{"action":"created","issue":{"url":"https://api.github.com/repos/km-git-acc/dbn_upper_bound/issues/113","repository_url":"https://api.github.com/repos/km-git-acc/dbn_upper_bound","labels_url":"https://api.github.com/repos/km-git-acc/dbn_upper_bound/issues/113/labels{/name}","comments_url":"https://api.github.com/repos/km-git-acc/dbn_upper_bound/issues/113/comments","events_url":"https://api.github.com/repos/km-git-acc/dbn_upper_bound/issues/113/events","html_url":"https://github.com/km-git-acc/dbn_upper_bound/issues/113","id":364966551,"node_id":"MDU6SXNzdWUzNjQ5NjY1NTE=","number":113,"title":"Next steps after conditional DBN <= 0.11","user":{"login":"km-git-acc","id":35831522,"node_id":"MDQ6VXNlcjM1ODMxNTIy","avatar_url":"https://avatars1.githubusercontent.com/u/35831522?v=4","gravatar_id":"","url":"https://api.github.com/users/km-git-acc","html_url":"https://github.com/km-git-acc","followers_url":"https://api.github.com/users/km-git-acc/followers","following_url":"https://api.github.com/users/km-git-acc/following{/other_user}","gists_url":"https://api.github.com/users/km-git-acc/gists{/gist_id}","starred_url":"https://api.github.com/users/km-git-acc/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/km-git-acc/subscriptions","organizations_url":"https://api.github.com/users/km-git-acc/orgs","repos_url":"https://api.github.com/users/km-git-acc/repos","events_url":"https://api.github.com/users/km-git-acc/events{/privacy}","received_events_url":"https://api.github.com/users/km-git-acc/received_events","type":"User","site_admin":false},"labels":[],"state":"open","locked":false,"assignee":{"login":"mariotrevi","id":1034367,"node_id":"MDQ6VXNlcjEwMzQzNjc=","avatar_url":"https://avatars0.githubusercontent.com/u/1034367?v=4","gravatar_id":"","url":"https://api.github.com/users/mariotrevi","html_url":"https://github.com/mariotrevi","followers_url":"https://api.github.com/users/mariotrevi/followers","following_url":"https://api.github.com/users/mariotrevi/following{/other_user}","gists_url":"https://api.github.com/users/mariotrevi/gists{/gist_id}","starred_url":"https://api.github.com/users/mariotrevi/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/mariotrevi/subscriptions","organizations_url":"https://api.github.com/users/mariotrevi/orgs","repos_url":"https://api.github.com/users/mariotrevi/repos","events_url":"https://api.github.com/users/mariotrevi/events{/privacy}","received_events_url":"https://api.github.com/users/mariotrevi/received_events","type":"User","site_admin":false},"assignees":[{"login":"mariotrevi","id":1034367,"node_id":"MDQ6VXNlcjEwMzQzNjc=","avatar_url":"https://avatars0.githubusercontent.com/u/1034367?v=4","gravatar_id":"","url":"https://api.github.com/users/mariotrevi","html_url":"https://github.com/mariotrevi","followers_url":"https://api.github.com/users/mariotrevi/followers","following_url":"https://api.github.com/users/mariotrevi/following{/other_user}","gists_url":"https://api.github.com/users/mariotrevi/gists{/gist_id}","starred_url":"https://api.github.com/users/mariotrevi/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/mariotrevi/subscriptions","organizations_url":"https://api.github.com/users/mariotrevi/orgs","repos_url":"https://api.github.com/users/mariotrevi/repos","events_url":"https://api.github.com/users/mariotrevi/events{/privacy}","received_events_url":"https://api.github.com/users/mariotrevi/received_events","type":"User","site_admin":false},{"login":"km-git-acc","id":35831522,"node_id":"MDQ6VXNlcjM1ODMxNTIy","avatar_url":"https://avatars1.githubusercontent.com/u/35831522?v=4","gravatar_id":"","url":"https://api.github.com/users/km-git-acc","html_url":"https://github.com/km-git-acc","followers_url":"https://api.github.com/users/km-git-acc/followers","following_url":"https://api.github.com/users/km-git-acc/following{/other_user}","gists_url":"https://api.github.com/users/km-git-acc/gists{/gist_id}","starred_url":"https://api.github.com/users/km-git-acc/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/km-git-acc/subscriptions","organizations_url":"https://api.github.com/users/km-git-acc/orgs","repos_url":"https://api.github.com/users/km-git-acc/repos","events_url":"https://api.github.com/users/km-git-acc/events{/privacy}","received_events_url":"https://api.github.com/users/km-git-acc/received_events","type":"User","site_admin":false},{"login":"rudolph-git-acc","id":36714969,"node_id":"MDQ6VXNlcjM2NzE0OTY5","avatar_url":"https://avatars0.githubusercontent.com/u/36714969?v=4","gravatar_id":"","url":"https://api.github.com/users/rudolph-git-acc","html_url":"https://github.com/rudolph-git-acc","followers_url":"https://api.github.com/users/rudolph-git-acc/followers","following_url":"https://api.github.com/users/rudolph-git-acc/following{/other_user}","gists_url":"https://api.github.com/users/rudolph-git-acc/gists{/gist_id}","starred_url":"https://api.github.com/users/rudolph-git-acc/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/rudolph-git-acc/subscriptions","organizations_url":"https://api.github.com/users/rudolph-git-acc/orgs","repos_url":"https://api.github.com/users/rudolph-git-acc/repos","events_url":"https://api.github.com/users/rudolph-git-acc/events{/privacy}","received_events_url":"https://api.github.com/users/rudolph-git-acc/received_events","type":"User","site_admin":false}],"milestone":null,"comments":102,"created_at":"2018-09-28T16:53:23Z","updated_at":"2018-11-02T12:12:04Z","closed_at":null,"author_association":"OWNER","body":"@rudolph-git-acc \r\nOpening the new thread..\r\nAgree dbn &lt; 0.1 is a good place to stop. I think the tloop part could potentially also be passed through Boinc. Will try out on a smaller X to see how it goes (essentially apart from t1,t2,y parameters (appropriately chosen for each job) we would also pass an additional parameter to the boinc job - the web address of the relevant storedsums file).\r\n\r\nI will check if there are readymade scripts for RH verification to help in detailed understanding of the process involved. The one at https://www.wstein.org/simuw/misc/zeta_grid.html seems to be a dead link. Is Gourdon-Demichel's code available?"},"comment":{"url":"https://api.github.com/repos/km-git-acc/dbn_upper_bound/issues/comments/435359016","html_url":"https://github.com/km-git-acc/dbn_upper_bound/issues/113#issuecomment-435359016","issue_url":"https://api.github.com/repos/km-git-acc/dbn_upper_bound/issues/113","id":435359016,"node_id":"MDEyOklzc3VlQ29tbWVudDQzNTM1OTAxNg==","user":{"login":"rudolph-git-acc","id":36714969,"node_id":"MDQ6VXNlcjM2NzE0OTY5","avatar_url":"https://avatars0.githubusercontent.com/u/36714969?v=4","gravatar_id":"","url":"https://api.github.com/users/rudolph-git-acc","html_url":"https://github.com/rudolph-git-acc","followers_url":"https://api.github.com/users/rudolph-git-acc/followers","following_url":"https://api.github.com/users/rudolph-git-acc/following{/other_user}","gists_url":"https://api.github.com/users/rudolph-git-acc/gists{/gist_id}","starred_url":"https://api.github.com/users/rudolph-git-acc/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/rudolph-git-acc/subscriptions","organizations_url":"https://api.github.com/users/rudolph-git-acc/orgs","repos_url":"https://api.github.com/users/rudolph-git-acc/repos","events_url":"https://api.github.com/users/rudolph-git-acc/events{/privacy}","received_events_url":"https://api.github.com/users/rudolph-git-acc/received_events","type":"User","site_admin":false},"created_at":"2018-11-02T12:12:04Z","updated_at":"2018-11-02T12:12:04Z","author_association":"COLLABORATOR","body":"Let me specify more precisely:\r\n\r\nThe main part of the script from Pugh's thesis works as follows:\r\n- Run through all gram points until you find a bad one.\r\n- If you found a bad one, keep checking for incremental bad ones until you hit a good one.\r\n- Now the gram block is complete and one should count all the zeros of Z(t) within each block.\r\n\r\nGram points can be found very fast, however evaluating Z(t) is the time critical component. So repairing each Gram block by counting the zeros of Z(t) takes time. Since a bad Gram point doesn't seem to propagate (i.e. solves itself over increasing T and therefore always retains a one to one connection to a non-trivial zero that occurs later), why couldn't we just skip all Gramblock fixing processes and just count the  Gram points (good and bad). This would be much faster and only requires the checking process S(g_m(t)) < 2 at the end. Here is the code I used to check whether it works. It appears to give the correct answer for all good Gram end points, but fails for the Bad ones, hence if you always end at a good Gram point this method could work. Try for instance main(100000) and main(100001) that are both bad Gram points (2 in a row actually) and then main(100002).\r\n\r\n```ruby\r\nN0(t)=return(imag(lngamma(1/4+I*t/2))/Pi-t/(2*Pi)*log(Pi)+imag(log(zeta(1/2+I*t)))/Pi+1);\r\n\r\n\\\\Riemann-Siegel Z-function\r\nZ(t) = return(exp(I*(imag(lngamma(I*t/2+1/4))-t/2*log(Pi)))*zeta(1/2+I*t));\r\n\r\n\\\\Function to establish a good approximation for the n-th Gram-point\r\ngram(n) = {\r\n    tn=0; tn1=0.5*n+20;\r\n    while(abs(tn-tn1) > 0.00000001, tn=tn1; tn1 = tn-(tn*log(tn/Pi/2)/2-tn/2-Pi/8+1/tn/48+7/5760/(tn^3)- n*Pi)/(log(tn/Pi/2)/2-1/(tn^2)/48-7/1920/(tn^4)));\r\nreturn(tn1);\r\n}\r\n\r\n\\\\main program\r\nmain(end) = {\r\n    gi=-1; gf=end; tot_roots = 0;\r\n    if (even(end)*real(Z(gram(end))) < 0, print(\"you chose a bad bad Gram point, so the outcomes will differ!\"));\r\n    while(gi < gf,\r\n        gi=gi+1;\r\n        tot_roots=tot_roots+1;\r\n    );\r\n    \r\n    printf(\"Gram point %3.0f counts on the line  N0(%3.3f)   = %3.0f zeros.\\n\", gi, gram(gi), N0(gram(gi)));    \r\n    printf(\"Gram point %3.0f counts in the strip main(%3.3f) = %3.0f zeros.\\n\", gi, gram(gi), tot_roots);    \r\n    \r\nreturn(tot_roots);\r\n}\r\n\r\nmain(100001);\r\n```\r\n\r\nEven though it seems it work numerically, I doubt that it is provable since the next step would then be to completely skip the Gram point counting and just take tot_roots = gi + 1 (and do the final step in Turing's method) and this would obviously be too good to be true. It is therefore more likely that the counting of zeros of Z(t) within each Gramblock is a mandatory part of the proving-process."}}
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