LYNN – With the state-mandated cap on charter schools a thing of the past, four groups have submitted charter prospectuses to the state this month, hoping to establish schools in the Greater Lynn area to serve the city’s underprivileged youth.With radical ideas and non-traditional concepts abound, the four proposed charters would span all grades – including the 13th grade, as suggested in one prospectus – and provide parents with a variety of unique options when choosing a school for their child.The state Department of Education received proposals from the Lynn Preparatory School, North Shore Charter School of Science, BridgeSmart Preparatory Academy and Road to Success Charter High School, all of which state an intention to either open a school in Lynn or serve the students of Lynn in a neighboring community.Of the four schools, only the Lynn Preparatory School is not listed as a regional school, meaning it would serve only students from Lynn.Proposed by the husband and wife education team of Mark Hathaway and Joanne Civitarese, the K-8 charter would be a cousin of the Hathaway School, a private elementary school run by the couple. Once located on Broadway in Lynn, the Hathaway School moved to Swampscott in 2007.The North Shore Charter School of Science lists its proposed location as Lynn or Saugus and is organized by the leaders of the Pioneer Charter School of Science in Revere. The K-12 school would use the Full Option Science System (FOSS) curriculum, which includes mainly research-based study.Serving grades 7-13, with a two-part senior year creating “13th grade,” the BridgeSmart Academy is perhaps the most radical of the four schools, proposing an 8 a.m.- 8 p.m., 210-day academically intensive schedule. Founded by Kiyoshi Yu, a former employee of Sens. John Kerry and Edward Kennedy, the school would be located in Lynn, Revere, Chelsea or Everett and specialize in serving bi-lingual students in their native languages.Finally, the Road to Success High School, proposed for Salem, would serve as an alternative to the area’s public high schools, providing a longer day and more structured environment for at-risk students. Unlike other charters, the RTS school would allow mid-year enrollments, breaking the 40-week schedule into four 10-week sessions.With boards of directors containing members from both the business and education worlds, all four charter schools cite the same problems and offer similar solutions to improving academics in the areas.While the schools differ on grade levels and academic philosophy in some areas, all are organized with the goal of improving the academic standards for economically and socially poor students through discipline, longer school days and hands-on instruction.If the schools, which are in the very first stage of the charter process, do eventually open, the results could be damning to the city if current charter school legislation remains unchanged.As it stands now, the city loses a percentage of Chapter 70 local aid funding for every Lynn student who attends a charter school in or out of the city – the money going to those charters as aid for the student’s education.If more charters open, the city will lose more local aid unless the policy is changed.Superintendent Catherine Latham was presented with the prospectuses Thursday and said she was not surprised to see proposals, although she did not agree with the statistics and statements made about the Lynn Public Schools in some cases.”I don’t object to charter schools as long as we are going to be able to play by the same rules,” said Latham. “Right now it doesn’t look like that is how it is going to be. Right now we aren’t playing by the same rules at all.”Much of the argument for charter schools is based on their reputation for drastically improving student achievement, as shown on state mandated tests, such as the MCAS. KIPP Academy Lynn, which serves students in grades 5-8 in the city, has boasted some of the most competitive MCAS scores