Washington (CNN) Seven months after he joined the US Supreme Court, the cloud of Christine Blasey Ford's sexual assault allegations still hangs over Justice Brett Kavanaugh , recalled in media reports across the political spectrum and unresolved in the US judiciary's own process for handling related ethics claims.

The names of Kavanaugh and Ford were repeatedly invoked in news stories as former Vice President Joe Biden entered the 2020 presidential race last week and began addressing his treatment of Anita Hill in the 1991 Supreme Court hearings for Clarence Thomas -- a point of comparison with the Ford-Kavanaugh face-off in the Senate last fall.

Stephen Moore, President Donald Trump's newly withdrawn nominee to the Federal Reserve, said his media critics were " pulling a Kavanaugh " against him with complaints related to his regard for women.

At the same time, formal ethics grievances filed against Kavanaugh based on his testimony in response to the Ford sexual-assault allegations are moving to a higher level of the judicial misconduct process.

The Ford connection was reinforced when Time Magazine recently named both as among the "100 Most Influential Americans," a move that itself generated a flood of public commentary, for and against. One of those comments, from actress Jessica Chastain, triggered a separate round of media coverage. She wrote on Twitter : "You put her on the same list as the man she said assaulted her. So disappointing @TIME."

The Time entry honoring Kavanaugh was penned by Republican Senate Majority Leader Mitch McConnell, who helped ensure the vote that got Kavanaugh on the bench, writing that the nominee's response demonstrated "his resilience."

Attention on Kavanaugh, now 54, will only rise as the Supreme Court finishes its term. The jurist who succeeded centrist conservative Justice Anthony Kennedy is likely to change the outcome of some closely watched cases, moving the law in America to the right.

Among the disputes to be resolved before the traditional end-of-June deadline are those over a 40-foot "Peace Cross" on public ground in Maryland, partisan gerrymanders in North Carolina and Maryland, and a proposed citizenship question on the 2020 census. The court could also soon announce whether it will consider an appeal over a controversial Indiana abortion law.

One question, particularly swirling in conservative circles, is whether Kavanaugh might mute his conservatism and join with Chief Justice John Roberts to avoid some social policy flashpoints such as abortion or rule narrowly to prevent a dramatic rightward shift.

Ongoing review of complaints

A Denver-based judicial council last December dismissed a total of 83 complaints (some of which were unconnected to Ford), saying it lacked authority to address the claims because Kavanaugh, as a Supreme Court justice, was no longer covered by the judiciary's ethics code. That decision was reinforced by the judicial council in March.

Now some of those complaints have been appealed to a conduct committee of the US Judicial Conference, the top policy-making arm of the third branch, overseen by Roberts. There is no deadline for any investigation or another dismissal.

The high-court exemption can protect justices from scrutiny, but it also leaves claims -- both frivolous and with merit -- unanswered in the public eye.

Ford, a Palo Alto University professor, accused Kavanaugh of sexually assaulting her when they were teenagers just outside of Washington.

Kavanaugh declined, through a spokeswoman, to comment on the ongoing claims or public attention tied to the Ford allegations. Palo Alto University referred questions for Ford to Ricki Seidman, a Democratic political strategist advising Ford. Seidman was a Senate Judiciary Committee staffer during the Hill-Thomas hearings in 1991 and in 2009 helped prepare Sonia Sotomayor, President Barack Obama's first high court nominee, for her confirmation.

"Christine hasn't made any public comments and doesn't have any current intentions to do so," Seidman wrote in an email to CNN.

Kavanaugh was sworn in at the Supreme Court on October 6, immediately after the Senate vote. A large crowd of protesters surged onto the front steps of the marble-columned building, pounding on doors and chanting , "Hey hey, ho ho, Kavanaugh has got to go."

Three days later at the White House, the President apologized to Kavanaugh for the hearing ordeal and said, as the other eight justices sat in the audience, that Kavanaugh had been "proven innocent."

But Ford's claim was never truly tested, neither conclusively dismissed nor conclusively validated. The continuing controversy over whether judicial ethics grievances can be resolved does not involve any behavior tied to Kavanaugh's teenage years but rather his testimony before senators last fall.

In his televised September 27 appearance before the Senate Judiciary Committee, Kavanaugh emphatically denied Ford's accusations. He asserted that her claims arose from "a calculated and orchestrated political hit, fueled with apparent pent-up anger about President Trump and the 2016 election ... revenge on behalf of the Clintons and millions of dollars in money from outside left-wing opposition groups."

JUST WATCHED Watch how senators grilled Anita Hill in 1991 Replay More Videos ... MUST WATCH Watch how senators grilled Anita Hill in 1991 02:39

Among the 83 misconduct claims filed against Kavanaugh were those alleging that his response to the Ford accusation was inappropriately partisan, demonstrating bias and a lack of judicial temperament. Others accused him of making false statements during the 2018 hearings and in 2004 and 2006 when he was being considered for a seat on the US Court of Appeals for the District of Columbia Circuit.

When a US appeals court's judicial council considered the complaints, which had been referred to it by Chief Justice Roberts, the council said the claims could not be examined or resolved because Kavanaugh, once confirmed to the high court, was exempt from the 1980 judicial misconduct law.

"The allegations contained in the complaints are serious," the 10th Circuit Chief Judge Timothy Tymkovich wrote, "but the Judicial Council is obligated to adhere to the Act. Lacking statutory authority to do anything more, the complaints must be dismissed because of an intervening event -- Justice Kavanaugh's confirmation to the Supreme Court -- has made the complaints no longer appropriate for consideration under the Act."

In March, after 20 of the complainants had appealed, the 10th Circuit council reaffirmed that decision. "The lack of jurisdiction over Justice Kavanaugh precludes an investigative and fact-finding process, even over conduct allegedly committed while Justice Kavanaugh was a covered judge," the council wrote

A number of complainants have now appealed to the US Judicial Conference Committee on Judicial Conduct and Disability. The National Law Journal first reported this week on the new, mostly confidential, Kavanaugh-related filings.

David Sellers, spokesman for the Administrative Office of the US Courts, said such appeals to the Judicial Conduct and Disability Committee are generally not made public and there is no timetable for the review. Any final opinion from the conduct committee regarding the appeals would be published online on the federal courts' site

Paul Horvitz, a financial writer based in Massachusetts and one of the few people who has spoken publicly about his complaint against Kavanaugh, told CNN he believes the silence of the judicial branch undermines public confidence in the courts.

He referred to the television audience that watched the Kavanaugh hearings last September. "Millions of Americans who assume that judges act impartially were eyewitnesses to a textbook violation, by no less than a Supreme Court nominee, of ... 'inappropriately partisan statements,' " Horvitz wrote in his petition. "The public at large may have been unaware of the specifics of the Code and Rules, but vast numbers undoubtedly saw something wrong."

Travel to England

In the meantime, as the 2018-19 court session winds down, Kavanaugh, like the other justices, has begun scheduling extracurricular activities.

That has not been without controversy. After the Virginia-based George Mason University law school hired him to teach a course on the origins of the US Constitution in Runnymede, England, this summer, some students protested and urged the university to cancel the teaching arrangement.

George Mason University President Angel Cabrera responded on March 27 that he has "respect" for those who disagreed with Kavanaugh's confirmation, but the invitation will not be rescinded.