib, events, [h])[h] + plan = [] + for run, rs in sorted(stream.items()): + answer = solve_run(rs) + if any(answer['path']): + plan.append({'run': run, 'terms': rs, **answer}) + wrapped_word = construct(lib, events, h, plan) + wrapped_price = lib.invoice(wrapped_word, 'copy-init') + need(wrapped_price['real_primitives'] - before['real_primitives'] == best_wrapped[1], + 'wrapped candidate full invoice') + need(wrapped_price['paid_profile'] == before['paid_profile'], 'wrapped profile') + receipt['wrapped_example'][orientation] = { + 'helper': h, 'delta': best_wrapped[1], 'rows': [best_wrapped], 'schedule': plan, + 'wrapped_helpers_checked': 240, 'before': before, 'after': wrapped_price, + 'candidate_endpoint': lib.replay(wrapped_word, orientation), + 'candidate_sha256': sha(canonical(wrapped_word)), + 'inserted_scales': len(wrapped_word) - len(events)} + witnesses['wrapped_' + orientation] = wrapped_word + # Retain the predecessor's fixed two-helper witness, independently + # reconstruct and price it; do not inherit its optimum as a new claim. + pair_info = json.loads((HERE / 'vendor/pr1214/CERTIFICATE.json').read_text()) + pair_winner = pair_info['orientations'][orientation]['winner'] + pair = events + for h, exponent in zip(pair_winner['helpers'], pair_winner['exponents']): + pair = lib.transform(pair, word, h, exponent) + pair_price = lib.invoice(pair, 'copy-init') + need(canonical(pair_price) == canonical(pair_info['orientations'][orientation]['prices']['copy-init']['after']), + 'PR1214 independently reconstructed invoice') + composed = census(lib, pair, helpers) + final = construct(lib, pair, composed['helper'], composed['schedule']) + composed['baseline_endpoint'] = lib.replay(pair, orientation) + composed['candidate_endpoint'] = lib.replay(final, orientation) + final_price = lib.invoice(final, 'copy-init') + need(final_price['paid_profile'] == before['paid_profile'], 'composed profile unchanged') + need(final_price['real_primitives'] - pair_price['real_primitives'] == composed['delta'], + 'composed full price agrees with DP') + composed['before'], composed['after'] = pair_price, final_price + composed['original_before'] = before + composed['candidate_sha256'] = sha(canonical(final)) + composed['inserted_scales'] = len(final) - len(pair) + receipt['on_pr1214'][orientation] = composed + witnesses['pr1214_' + orientation] = final + return receipt, witnesses + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--write', action='store_true') + args = parser.parse_args() + receipt, _ = compute() + path = HERE / 'CERTIFICATE.json' + if args.write: + path.write_bytes(canonical(receipt) + b'\n') + else: + need(canonical(receipt) == canonical(json.loads(path.read_text())), 'certificate mismatch') + print(receipt['status']) + for orientation, result in receipt['orientations'].items(): + print(orientation, 'helper', result['helper'], 'real saving', -result['delta'], + 'scales', result['inserted_scales'], 'helpers checked', result['helpers']) + for orientation, result in receipt['on_pr1214'].items(): + print('on_pr1214', orientation, 'helper', result['helper'], 'extra per-component saving', + -result['delta'], 'complete complex invoice', result['after']['complex_primitives']) + for orientation, result in receipt['wrapped_example'].items(): + print('wrapped', orientation, 'helper', result['helper'], 'per-component saving', -result['delta']) + + +if __name__ == '__main__': + main() diff --git a/research/k8-phase-local-gauges/wrapped_FRAME-RECEIPT.json b/research/k8-phase-local-gauges/wrapped_FRAME-RECEIPT.json new file mode 100644 index 0000000000..235d19a1f0 --- /dev/null +++ b/research/k8-phase-local-gauges/wrapped_FRAME-RECEIPT.json @@ -0,0 +1,71 @@ +{ + "status": "PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY", + "canonical_word_sha256": "16bc0ebb04b4be6c0ade74badc6a0c0cdba4215eda86e4ff9f13abf8ecebd219", + "local_programs_sha256": "c02ba361b82dd9356959a54fbe8173390df67486ba2e9f99276a8ec41e0f3d5c", + "v": 112, + "helpers": 480, + "local": { + "forward": { + "all_exact_columns": 704, + "prefix_l1_upper": "2765345294379392599/1024", + "prefix_bits_upper": 52, + "charged_payload_bits": 192, + "private_work_erased": true + }, + "backward": { + "all_exact_columns": 704, + "prefix_l1_upper": "14824960514781440791821/64", + "prefix_bits_upper": 68, + "charged_payload_bits": 192, + "private_work_erased": true + } + }, + "paid_profiles": { + "forward": { + "1": 2412, + "4": 142, + "8": 8, + "3": 432, + "2": 418, + "5": 82 + }, + "backward": { + "1": 2412, + "4": 142, + "8": 8, + "3": 432, + "2": 418, + "5": 82 + } + }, + "entering_helpers": 192, + "cold_hyperplane_ended_helpers": 48, + "negative_controls_rejected": [ + "wrong_scale", + "missing_center", + "wrong_common_frame", + "wrong_child_rank", + "missing_pre_wrapper", + "missing_post_wrapper", + "wrapper_with_wrong_frame", + "wrapper_in_wrong_phase", + "wrapper_on_a_data_register", + "wrapper_on_a_target_register", + "wrapper_on_a_centre_register", + "hpe_pre_wrapper_resolved_to_full_recipe", + "hpe_post_wrapper_without_terminal_frame", + "hpe_post_wrapper_wrong_terminal_frame", + "hpe_tail_gate_at_full_frame", + "hpe_tail_climb_dropped", + "hpe_helper_exit_adapter_to_full", + "hpe_tail_gate_moved_into_full_cleanup", + "cold_hpe_pre_wrapper_replaced_by_identity_entry_adapter", + "cold_hpe_pre_wrapper_dropped", + "cold_hpe_post_wrapper_replaced_by_exit_adapter", + "cold_hpe_pre_wrapper_resolved_to_cold_full_convention", + "cold_hpe_wrapper_with_nonzero_entrance", + "cold_hpe_post_wrapper_wrong_terminal_frame", + "cold_hpe_premix_gate_before_pre_wrapper" + ], + "scope": "Literal forward and inverse-transpose replay on every arbitrary data/helper column, physical frame incidence, ordered paid wrappers, cleared private work and prefix coefficients. Global hosting and outer exponent are separate." +}