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A lawsuit that claims Harvard caps the number of high achieving Asian-Americans it admits could go to trial in Boston as early as this summer, according to a new filing in the case.

The lawsuit, begun in 2014 by a conservative advocate who has long challenged affirmative action that benefits blacks and other historically disadvantaged racial minorities, could affect who gets a place on the selective Ivy League campus.

It could have even greater consequences nationwide. The case was devised ultimately to topple a 1978 US Supreme Court decision that first endorsed college affirmative action, Regents of the University of California v. Bakke.

Lawyers for both sides submitted a status report and proposed schedule Friday in US District Court in Boston. Harvard has asked that a trial begin in July or August. Students for Fair Admissions, the group that filed the complaint, wants a trial to begin no earlier than October 1. It says it would need the extra time to prepare for a trial of the size and scope anticipated.

The Students for Fair Admissions challengers, however, also say they want to file a summary-judgment motion by June 15, which would test whether they have already made the case that Harvard intentionally discriminates against Asian-Americans. Harvard contends that the group lacks the grounds even to make the motion and urged US District Judge Allison Burroughs to move directly to a trial.

The challengers recently finished data analysis of about 200,000 Harvard undergraduate admissions files from a six-year period. The files included students’ grades, test scores and extracurricular activities; demographic and legacy information; and admissions officers’ ratings.

Students for Fair Admissions’ team of analysts have been trying to detect patterns that would support the group’s claim that Asian-Americans are held to a higher standard than other applicants while the college puts a thumb on the scale for African-Americans and other minorities. The group contends that Harvard engages in unlawful racial balancing, violating Title VI of the 1964 Civil Rights Act.

In their Friday submission, the challengers said they had collected 37 deposition transcripts and other documentary evidence that includes “incriminating emails” and “Harvard’s own inculpatory studies.”

Harvard lawyers rejoined that “it is unsurprising that SFFA wishes to project confidence” and noted that Harvard, too, is confident in its case. The lawyers said the parties’ experts have offered competing analyses of the same set of admissions data.

From the start, Harvard has rejected the assertion that it sets Asian-American caps, and its officials emphasize the college’s goal of broad student diversity.

“To deliver on our educational mission,” Harvard spokeswoman Anna Cowenhoven told CNN in a recent statement, “our admissions practices consider the whole person, their capacity not only for academic excellence, but also their ability to contribute to and learn from people profoundly different from themselves.”

The case of Students for Fair Admissions v. Harvard is moving into a new phase as the Trump administration has separately begun investigating Harvard admissions policies.

Department of Justice officials said last fall that they were re-examining a 2015 discrimination complaint filed by 64 Asian-American groups against Harvard. That investigation is at an early stage, and it is not known whether the Trump administration would become involved in the Students for Fair Admissions case. The department could also bring its own lawsuit against Harvard if it finds the school wrongly discriminated based on race.

Affirmative action challenger

The case against Harvard was begun by conservative advocate Edward Blum, who has devised a series of US Supreme Court battles over racial remedies, typically enlisting white plaintiffs to challenge policies that give a boost to blacks and Hispanics. He created Students for Fair Admissions and sought Asian-Americans rejected by Harvard.

In taking up the cause of Asian Americans, Blum tapped into simmering complaints that Ivy League schools set caps on Asian applicants, as happened to Jewish applicants in early decades of the 20th century.

Yukong Zhao, president of the Asian American Coalition for Education, which has supported Blum’s effort and, separately, coordinated the groups that filed the complaint with the Justice Department, said Friday that Harvard is using “de facto racial quotas.” He said he hoped that the Department of Justice would lend its weight to the lawsuit in the form of an amicus “friend of the court” brief. Zhao said the coalition had recently provided additional information to the Justice Department regarding the exclusion of Asian-American applicants.

Harvard says it is seeking highly qualified individuals from different backgrounds and life experiences.

Harvard’s Cowenhoven provided numbers that showed that the percentages of admitted students, by race, have remained steady in recent years. For the class of 2021 (admitted last year), 22.2% were Asian-American, 14.6% were African-American, 11.6% were Hispanic or Latino and 2% were Native American. The “all other” category, which is mainly white, was 49.6%.

For the lawsuit, Harvard gave Students for Fair Admissions files from applicants covering six admissions cycles (beginning with 2009-2010), under strict terms of confidentiality. Names were redacted, and a protective order prohibited the group from trying to discover applicants’ identities.

None of its analysis has yet been made public, and Friday’s submission notes that the parties will be conferring in upcoming weeks to try to resolve what materials would become part of the public record.

Lawyers on both sides, as well as Judge Burroughs, have said they expect the case to be eventually resolved at the Supreme Court.

Blum, who relies on a battery of conservative donors for his efforts, engineered the high court case of Fisher v. University of Texas at Austin, which began in 2008 after a white student from suburban Houston, Abigail Fisher, was rejected by the flagship campus.

After two rounds before the justices, the court in 2016 upheld the University of Texas policy of considering race to enhance campus diversity, by a single vote.

Such narrow votes have been the pattern for Supreme Court disputes over affirmative action, beginning with the 5-4 Bakke in 1978.

CNN’s Laura Jarrett contributed to this report.