Doubly-Periodic Synthesis

O. Ziep Doubly-Periodic Synthesis Otto Ziep Independent Research, 13089 Berlin, Germany Email: [email protected] Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Ut purus elit, vestibulum ut, placerat ac, adipiscing vitae, felis. Curabitur dictum gravida mauris. Nam arcu libero, nonummy eget, consectetuer id, vulputate a, magna. Donec vehicula augue eu neque. Pellentesque habitant morbi tristique senectus et netus et malesuada fames ac turpis egestas. Mauris ut leo. Cras viverra metus rhoncus sem. Nulla et lectus vestibulum urna fringilla ultrices. Phasellus eu tellus sit amet tortor gravida placerat. Integer sapien est, iaculis in, pretium quis, viverra ac, nunc. Praesent eget sem vel leo ultrices bibendum. Aenean faucibus. Morbi dolor nulla, malesuada eu, pulvinar at, mollis ac, nulla. Curabitur auctor semper nulla. Donec varius orci eget risus. Duis nibh mi, congue eu, accumsan eleifend, sagittis quis, diam. Duis eget orci sit amet orci dignissim rutrum. Nam dui ligula, fringilla a, euismod sodales, sollicitudin vel, wisi. Morbi auctor lorem non justo. Nam lacus libero, pretium at, lobortis vitae, ultricies et, tellus. Donec aliquet, tortor sed accumsan bibendum, erat ligula aliquet magna, vitae ornare odio metus a mi. Morbi ac orci et nisl hendrerit mollis. Suspendisse ut massa. Cras nec ante. Pellentesque a nulla. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Aliquam tincidunt urna. Nulla ullamcorper vestibulum turpis. Pellentesque cursus luctus mauris. Nulla malesuada porttitor diam. Donec felis erat, congue non, volutpat at, tincidunt tristique, libero. Vivamus viverra fermentum felis. Donec nonummy pellentesque ante. Phasellus adipiscing semper elit. Proin fermentum massa ac quam. Sed diam turpis, molestie vitae, placerat a, molestie nec, leo. Maecenas lacinia. Nam ipsum ligula, eleifend at, accumsan nec, suscipit a, ipsum. Morbi blandit ligula feugiat magna. Nunc eleifend consequat lorem. Sed lacinia nulla vitae enim. Pellentesque tincidunt purus vel magna. Integer non enim. Praesent euismod nunc eu purus. Donec bibendum quam in tellus. Nullam cursus pulvinar lectus. Donec et mi. Nam vulputate metus eu enim. Vestibulum pellentesque felis eu massa. Quisque ullamcorper placerat ipsum. Cras nibh. Morbi vel justo vitae lacus tincidunt ultrices. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. In hac habitasse platea dictumst. Integer tempus convallis augue. Etiam facilisis. Nunc elementum fermentum wisi. Aenean placerat. Ut imperdiet, enim sed gravida sollicitudin, felis odio placerat quam, ac pulvinar elit purus eget enim. Nunc vitae tortor. Proin tempus nibh sit amet nisl. Vivamus quis tortor vitae risus porta vehicula. Fusce mauris. Vestibulum luctus nibh at lectus. Sed bibendum, nulla a faucibus semper, leo velit ultricies tellus, ac venenatis arcu wisi vel nisl. Vestibulum diam. Aliquam pellentesque, augue quis sagittis posuere, turpis lacus congue quam, in hendrerit risus eros eget felis. Maecenas eget erat in sapien mattis porttitor. Vestibulum porttitor. Nulla facilisi. Sed a turpis eu lacus commodo facilisis. Morbi fringilla, wisi in dignissim interdum, justo lectus sagittis dui, et vehicula libero dui cursus dui. Mauris tempor ligula sed lacus. Duis cursus enim ut augue. Cras ac magna. Cras nulla. Nulla egestas. Curabitur a leo. Quisque egestas wisi eget nunc. Nam feugiat lacus vel est. Curabitur consectetuer. Suspendisse vel felis. Ut lorem lorem, interdum eu, tincidunt sit amet, laoreet vitae, arcu. Aenean faucibus pede eu ante. Praesent enim elit, rutrum at, molestie non, nonummy vel, nisl. Ut lectus eros, malesuada sit amet, fermentum eu, sodales cursus, magna. Donec eu purus. Quisque vehicula, urna sed ultricies auctor, pede lorem egestas dui, et convallis elit erat sed nulla. Donec luctus. Curabitur et nunc. Aliquam dolor odio, commodo pretium, ultricies non, pharetra in, velit. Integer arcu est, nonummy in, fermentum faucibus, egestas vel, odio. Sed commodo posuere pede. Mauris ut est. Ut quis purus. Sed ac odio. Sed vehicula hendrerit sem. Duis non odio. Morbi ut dui. Sed accumsan risus eget odio. In hac habitasse platea dictumst. Pellentesque non elit. Fusce sed justo eu urna porta tincidunt. Mauris felis odio, sollicitudin sed, volutpat a, ornare ac, erat. Morbi quis dolor. Donec pellentesque, erat ac sagittis semper, nunc dui lobortis purus, quis congue purus metus ultricies tellus. Proin et quam. Class aptent taciti sociosqu ad litora torquent per conubia nostra, per inceptos hymenaeos. Praesent sapien turpis, fermentum vel, eleifend faucibus, vehicula eu, lacus. Pellentesque habitant morbi tristique senectus et netus et malesuada fames ac turpis egestas. Donec odio elit, dictum in, hendrerit sit amet, egestas sed, leo. Praesent feugiat sapien aliquet odio. Integer vitae justo. Aliquam vestibulum fringilla lorem. Sed neque lectus, consectetuer at, consectetuer sed, eleifend ac, lectus. Nulla facilisi. Pellentesque eget lectus. Proin eu metus. Sed porttitor. In hac habitasse platea dictumst. Suspendisse eu lectus. Ut mi mi, lacinia sit amet, placerat et, mollis vitae, dui. Sed ante tellus, tristique ut, iaculis eu, malesuada ac, dui. Mauris nibh leo, facilisis non, adipiscing quis, ultrices a, dui. Morbi luctus, wisi viverra faucibus pretium, nibh est placerat odio, nec commodo wisi enim eget quam. Quisque libero justo, consectetuer a, feugiat vitae, porttitor eu, libero. Suspendisse sed mauris vitae elit sollicitudin malesuada. Maecenas ultricies eros sit amet ante. Ut venenatis velit. Maecenas sed mi eget dui varius euismod. Phasellus aliquet volutpat odio. Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia Curae; Pellentesque sit amet pede ac sem eleifend consectetuer. Nullam elementum, urna vel imperdiet sodales, elit ipsum pharetra ligula, ac pretium ante justo a nulla. Curabitur tristique arcu eu metus. Vestibulum lectus. Proin mauris. Proin eu nunc eu urna hendrerit faucibus. Aliquam auctor, pede consequat laoreet varius, eros tellus scelerisque quam, pellentesque hendrerit ipsum dolor sed augue. Nulla nec lacus. Suspendisse vitae elit. Aliquam arcu neque, ornare in, ullamcorper quis, commodo eu, libero. Fusce sagittis erat at erat tristique mollis. Maecenas sapien libero, molestie et, lobortis in, sodales eget, dui. Morbi ultrices rutrum lorem. Nam elementum ullamcorper leo. Morbi dui. Aliquam sagittis. Nunc placerat. Pellentesque tristique sodales est. Maecenas imperdiet lacinia velit. Cras non urna. Morbi eros pede, suscipit ac, varius vel, egestas non, eros. Praesent malesuada, diam id pretium elementum, eros sem dictum tortor, vel consectetuer odio sem sed wisi. Sed feugiat. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Ut pellentesque augue sed urna. Vestibulum diam eros, fringilla et, consectetuer eu, nonummy id, sapien. Nullam at lectus. In sagittis ultrices mauris. Curabitur malesuada erat sit amet massa. Fusce blandit. Aliquam erat volutpat. Aliquam euismod. Aenean vel lectus. Nunc imperdiet justo nec dolor. Etiam euismod. Fusce facilisis lacinia dui. Suspendisse potenti. In mi erat, cursus id, nonummy sed, ullamcorper eget, sapien. Praesent pretium, magna in eleifend egestas, pede pede pretium lorem, quis consectetuer tortor sapien facilisis magna. Mauris quis magna varius nulla scelerisque imperdiet. Aliquam non quam. Aliquam porttitor quam a lacus. Praesent vel arcu ut tortor cursus volutpat. In vitae pede quis diam bibendum placerat. Fusce elementum convallis neque. Sed dolor orci, scelerisque ac, dapibus nec, ultricies ut, mi. Duis nec dui quis leo sagittis commodo. Aliquam lectus. Vivamus leo. Quisque ornare tellus ullamcorper nulla. Mauris porttitor pharetra tortor. Sed fringilla justo sed mauris. Mauris tellus. Sed non leo. Nullam elementum, magna in cursus sodales, augue est scelerisque sapien, venenatis congue nulla arcu et pede. Ut suscipit enim vel sapien. Donec congue. Maecenas urna mi, suscipit in, placerat ut, vestibulum ut, massa. Fusce ultrices nulla et nisl. Etiam ac leo a risus tristique nonummy. Donec dignissim tincidunt nulla. Vestibulum rhoncus molestie odio. Sed lobortis, justo et pretium lobortis, mauris turpis condimentum augue, nec ultricies nibh arcu pretium enim. Nunc purus neque, placerat id, imperdiet sed, pellentesque nec, nisl. Vestibulum imperdiet neque non sem accumsan laoreet. In hac habitasse platea dictumst. Etiam condimentum facilisis libero. Suspendisse in elit quis nisl aliquam dapibus. Pellentesque auctor sapien. Sed egestas sapien nec lectus. Pellentesque vel dui vel neque bibendum viverra. Aliquam porttitor nisl nec pede. Proin mattis libero vel turpis. Donec rutrum mauris et libero. Proin euismod porta felis. Nam lobortis, metus quis elementum commodo, nunc lectus elementum mauris, eget vulputate ligula tellus eu neque. Vivamus eu dolor. Nulla in ipsum. Praesent eros nulla, congue vitae, euismod ut, commodo a, wisi. Pellentesque habitant morbi tristique senectus et netus et malesuada fames ac turpis egestas. Aenean nonummy magna non leo. Sed felis erat, ullamcorper in, dictum non, ultricies ut, lectus. Proin vel arcu a odio lobortis euismod. Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia Curae; Proin ut est. Aliquam odio. Pellentesque massa turpis, cursus eu, euismod nec, tempor congue, nulla. Duis viverra gravida mauris. Cras tincidunt. Curabitur eros ligula, varius ut, pulvinar in, cursus faucibus, augue. Nulla mattis luctus nulla. Duis commodo velit at leo. Aliquam vulputate magna et leo. Nam vestibulum ullamcorper leo. Vestibulum condimentum rutrum mauris. Donec id mauris. Morbi molestie justo et pede. Vivamus eget turpis sed nisl cursus tempor. Curabitur mollis sapien condimentum nunc. In wisi nisl, malesuada at, dignissim sit amet, lobortis in, odio. Aenean consequat arcu a ante. Pellentesque porta elit sit amet orci. Etiam at turpis nec elit ultricies imperdiet. Nulla facilisi. In hac habitasse platea dictumst. Suspendisse viverra aliquam risus. Nullam pede justo, molestie nonummy, scelerisque eu, facilisis vel, arcu. Curabitur tellus magna, porttitor a, commodo a, commodo in, tortor. Donec interdum. Praesent scelerisque. Maecenas posuere sodales odio. Vivamus metus lacus, varius quis, imperdiet quis, rhoncus a, turpis. Etiam ligula arcu, elementum a, venenatis quis, sollicitudin sed, metus. Donec nunc pede, tincidunt in, venenatis vitae, faucibus vel, nibh. Pellentesque wisi. Nullam malesuada. Morbi ut tellus ut pede tincidunt porta. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam congue neque id dolor. Donec et nisl at wisi luctus bibendum. Nam interdum tellus ac libero. Sed sem justo, laoreet vitae, fringilla at, adipiscing ut, nibh. Maecenas non sem quis tortor eleifend fermentum. Etiam id tortor ac mauris porta vulputate. Integer porta neque vitae massa. Maecenas tempus libero a libero posuere dictum. Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia Curae; Aenean quis mauris sed elit commodo placerat. Class aptent taciti sociosqu ad litora torquent per conubia nostra, per inceptos hymenaeos. Vivamus rhoncus tincidunt libero. Etiam elementum pretium justo. Vivamus est. Morbi a tellus eget pede tristique commodo. Nulla nisl. Vestibulum sed nisl eu sapien cursus rutrum. Nulla non mauris vitae wisi posuere convallis. Sed eu nulla nec eros scelerisque pharetra. Nullam varius. Etiam dignissim elementum metus. Vestibulum faucibus, metus sit amet mattis rhoncus, sapien dui laoreet odio, nec ultricies nibh augue a enim. Fusce in ligula. Quisque at magna et nulla commodo consequat. Proin accumsan imperdiet sem. Nunc porta. Donec feugiat mi at justo. Phasellus facilisis ipsum quis ante. In ac elit eget ipsum pharetra faucibus. Maecenas viverra nulla in massa. Nulla ac nisl. Nullam urna nulla, ullamcorper in, interdum sit amet, gravida ut, risus. Aenean ac enim. In luctus. Phasellus eu quam vitae turpis viverra pellentesque. Duis feugiat felis ut enim. Phasellus pharetra, sem id porttitor sodales, magna nunc aliquet nibh, nec blandit nisl mauris at pede. Suspendisse risus risus, lobortis eget, semper at, imperdiet sit amet, quam. Quisque scelerisque dapibus nibh. Nam enim. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Nunc ut metus. Ut metus justo, auctor at, ultrices eu, sagittis ut, purus. Aliquam aliquam. Etiam pede massa, dapibus vitae, rhoncus in, placerat posuere, odio. Vestibulum luctus commodo lacus. Morbi lacus dui, tempor sed, euismod eget, condimentum at, tortor. Phasellus aliquet odio ac lacus tempor faucibus. Praesent sed sem. Praesent iaculis. Cras rhoncus tellus sed justo ullamcorper sagittis. Donec quis orci. Sed ut tortor quis tellus euismod tincidunt. Suspendisse congue nisl eu elit. Aliquam tortor diam, tempus id, tristique eget, sodales vel, nulla. Praesent tellus mi, condimentum sed, viverra at, consectetuer quis, lectus. In auctor vehicula orci. Sed pede sapien, euismod in, suscipit in, pharetra placerat, metus. Vivamus commodo dui non odio. Donec et felis. Etiam suscipit aliquam arcu. Aliquam sit amet est ac purus bibendum congue. Sed in eros. Morbi non orci. Pellentesque mattis lacinia elit. Fusce molestie velit in ligula. Nullam et orci vitae nibh vulputate auctor. Aliquam eget purus. Nulla auctor wisi sed ipsum. Morbi porttitor tellus ac enim. Fusce ornare. Proin ipsum enim, tincidunt in, ornare venenatis, molestie a, augue. Donec vel pede in lacus sagittis porta. Sed hendrerit ipsum quis nisl. Suspendisse quis massa ac nibh pretium cursus. Sed sodales. Nam eu neque quis pede dignissim ornare. Maecenas eu purus ac urna tincidunt congue. Donec et nisl id sapien blandit mattis. Aenean dictum odio sit amet risus. Morbi purus. Nulla a est sit amet purus venenatis iaculis. Vivamus viverra purus vel magna. Donec in justo sed odio malesuada dapibus. Nunc ultrices aliquam nunc. Vivamus facilisis pellentesque velit. Nulla nunc velit, vulputate dapibus, vulputate id, mattis ac, justo. Nam mattis elit dapibus purus. Quisque enim risus, congue non, elementum ut, mattis quis, sem. Quisque elit. Maecenas non massa. Vestibulum pharetra nulla at lorem. Duis quis quam id lacus dapibus interdum. Nulla lorem. Donec ut ante quis dolor bibendum condimentum. Etiam egestas tortor vitae lacus. Praesent cursus. Mauris bibendum pede at elit. Morbi et felis a lectus interdum facilisis. Sed suscipit gravida turpis. Nulla at lectus. Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia Curae; Praesent nonummy luctus nibh. Proin turpis nunc, congue eu, egestas ut, fringilla at, tellus. In hac habitasse platea dictumst. Vivamus eu tellus sed tellus consequat suscipit. Nam orci orci, malesuada id, gravida nec, ultricies vitae, erat. Donec risus turpis, luctus sit amet, interdum quis, porta sed, ipsum. Suspendisse condimentum, tortor at egestas posuere, neque metus tempor orci, et tincidunt urna nunc a purus. Sed facilisis blandit tellus. Nunc risus sem, suscipit nec, eleifend quis, cursus quis, libero. Curabitur et dolor. Sed vitae sem. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Maecenas ante. Duis ullamcorper enim. Donec tristique enim eu leo. Nullam molestie elit eu dolor. Nullam bibendum, turpis vitae tristique gravida, quam sapien tempor lectus, quis pretium tellus purus ac quam. Nulla facilisi. Duis aliquet dui in est. Donec eget est. Nunc lectus odio, varius at, fermentum in, accumsan non, enim. Aliquam erat volutpat. Proin sit amet nulla ut eros consectetuer cursus. Phasellus dapibus aliquam justo. Nunc laoreet. Donec consequat placerat magna. Duis pretium tincidunt justo. Sed sollicitudin vestibulum quam. Nam quis ligula. Vivamus at metus. Etiam imperdiet imperdiet pede. Aenean turpis. Fusce augue velit, scelerisque sollicitudin, dictum vitae, tempor et, pede. Donec wisi sapien, feugiat in, fermentum ut, sollicitudin adipiscing, metus. Donec vel nibh ut felis consectetuer laoreet. Donec pede. Sed id quam id wisi laoreet suscipit. Nulla lectus dolor, aliquam ac, fringilla eget, mollis ut, orci. In pellentesque justo in ligula. Maecenas turpis. Donec eleifend leo at felis tincidunt consequat. Aenean turpis metus, malesuada sed, condimentum sit amet, auctor a, wisi. Pellentesque sapien elit, bibendum ac, posuere et, congue eu, felis. Vestibulum mattis libero quis metus scelerisque ultrices. Sed purus. Donec molestie, magna ut luctus ultrices, tellus arcu nonummy velit, sit amet pulvinar elit justo et mauris. In pede. Maecenas euismod elit eu erat. Aliquam augue wisi, facilisis congue, suscipit in, adipiscing et, ante. In justo. Cras lobortis neque ac ipsum. Nunc fermentum massa at ante. Donec orci tortor, egestas sit amet, ultrices eget, venenatis eget, mi. Maecenas vehicula leo semper est. Mauris vel metus. Aliquam erat volutpat. In rhoncus sapien ac tellus. Pellentesque ligula. Cras dapibus, augue quis scelerisque ultricies, felis dolor placerat sem, id porta velit odio eu elit. Aenean interdum nibh sed wisi. Praesent sollicitudin vulputate dui. Praesent iaculis viverra augue. Quisque in libero. Aenean gravida lorem vitae sem ullamcorper cursus. Nunc adipiscing rutrum ante. Nunc ipsum massa, faucibus sit amet, viverra vel, elementum semper, orci. Cras eros sem, vulputate et, tincidunt id, ultrices eget, magna. Nulla varius ornare odio. Donec accumsan mauris sit amet augue. Sed ligula lacus, laoreet non, aliquam sit amet, iaculis tempor, lorem. Suspendisse eros. Nam porta, leo sed congue tempor, felis est ultrices eros, id mattis velit felis non metus. Curabitur vitae elit non mauris varius pretium. Aenean lacus sem, tincidunt ut, consequat quis, porta vitae, turpis. Nullam laoreet fermentum urna. Proin iaculis lectus. Sed mattis, erat sit amet gravida malesuada, elit augue egestas diam, tempus scelerisque nunc nisl vitae libero. Sed consequat feugiat massa. Nunc porta, eros in eleifend varius, erat leo rutrum dui, non convallis lectus orci ut nibh. Sed lorem massa, nonummy quis, egestas id, condimentum at, nisl. Maecenas at nibh. Aliquam et augue at nunc pellentesque ullamcorper. Duis nisl nibh, laoreet suscipit, convallis ut, rutrum id, enim. Phasellus odio. Nulla nulla elit, molestie non, scelerisque at, vestibulum eu, nulla. Ut odio nisl, facilisis id, mollis et, scelerisque nec, enim. Aenean sem leo, pellentesque sit amet, scelerisque sit amet, vehicula pellentesque, sapien. Sed consequat tellus et tortor. Ut tempor laoreet quam. Nullam id wisi a libero tristique semper. Nullam nisl massa, rutrum ut, egestas semper, mollis id, leo. Nulla ac massa eu risus blandit mattis. Mauris ut nunc. In hac habitasse platea dictumst. Aliquam eget tortor. Quisque dapibus pede in erat. Nunc enim. In dui nulla, commodo at, consectetuer nec, malesuada nec, elit. Aliquam ornare tellus eu urna. Sed nec metus. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Pellentesque habitant morbi tristique senectus et netus et malesuada fames ac turpis egestas. Phasellus id magna. Duis malesuada interdum arcu. Integer metus. Morbi pulvinar pellentesque mi. Suspendisse sed est eu magna molestie egestas. Quisque mi lorem, pulvinar eget, egestas quis, luctus at, ante. Proin auctor vehicula purus. Fusce ac nisl aliquam ante hendrerit pellentesque. Class aptent taciti sociosqu ad litora torquent per conubia nostra, per inceptos hymenaeos. Morbi wisi. Etiam arcu mauris, facilisis sed, eleifend non, nonummy ut, pede. Cras ut lacus tempor metus mollis placerat. Vivamus eu tortor vel metus interdum malesuada. Sed eleifend, eros sit amet faucibus elementum, urna sapien consectetuer mauris, quis egestas leo justo non risus. Morbi non felis ac libero vulputate fringilla. Mauris libero eros, lacinia non, sodales quis, dapibus porttitor, pede. Class aptent taciti sociosqu ad litora torquent per conubia nostra, per inceptos hymenaeos. Morbi dapibus mauris condimentum nulla. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Etiam sit amet erat. Nulla varius. Etiam tincidunt dui vitae turpis. Donec leo. Morbi vulputate convallis est. Integer aliquet. Pellentesque aliquet sodales urna. Nullam eleifend justo in nisl. In hac habitasse platea dictumst. Morbi nonummy. Aliquam ut felis. In velit leo, dictum vitae, posuere id, vulputate nec, ante. Maecenas vitae pede nec dui dignissim suscipit. Morbi magna. Vestibulum id purus eget velit laoreet laoreet. Praesent sed leo vel nibh convallis blandit. Ut rutrum. Donec nibh. Donec interdum. Fusce sed pede sit amet elit rhoncus ultrices. Nullam at enim vitae pede vehicula iaculis. Class aptent taciti sociosqu ad litora torquent per conubia nostra, per inceptos hymenaeos. Aenean nonummy turpis id odio. Integer euismod imperdiet turpis. Ut nec leo nec diam imperdiet lacinia. Etiam eget lacus eget mi ultricies posuere. In placerat tristique tortor. Sed porta vestibulum metus. Nulla iaculis sollicitudin pede. Fusce luctus tellus in dolor. Curabitur auctor velit a sem. Morbi sapien. Class aptent taciti sociosqu ad litora torquent per conubia nostra, per inceptos hymenaeos. Donec adipiscing urna vehicula nunc. Sed ornare leo in leo. In rhoncus leo ut dui. Aenean dolor quam, volutpat nec, fringilla id, consectetuer vel, pede. Nulla malesuada risus ut urna. Aenean pretium velit sit amet metus. Duis iaculis. In hac habitasse platea dictumst. Nullam molestie turpis eget nisl. Duis a massa id pede dapibus ultricies. Sed eu leo. In at mauris sit amet tortor bibendum varius. Phasellus justo risus, posuere in, sagittis ac, varius vel, tortor. Quisque id enim. Phasellus consequat, libero pretium nonummy fringilla, tortor lacus vestibulum nunc, ut rhoncus ligula neque id justo. Nullam accumsan euismod nunc. Proin vitae ipsum ac metus dictum tempus. Nam ut wisi. Quisque tortor felis, interdum ac, sodales a, semper a, sem. Curabitur in velit sit amet dui tristique sodales. Vivamus mauris pede, lacinia eget, pellentesque quis, scelerisque eu, est. Aliquam risus. Quisque bibendum pede eu dolor. Donec tempus neque vitae est. Aenean egestas odio sed risus ullamcorper ullamcorper. Sed in nulla a tortor tincidunt egestas. Nam sapien tortor, elementum sit amet, aliquam in, porttitor faucibus, enim. Nullam congue suscipit nibh. Quisque convallis. Praesent arcu nibh, vehicula eget, accumsan eu, tincidunt a, nibh. Suspendisse vulputate, tortor quis adipiscing viverra, lacus nibh dignissim tellus, eu suscipit risus ante fringilla diam. Quisque a libero vel pede imperdiet aliquet. Pellentesque nunc nibh, eleifend a, consequat consequat, hendrerit nec, diam. Sed urna. Maecenas laoreet eleifend neque. Vivamus purus odio, eleifend non, iaculis a, ultrices sit amet, urna. Mauris faucibus odio vitae risus. In nisl. Praesent purus. Integer iaculis, sem eu egestas lacinia, lacus pede scelerisque augue, in ullamcorper dolor eros ac lacus. Nunc in libero. Fusce suscipit cursus sem. Vivamus risus mi, egestas ac, imperdiet varius, faucibus quis, leo. Aenean tincidunt. Donec suscipit. Cras id justo quis nibh scelerisque dignissim. Aliquam sagittis elementum dolor. Aenean consectetuer justo in pede. Curabitur ullamcorper ligula nec orci. Aliquam purus turpis, aliquam id, ornare vitae, porttitor non, wisi. Maecenas luctus porta lorem. Donec vitae ligula eu ante pretium varius. Proin tortor metus, convallis et, hendrerit non, scelerisque in, urna. Cras quis libero eu ligula bibendum tempor. Vivamus tellus quam, malesuada eu, tempus sed, tempor sed, velit. Donec lacinia auctor libero. Praesent sed neque id pede mollis rutrum. Vestibulum iaculis risus. Pellentesque lacus. Ut quis nunc sed odio malesuada egestas. Duis a magna sit amet ligula tristique pretium. Ut pharetra. Vestibulum imperdiet magna nec wisi. Mauris convallis. Sed accumsan sollicitudin massa. Sed id enim. Nunc pede enim, lacinia ut, pulvinar quis, suscipit semper, elit. Cras accumsan erat vitae enim. Cras sollicitudin. Vestibulum rutrum blandit massa. Sed gravida lectus ut purus. Morbi laoreet magna. Pellentesque eu wisi. Proin turpis. Integer sollicitudin augue nec dui. Fusce lectus. Vivamus faucibus nulla nec lacus. Integer diam. Pellentesque sodales, enim feugiat cursus volutpat, sem mauris dignissim mauris, quis consequat sem est fermentum ligula. Nullam justo lectus, condimentum sit amet, posuere a, fringilla mollis, felis. Morbi nulla nibh, pellentesque at, nonummy eu, sollicitudin nec, ipsum. Cras neque. Nunc augue. Nullam vitae quam id quam pulvinar blandit. Nunc sit amet orci. Aliquam erat elit, pharetra nec, aliquet a, gravida in, mi. Quisque urna enim, viverra quis, suscipit quis, tincidunt ut, sapien. Cras placerat consequat sem. Curabitur ac diam. Curabitur diam tortor, mollis et, viverra ac, tempus vel, metus. Curabitur ac lorem. Vivamus non justo in dui mattis posuere. Etiam accumsan ligula id pede. Maecenas tincidunt diam nec velit. Praesent convallis sapien ac est. Aliquam ullamcorper euismod nulla. Integer mollis enim vel tortor. Nulla sodales placerat nunc. Sed tempus rutrum wisi. Duis accumsan gravida purus. Nunc nunc. Etiam facilisis dui eu sem. Vestibulum semper. Praesent eu eros. 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Duis pretium iaculis arcu. Curabitur ut lacus. Aliquam vulputate. Suspendisse ut purus sed sem tempor rhoncus. Ut quam dui, fringilla at, dictum eget, ultricies quis, quam. Etiam sem est, pharetra non, vulputate in, pretium at, ipsum. Nunc semper sagittis orci. Sed scelerisque suscipit diam. Ut volutpat, dolor at ullamcorper tristique, eros purus mollis quam, sit amet ornare ante nunc et enim. Phasellus fringilla, metus id feugiat consectetuer, lacus wisi ultrices tellus, quis lobortis nibh lorem quis tortor. Donec egestas ornare nulla. Mauris mi tellus, porta faucibus, dictum vel, nonummy in, est. Aliquam erat volutpat. In tellus magna, porttitor lacinia, molestie vitae, pellentesque eu, justo. Class aptent taciti sociosqu ad litora torquent per conubia nostra, per inceptos hymenaeos. Sed orci nibh, scelerisque sit amet, suscipit sed, placerat vel, diam. Vestibulum nonummy vulputate orci. Donec et velit ac arcu interdum semper. Morbi pede orci, cursus ac, elementum non, vehicula ut, lacus. Cras volutpat. Nam vel wisi quis libero venenatis placerat. Aenean sed odio. Quisque posuere purus ac orci. Vivamus odio. Vivamus varius, nulla sit amet semper viverra, odio mauris consequat lacus, at vestibulum neque arcu eu tortor. Donec iaculis tincidunt tellus. Aliquam erat volutpat. Curabitur magna lorem, dignissim volutpat, viverra et, adipiscing nec, dolor. Praesent lacus mauris, dapibus vitae, sollicitudin sit amet, nonummy eget, ligula. Cras egestas ipsum a nisl. Vivamus varius dolor ut dolor. Fusce vel enim. Pellentesque accumsan ligula et eros. Cras id lacus non tortor facilisis facilisis. Etiam nisl elit, cursus sed, fringilla in, congue nec, urna. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Integer at turpis. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Duis fringilla, ligula sed porta fringilla, ligula wisi commodo felis, ut adipiscing felis dui in enim. Suspendisse malesuada ultrices ante. Pellentesque scelerisque augue sit amet urna. Nulla volutpat aliquet tortor. Cras aliquam, tellus at aliquet pellentesque, justo sapien commodo leo, id rhoncus sapien quam at erat. Nulla commodo, wisi eget sollicitudin pretium, orci orci aliquam orci, ut cursus turpis justo et lacus. Nulla vel tortor. Quisque erat elit, viverra sit amet, sagittis eget, porta sit amet, lacus. In hac habitasse platea dictumst. Proin at est. Curabitur tempus vulputate elit. Pellentesque sem. Praesent eu sapien. Duis elit magna, aliquet at, tempus sed, vehicula non, enim. Morbi viverra arcu nec purus. Vivamus fringilla, enim et commodo malesuada, tortor metus elementum ligula, nec aliquet est sapien ut lectus. Aliquam mi. Ut nec elit. Fusce euismod luctus tellus. Curabitur scelerisque. Nullam purus. Nam ultricies accumsan magna. Morbi pulvinar lorem sit amet ipsum. Donec ut justo vitae nibh mollis congue. Fusce quis diam. Praesent tempus eros ut quam. Donec in nisl. Fusce vitae est. Vivamus ante ante, mattis laoreet, posuere eget, congue vel, nunc. Fusce sem. Nam vel orci eu eros viverra luctus. Pellentesque sit amet augue. Nunc sit amet ipsum et lacus varius nonummy. Integer rutrum sem eget wisi. Aenean eu sapien. Quisque ornare dignissim mi. Duis a urna vel risus pharetra imperdiet. Suspendisse potenti. Morbi justo. Aenean nec dolor. In hac habitasse platea dictumst. Proin nonummy porttitor velit. Sed sit amet leo nec metus rhoncus varius. Cras ante. Vestibulum commodo sem tincidunt massa. Nam justo. Aenean luctus, felis et condimentum lacinia, lectus enim pulvinar purus, non porta velit nisl sed eros. Suspendisse consequat. Mauris a dui et tortor mattis pretium. Sed nulla metus, volutpat id, aliquam eget, ullamcorper ut, ipsum. Morbi eu nunc. Praesent pretium. Duis aliquam pulvinar ligula. Ut blandit egestas justo. Quisque posuere metus viverra pede. Vivamus sodales elementum neque. Vivamus dignissim accumsan neque. Sed at enim. Vestibulum nonummy interdum purus. Mauris ornare velit id nibh pretium ultricies. Fusce tempor pellentesque odio. Vivamus augue purus, laoreet in, scelerisque vel, commodo id, wisi. Duis enim. Nulla interdum, nunc eu semper eleifend, enim dolor pretium elit, ut commodo ligula nisl a est. Vivamus ante. Nulla leo massa, posuere nec, volutpat vitae, rhoncus eu, magna. Quisque facilisis auctor sapien. Pellentesque gravida hendrerit lectus. Mauris rutrum sodales sapien. Fusce hendrerit sem vel lorem. Integer pellentesque massa vel augue. Integer elit tortor, feugiat quis, sagittis et, ornare non, lacus. Vestibulum posuere pellentesque eros. Quisque venenatis ipsum dictum nulla. Aliquam quis quam non metus eleifend interdum. Nam eget sapien ac mauris malesuada adipiscing. Etiam eleifend neque sed quam. Nulla facilisi. Proin a ligula. Sed id dui eu nibh egestas tincidunt. Suspendisse arcu. Maecenas dui. Aliquam volutpat auctor lorem. Cras placerat est vitae lectus. Curabitur massa lectus, rutrum euismod, dignissim ut, dapibus a, odio. Ut eros erat, vulputate ut, interdum non, porta eu, erat. Cras fermentum, felis in porta congue, velit leo facilisis odio, vitae consectetuer lorem quam vitae orci. Sed ultrices, pede eu placerat auctor, ante ligula rutrum tellus, vel posuere nibh lacus nec nibh. Maecenas laoreet dolor at enim. Donec molestie dolor nec metus. Vestibulum libero. Sed quis erat. Sed tristique. Duis pede leo, fermentum quis, consectetuer eget, vulputate sit amet, erat. Donec vitae velit. Suspendisse porta fermentum mauris. Ut vel nunc non mauris pharetra varius. Duis consequat libero quis urna. Maecenas at ante. Vivamus varius, wisi sed egestas tristique, odio wisi luctus nulla, lobortis dictum dolor ligula in lacus. Vivamus aliquam, urna sed interdum porttitor, metus orci interdum odio, sit amet euismod lectus felis et leo. Praesent ac wisi. Nam suscipit vestibulum sem. Praesent eu ipsum vitae pede cursus venenatis. Duis sed odio. Vestibulum eleifend. Nulla ut massa. Proin rutrum mattis sapien. Curabitur dictum gravida ante. Phasellus placerat vulputate quam. Maecenas at tellus. Pellentesque neque diam, dignissim ac, venenatis vitae, consequat ut, lacus. Nam nibh. Vestibulum fringilla arcu mollis arcu. Sed et turpis. Donec sem tellus, volutpat et, varius eu, commodo sed, lectus. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Quisque enim arcu, suscipit nec, tempus at, imperdiet vel, metus. Morbi volutpat purus at erat. Donec dignissim, sem id semper tempus, nibh massa eleifend turpis, sed pellentesque wisi purus sed libero. Nullam lobortis tortor vel risus. Pellentesque consequat nulla eu tellus. Donec velit. Aliquam fermentum, wisi ac rhoncus iaculis, tellus nunc malesuada orci, quis volutpat dui magna id mi. Nunc vel ante. Duis vitae lacus. Cras nec ipsum. Morbi nunc. Aliquam consectetuer varius nulla. Phasellus eros. Cras dapibus porttitor risus. Maecenas ultrices mi sed diam. Praesent gravida velit at elit vehicula porttitor. Phasellus nisl mi, sagittis ac, pulvinar id, gravida sit amet, erat. Vestibulum est. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Curabitur id sem elementum leo rutrum hendrerit. Ut at mi. Donec tincidunt faucibus massa. Sed turpis quam, sollicitudin a, hendrerit eget, pretium ut, nisl. Duis hendrerit ligula. Nunc pulvinar congue urna. Nunc velit. Nullam elit sapien, eleifend eu, commodo nec, semper sit amet, elit. Nulla lectus risus, condimentum ut, laoreet eget, viverra nec, odio. Proin lobortis. Curabitur dictum arcu vel wisi. Cras id nulla venenatis tortor congue ultrices. Pellentesque eget pede. Sed eleifend sagittis elit. Nam sed tellus sit amet lectus ullamcorper tristique. Mauris enim sem, tristique eu, accumsan at, scelerisque vulputate, neque. Quisque lacus. Donec et ipsum sit amet elit nonummy aliquet. Sed viverra nisl at sem. Nam diam. Mauris ut dolor. Curabitur ornare tortor cursus velit. Morbi tincidunt posuere arcu. Cras venenatis est vitae dolor. Vivamus scelerisque semper mi. Donec ipsum arcu, consequat scelerisque, viverra id, dictum at, metus. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Ut pede sem, tempus ut, porttitor bibendum, molestie eu, elit. Suspendisse potenti. Sed id lectus sit amet purus faucibus vehicula. Praesent sed sem non dui pharetra interdum. Nam viverra ultrices magna. Aenean laoreet aliquam orci. Nunc interdum elementum urna. Quisque erat. Nullam tempor neque. Maecenas velit nibh, scelerisque a, consequat ut, viverra in, enim. Duis magna. Donec odio neque, tristique et, tincidunt eu, rhoncus ac, nunc. Mauris malesuada malesuada elit. Etiam lacus mauris, pretium vel, blandit in, ultricies id, libero. Phasellus bibendum erat ut diam. In congue imperdiet lectus. Aenean scelerisque. Fusce pretium porttitor lorem. In hac habitasse platea dictumst. Nulla sit amet nisl at sapien egestas pretium. Nunc non tellus. Vivamus aliquet. Nam adipiscing euismod dolor. Aliquam erat volutpat. Nulla ut ipsum. Quisque tincidunt auctor augue. Nunc imperdiet ipsum eget elit. Aliquam quam leo, consectetuer non, ornare sit amet, tristique quis, felis. Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia Curae; Pellentesque interdum quam sit amet mi. Pellentesque mauris dui, dictum a, adipiscing ac, fermentum sit amet, lorem. Ut quis wisi. Praesent quis massa. Vivamus egestas risus eget lacus. Nunc tincidunt, risus quis bibendum facilisis, lorem purus rutrum neque, nec porta tortor urna quis orci. Aenean aliquet, libero semper volutpat luctus, pede erat lacinia augue, quis rutrum sem ipsum sit amet pede. Vestibulum aliquet, nibh sed iaculis sagittis, odio dolor blandit augue, eget mollis urna tellus id tellus. Aenean aliquet aliquam nunc. Nulla ultricies justo eget orci. Phasellus tristique fermentum leo. Sed massa metus, sagittis ut, semper ut, pharetra vel, erat. Aliquam quam turpis, egestas vel, elementum in, egestas sit amet, lorem. Duis convallis, wisi sit amet mollis molestie, libero mauris porta dui, vitae aliquam arcu turpis ac sem. Aliquam aliquet dapibus metus. Vivamus commodo eros eleifend dui. Vestibulum in leo eu erat tristique mattis. Cras at elit. Cras pellentesque. Nullam id lacus sit amet libero aliquet hendrerit. Proin placerat, mi non elementum laoreet, eros elit tincidunt magna, a rhoncus sem arcu id odio. Nulla eget leo a leo egestas facilisis. Curabitur quis velit. Phasellus aliquam, tortor nec ornare rhoncus, purus urna posuere velit, et commodo risus tellus quis tellus. Vivamus leo turpis, tempus sit amet, tristique vitae, laoreet quis, odio. Proin scelerisque bibendum ipsum. Etiam nisl. Praesent vel dolor. Pellentesque vel magna. Curabitur urna. Vivamus congue urna in velit. Etiam ullamcorper elementum dui. Praesent non urna. Sed placerat quam non mi. Pellentesque diam magna, ultricies eget, ultrices placerat, adipiscing rutrum, sem. Abstract Vacuum energy is understood by one-periodic frequencies with a possible lowering by confined Casimir forces. Doubly-periodic processed vacuum energy is a non-stationary energy state of a complex Lagrangian. Its is suspected that a doubly-periodic processing in the vicinity of zeros of zeta functions lowers vaccum energy as compared to a real physical field. This quadratic model compensates positive energy of molecules mainly by dark, complex phantom energy and negligible ion energy. A proposed doublyperiodic synthesis gains cooling energy by a minimum amount of energy. Created matter is a zero-energy state of biomass and dark energy which is capable to compost into a zero-energy state. Keywords information density universe, doubly-periodic processing, elliptic involution, breathing modes, atmospheric power plant, bifurcation, onedimensional chaotic map. 1. Introduction The present paper describes in high generality breathing modi in information-based universes with two flows each with an infinite number of frequencies. This state of a self-consistent confinement is understandable as a Casimir effect but with complex non-dissipative energies. Rational coordinates xµand entropy current densities jeare like addresses in a computer memory. The quadratic map deserves attention as a minimal regular map and a maximal regular map. Consecutive γ◦zcreate binary invariants f(ωk) and lattice periods δωkwith complex multiplication (CM). Addition on iterated elliptic curves is in one-to-one relation to bifurcation [1]. Iterated holomorph binary f(ω)=(f1 f2) = dx +idy dz −dt ≃D= [γµγν]Dµν O. Ziep in C∞ensures Minkowski spacetime by a stereographic holomorphicmeromorphic projection to Riemann sphere with Dirac matrices γmu. Chaotic sums of iterated f(ω) with D3≃zD2yield Minkowski spacetime exponents eDwhich explains the velocity of light cby simplest cycles. This onedimensional complex self-similar set is an open system fractal zeta universe (FZU). Regular frayed Cayley-Newton iterates are supposed to exist only in the vicinity of nontrivial zeros znt in a linear expansion of zeta functions. A large number hypothesis (LNH) correlates low and high energies [2, 3]. As shown in Section 2 invariant f(ω) is conformal stress-energy which offers a technological application described in Section 3. The 10∞zoom gauge coupling predicts continuous creation of matter in FZU and lower vacuum densities. The present paper proposes a laboratory to test generation of newly generated matter in FZU which is called doubly-periodic atmospheric power plant (DPAPP). Up to now power plants process subsequent one-periodic cycles. Isothermal and isentropic Carnot processes are e.g. consecutive one-periodic cycles converting vacuum energy ρvac of one-periodic inertial systems in Minkowski spacetime. In quantum statistics ρvac are one-periodic zero-point oscillations ρvac(QS) of periods 11/m where ρvac(QS)≃1050−20ρvac(GR). ρvac(GR) in general relativity is confirmed by experiment. This cosmological constant problem (CCP) is resolvable by unified fields with elliptic involution in an open FZU whereas laws of thermodynamics apply to closed systems [4]. The present paper describes a technology to obtain lower local values ρvac < ρvac(GR) by breathing acting doublyperiodic on a bifurcating potential flow. FZU allows local breathing modes as quasi-stationary vacua to extract heat energy in Section 3. Local creation of matter is analogous to a breathing process of living beings. This local Big Bang-Big Rip scenario would preferentially create molecules H2Oand CO2[4]. Energies comparable to the Planck energy Mpare detectable by e.g. lightning energy of 1 GJ ≃10−5g≃0.5Mp≃1028 eV . The present theory of lightning is that opposite charges (positive and negative) accumulate in different regions. At lightning potential breakdown discharge occurs if an accumulating one-periodic electrical potential up to 105−108Vin a thundercloud exceeds the insulating capacity of the air, causing a rapid, massive discharge of electricity known as a lightning flash. This theory is extended to terrestrial gamma ray flashes and cosmic rays (CR) [5]. Recently reported evidence indicates apparent ignition of lightning by cosmic-ray showers or from an avalanche of electrons seeded by extraterrestrial cosmic rays [5]. Analogous to CR-lightning coupling FZU is capable to store dark existing energy as complex dark matter of five unified fields instead of electromagnetic polarization induced by clouds. A FZU cosmic-ray-charged-cloud superfluid (CRCCS) stores unified energy in a non-turbulent open system. Tropical regions with highest lightning rates limit DPAPP processing temperatures to about 50 ° C in order to avoid lightning which would discharge the CRCCSatmospheric capacitor. Every stationary point is surrounded by a three-component doubly-periodic stable state in Section 4. Theory and experiment of the open FZU system is sketched in Section 2 and 3. Topological entropy variation by altitude is superimposed by lateral temperature gradients. Already moderate temperature gradients are suspected to induce a bifurcating spacetime (BST) giving complex non-detectable O. Ziep energies [6] [7]. Non-detectable particles are viewed as complex dark vacuum energy. A Planck energy can be stored permanently as a doublyperiodic cycle by avoiding turbulences. DPAPP tests the ability to generate lower vacuum energy density by doubly-periodic processes by ‘creatio ex nihilo’ to a certain amount in CR, atmospheric clouds and photosynthesis in [4]. Cloud motion, plant growth (photosynthesis) and CR are united by regular chaotic iterates of complex BSTcurvature f(ω) near simple zeros znt [4]. Section 6 confirms a cloud radiative forcing triggered by negative phantom dark energy. 2. Atmospherean algorithmic chaotic RC circuit FZUvacuum energy is fractal. Low iterated k-components is identified as ultra-high energies above the detection limit which is known as the GZK cutoff. The step k=0 is above the detection limit. Earth ' s atmosphere is viewed as being describable by an entire transcendent, smooth onedimensional complex function related holomorphic-meromorphic to Riemann sphere in variable z=h+il of altitude h and latitude l in tangential plane. The Weierstrass sigma function σ(z) = −∂jσ(z) ∂z or ξfunction ξ(z) = −∂jξ(z) ∂z of the Riemann zeta function ζ(z) represents a quantum Hall topology (QHT) [8] [9]. QHT dynamical variables are non-analytic potential flow lines ϕσ(x, y), ϕξ(x, y) : ϕσ(x, y) = jσ(z) + ¯ jσ(¯z) whereas ∂zσ(z) depend on ∂2 zσ(z) and ∂g2,3σ(z) QHT yields the Laplace equation ∂z∂¯zσ(z) = 0. CRCCS is non-turbulent on osculation planes of a twisted cubic Ctw in space. The hyperelliptic Kummer surface K(X(f)) is parametrized by a quadratic Hermite-Tschirnhausen process z←F(t, z)≃ γ◦z. Elliptic and hyperelliptic ' current densities ' jσor jξare thought as a flow in an atmospheric spherical capacitor circuit jσ=dZdzσ(z) = d(Q C) = 1 4πεε0 (1 R++ −1 R+− +1 R−+−1 R−− ) (1) with two capacitor stripes znt =±1 2±imnfor nontrivial zeros ξ(znt) = 0 or σ(znt). A quadrupole tensor d(Q C) for complex conjugates ξ(z),¯ ξ(z), ξ(¯z),¯ ξ(¯z) depends on four radii R±± creating a moment of inertia. Variable z, the Legendre module λand the Weber invariant f(ω) are interrelated. K(X(f)) points are hyperelliptic ℘-functions parametrized by f=f(ω) X(f) = (1,−f, f2,1) = (℘±±,1) ≃ {jσ(u±, u±},1) ≃(T++, T+−, T−−,1) (2) Like ξ(z) the sigma function is entire and allows a Cayley quotient. σ(u±) = −∂jσ(u±) ∂u±→ −∆jσ(u±) ∆u± The discrete ℘-function in (2) transmits to a Schwarzian derivative {jσ(u±), u±}as conformal stress-energy T±± where {F(t, z), z}= 6∂z∂z′ln∆F ∆z(3) O. Ziep Points on Ctw of K(X) are f-parametrized zeros of σ(u±)σ(v±)) ≃ζ(z)ζ(z′)≃X(f)⊗X(f) = 0 (4) which is quadratic in stress-energy T(u±)[T(z)] which allows quadratic f-iterates for σ(u±) in (4). Like a holomorphic-meromorphic transition dxµ(f) steps k+ 1 and kare involute, i.e. f(ωk+1)f(ωk)≃const. If f(ωk) is diffusive, f(ωk+1) is drifting which requires to map ζ(z) zeros to its poles. resζ(z), the residuum of ζ(z) is proportional to the regulator R(K) = logEν. Its exponential map allows to introduce a complex Lagrangian L[ν] for units Eνwith frequency νof a number field K R(K)≃eRdν[f(ω)]logf(ω)≃eRdν[f(ω)]L(ν[f(ω)]) (5) The ideal residuum resζ(z) = 1 corresponds to an infinite set ν. Residua of the Dedekind zeta function ζ(z, K) are used to map σ(u) zeros for optimal regulator values. ξ(z)-zeros znt differ from σ(u) by replacing the mass mn in znt by ω≃√∆ with discriminant ∆ and performing a multiplication over lattice stripes. Eqs. (2) and (4) prove that f(ωk) unifies curvature, time and temperature. Iterates f(ωk+1)←γ◦f(ωk) is chaotic if {F(t, z), z}<0. γ◦f(ω) is related to rational coordinates by holomorphic functions from Riemann sphere and meromorphic functions from complex plane. Iterates k→k+1 is entangled and dynamical in FZU [10]. Accordingly, Minkowski spacetime is a mean field where time is quadrupolar, the scale factor (9) and derivatives ∂zis drift-diffusive. This dualism maps diffusion coefficient Dto the velocity of light c D=1=(∆u)2 ω→(∆u)2 ω2+c→(∆u)2 (∆ω)2→c2(6) Stable orbiting laps and Lorentz-invariant are compatible for f(ω)=(f1 f2) γ→γeFµν [γµ,γν]→γeiσz (7) where deteFµν [γµ,γν]= 1 with Dirac matrices γµ, skew Fµν is equivalent to complex ωk+1 →ω2 k+c. Simplest γ-cycles written for the driftdiffusion term ∆f= (γ−1) ◦fas γ◦γ=γprove that squared invariants are coordinates. A quadratic map contains alternately coordinates. For fluctuating lattice periods ωcoordinates in space are attached to osculating planes and stationary points. Weierstrass zeta function ζ(u, ωk) in ∆fi=Pj=1,..,4cij∆ζ(uj−u0, ωk), i=1,2,3 require four points j= 1,···,4 [11]. Complex time δt →δt2in (5) is related to additive creation of matter t→t2in LNH [3]. Addition on elliptic curves sets lengths δz equivalent to areas δz2modulo a cubic invariant ϕ3(δz). A cubic congruence δz mod ϕ3(δz)≃δz2≃δz−1qualifies a quadratic map as involution. Bifurcating chaotic line segments dlxy ∈z=h+il store thermal energy ≃ϑ2(uk=akωk, ωk) and drift in a global temperature potential VTglobal (z) = Z∇VTcloud dlxy (8) where dlxy are geometric zeta function sequences. In quantum statistics kinematic temperature Tkin is real mean energy Ekin, i.e. Tkin is oneperiodic. Complex Ekin is collisional damping and. In CRCCS complex O. Ziep energy is of the order of rest mass, i.e. both energy (time) and temperature are independent doubly-periodic complex quantities of a superfluid flow. Approximating dlxy in (8) by straight lines between znt is multiplying by a charge e. It is claimed that VTglobal (z) governs time-thermal cycles in atmosphere, biosphere and geosphere which can be written as a drift-diffusion potential VTglobal (z) = T+µn[#znt]. The number of zeros n[#znt] with Lagrange parameter µapplies to created charge pairs, i.e. CR, organic aerosols, photosynthesis and vegetational air ions [4]. 3. Breathing DPAPP A Carnot process is a thin rectangle of length t→akttraversed by the number of cycles k. In distinction doubly-periodic complex temperature and entropy is ultra-high complex energy for iterated t←γ◦twith deg(t)=22k. An open system CRCCS DPAPP contains already an amount of matter with highest information densities, e.g. plant branching and atmosphericgaseous-liquid-solid slush around the triple point of water (TPW). Instead of one-periodic electromagnetic nonequilibrium artificial photosynthesis a doubly-periodic process is proposed with complex oscillations of temperature and entropy. Already processing by temperature gradients of 101···102 ° Kon fluctuating time-thermal contours should create complex a finite ρdark. A test of this model is that the density of ionized particles changes. DPAPP is based on a complex contour for a superfluid flow potential (8) without turbulences. Seasons are simulated changing topological entropy δhtby altitude δh. Simultaneous temperature gradients T(z) induced e.g. changing radiation frequency and intensity in varying directions on complex plane are suspected to induce BST and CR. A fluctuating contour δTδS < 0 replaces a Carnot process rectangle. Instead of plates and contacts of the atmospheric capacitor DPAPP a Carnot battery thermal energy storage (TES) and thermal to power (T2P) are proposed to control a cooling by phantom energy ρdark as sketched in Figure 3. Figure 1:Breathing mode of DPAPP with drift-diffusing doubly-periodic Carnot process. Lower kinetic energy Ekin is in inversion to higher tem- O. Ziep perature T at ground level. On a closed path between atmosphere and ground level a potential difference Va−Vgis generated if a certain amount of matter is created which is triggered by existing matter. The encircled area by branches the vertical z-plane into a tree of chaotic flow lines. Within FZU five interaction participate. DPAPP operates as a statistical zoom by 1020 ≃226comparable to the Avogadro constant. Quadratic forces in ρmin (4),(11),(3) overwhelm a rest mass threshold which favors statistically organic molecules. Season-dependent DPAPP Big Bang -Big Rip processes create molecules (discriminants [4]) consisting of atoms H, C, O, N [4]. This real matter ρm is compensated by complex dark matter ρdark. Created matter is accompanied by complex phantom energy which induces cooling in DPAPP by a product of low count rate jdark and high energy Edark. DPAPP trigger are existing bifurcating flow lines which are realized at lant growth and near TPW which require low temperature gradients of 102 ° K. Accordingly, ± 50 ° Karound 0 ° Ccould induce ultrahigh CR energies and ρion even at ground level [6]. 4. Entangled three-component matter The algorithm is easy to understand by non-stationary distorted contour instead of a constant temperature rectangle with modular unit ϑ2(u=aω, ω) for ωkwith rational a= (a1, a2) in universal covering u. CR is understandable by theta constant sources [4]. Complex energies are identified with ρdark where fractional γcreate singularities at each second step. The experimental atmospheric temperature gradient is S-shaped: The rate at which temperature changes with altitude has negative differential branches which confirms cubic f(ω). According to (4) variable f(ω) iterates the hyperelliptic function ℘±± i.e. stress-energy. The underdetermined complex Lagrangian L(ν[f(ω)]) has an infinity of least squares solutions as a branching tree of doubly-periodic ν[f(ω)]. In natural science the doubly-periodic minimum is seasonal plant growth and birth of livings being. A real minimum L(ν[f(ω)]) = 0 yields regulator index R(K) = 1. This corresponds to imaginary quadratic fields of norm f¯ f= 1 which are used in physical field theory. A pure cubic case R(K)≥1 is not preferred. Cyclotomic extensions of yield local minima R(K) yield infinitely many local minima R(K)≪1 above the theoretical lowest achievable value ρvac = 0 [12]. For quasi-stationary cyclotomic states of a complex Lagrangian with lower vacuum energy density Minkowski spacetime is the real hull due to D= 1 for all iterations. The claim that local L(ν[f(ω)]) minima are charge quanta in nontrivial zeros znt of holomorphic functions ξ(znt) = 0 or σ(u±) = 0 as solutions of (4) can be tested by measuring a small amount of δρion.σ(u±) = 0 or ∆hσ(z) = 0 allows γ◦zor γ◦uand γ◦ξor γ◦σ(u) with hyperbolic Laplacian ∆h. An algebraic map γbranches into the infinity of stable orbiting laps ( ion pairs ) and unstable bifurcating k-components ( CR ) [12]. Odd k-components and even kcomponents yield diffusive f(ωk) and drifting λ(ωk) charges, alternately. Stable laps as oscillations of the Lyapunovexponent λLaround zero yield the Lagrangian L(ν[f(ω)]) ≃ {F, z}=L(F, ˙ F, ¨ F, ... F) in (3),(4) and (5). The discrete γ-invariant derivative already contains the drift- O. Ziep diffusion scale factor R≃zk+1 −zk ˙ F=∂zF=R= 22k Y i=1 ˙ Fi=eλL(9) ρvac(GR) can be clasiief by the Friedmann solution with Lagrangian L=R˙ R2−ϕ3(R) and polynomial VTglobal ≃ϕ3(z=ϕ2k) (10) (11) is cubic whenever the Feigenbaum renormalized iterated degree 2k polynomial ϕ2kmeets cubic roots. Energies of k-components should follow a 1/22klaw. Eq. (4) is quadratic in ρvac e.g. δmδm´ ≃0 αm2 ++βm+m−+γm2 −= 0 (11) Masses m±itself are f(ω)- quadratic due to 4. Hyperelliptic based coefficients are integer (αβγ) = (1,−136,10) which recover an electron - to-proton mass ratio up to precision of 10−3[13]. Masses m±≃f(ω), f2(ω) are related to the areal density ρres of residua of iterated f(ωk). Optimized values ρres allow to refine (11) and the conjecture about the fine structure constant α−1 f≃2πδF[14]. Up to second order L(ν[f(ω)] has three-components 1, ∂zand ∂z∂z′acting on logE: (i) real matter ρm≃ logf(ω) (ii) inert drift-diffusion fields (∂zlogf = 0) with real ions ρion (iii) complex dark matter ρdark in L(F, ˙ F, ¨ F, ... F)≃ {F(t, z), z}as sketched in Figure 4. ρvac ≃ρm+ρion +ρdark ≃0 (12) A square in ρvac in 4 is limited by the identity ϑ4 [00] =ϑ4 [01] +ϑ4 [10]. The real density ρm=ρr+ρexc,vdW is a sum of rest mass ρr, excitonic binding energy and quadratic van der Waals interaction ρexc,vdW which is (3) ρm≃T(f)≃∂f∂f′ln∆F ∆f. The scale factor and ∆F ∆f≃K(λ) is a product of theta constants related to quarter periods K(λ) [15]. The differential equation for K(λ) a local wave function Hermite polynomial with frequency νn. Then, ρm=Pn1 2νnare zero-point oscillations. Rest masses ρrare stable iterates of the Big Bang-Big Rip solution for nine discriminants ∆ reducing to a φ3. The inverse Fermion Green ' s function G−1in quantum statistics is related to F(t, z) = γ◦zin [2]. Figure 2: Real and complex energies within a BST-environment, variable R is the radius of an apparent singularity (charge, universe) variable z is curvature, ρion contains CR [4]. O. Ziep 5. Elliptic involution and various vacuum energy minima Iterated complex unified fields describe a superfluid state of an open universe where self-organization in dissipative structures occurs for closed subsystems, e.g. DPAPP. The claim is that doubly-periodic processed unified fields are capable to exhibit local minima of vacuum energy density. The k-iterated Legendre module λ=1 2+¯ ψλmψ menters FZU as a fourcomponent Dirac current [6] [15] [4] . FZU is an iterated potential flow where vacuum density ρvac[{F, z}, λ] depends on elliptic involution i(λ)=1−λwhich solves the longstanding CCP [12] [10]. Iteration steps γ(ϕ3(f(√∆)) ◦z=F(t, z) with change periods ωvia discriminants ∆ and yield a Gaussian-like diffusion process like measured CR. Quadratic transformed periods (1−1 1 1 )ωobey involution f(ω′) = √2/f(ω) . Equivalent periods (1 0 0 1)ω, (0−1 1 0 )ωobey invariances λ→i(λ),1/λ, 1/i(λ),1− 1/λ, −λ/i(λ) which are (1 −λi(λ))3/(λi(λ))2=const (13) Elliptic involution undercuts a given vacuum energy in a fractal DPAPP as a non-local correlation between low and high values of dimensionless energy density. For energy density ρcore ≃101gcm−3at ground level and at ρvac ≃10−31 gcm−3atmospheric level CR air shower moving with velocity of light are correlated with slow plant grow [4]. The density in FZU is like that of a black hole density which is not a well-defined [2] [15] . This uncertainty in density enables a continuous creation of matter in holomorphic environment near zeros of ξ(z) or σ(z) which is equivalent to QHT. 6. Plant growth, Air ions and Cooling in Atmosphere Measured ion fluxes 2 or 20 −30 ≃cm−3s−1ion-pairs at atmospheric or ground level yield simulated and measured concentrations of about 105cm−3[16, 17] which are negligible ρion of about 10−11kWh ·cm−3 in (12). At cloud-radiative forcing atmospheric cooling is attributed to cloud cover changes. At CRCCS atmospheric cooling is attributed to phantom energy ρdark which compensates created rest mass ρm. OMG energy 1021 eV at GZK cutoff or the Planck energy Mp≃10−5g≃1028 eV content of a lightning is equivalent to heat or cool 12 gwater or an atmospheric cloud of 5˙ 108gby 1 ° K. Phantom dark matter ρdark is claimed as a thermodynamic cooling effect. Lightning consist of 5 −15 Coulomb which are up to 1030 charge quanta, i.e. #znt in CRCCS. Accordingly, a minimal generated matter of 10−5gis capable to induce a strong energy effect felt as cooling within DPAPP. As a result, one has the relations ρion ≪ρdark, ρmand ρdark ≃ −ρm. Vacuum energies ρvac(GR), ρvac(QS) mainly split into positive and negative parts ρm,ρion,ρdark which would be capable to explain the Dirac Sea. The DPAPP energy gain δρdark is achieved by a certain amount of created organic matter which lowers ρdark. In distinction to the CRCCS gain δρdark present bioenergy extracts energy from the O. Ziep excitonic binding energy δρexc,vdW . In distinction to ion-aerosol clear-sky mechanism of condensation nuclei through cloud brightness and cover the CRCCS-cooling effect in VTglobal (z) is due to complex matter ρdark. Within CRCCS zeros ξ(z) = 0 generate compensating negative phantom energy ρdark and positive large rest mass energy. Composting within ξ(z)=0 states (4) makes the cooling effect disappear [18] [19] [20]. 7. Conclusions A doubly-periodic processing is a current-current correlation of many participating periods. In natural science it is realized by breathing of plants and living and cellular respiration, photosynthesis. Simultaneous oneperiodic cycles of complex energy/time superimposed by one-periodic cycles of complex entropy/temperature are shown to dominate the behavior of zeta functions in the vicinity of nontrivial zeros. Instead of being an exotic state of matter it is a breathing by growing plants and livings being. A fluctuating complex time-thermal contour process is claimed to achieve lower vacuum densities which is capable to derive quantum statistics [21, 22]. Ranges of measured vacuum density vary from general relativistic values ρvac ≃1eV ·cm−3, ρvac(CMB)≃0,26 eV ·cm−3, ρvac(star)≃ 0,3eV ·cm−3which are to at ground level. Theory of the CCP ρvac(QS)≃ 1050−20, ρvac(GR) indicates the validity of elliptic involution. CRCCS is based on complex phantom dark energy ρdark of the order rest energy of a molecule but with opposite sign which would be stored in a DPAPP. DPAPP processing as breathing works on the background of existing branching and ramification in clouds and plant growth and claims a certain amount of ‘creatio ex nihilo’ of matter in zero states ξ= 0 or σ= 0 of a holomorphic atmospheric environment. References [1] Heegner, K. Diophantische Analysis und Modulfunktionen. Mathematische Zeitschrift 56, 227–253 (1952) [2] Ziep, O. Fractal Universe and Atoms. Scholars Journal of Physics, Mathematics and Statistics 12, 89–96 (2025) 10.36347/sjpms.2025. v12i04.002 [3] Dirac, P A M (19M4) Cosmological Models And The Large Numbers Hypothesis, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 338, 439–446. https://doi.org/10.1098/ rspa.1974.0095 [4] Ziep, O. Cosmic Rays, Aerosol-Photosynthesis and Vegetational Air Ion. 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