“It’s a nice ‘tip of the cap,’” Wallack said. “It also allows us to settle, once and for all, the question of whether the charters are operating with any selection bias because all families would use exactly the same admissions process. Equity. One system.”

Common — sometimes known as “universal” — enrollment systems exist in cities from Newark to Indianapolis. Backers of the approach argue it can simplify the often complex and time-intensive process required to apply to either district or charter schools in cities that allow parents to choose among both. Streamlining the process can put parents on equal footing instead of allowing those with more time, knowledge or resources from automatically getting a leg up.

Kavanaugh displayed no such poise or sense of the world beyond himself. His opening remarks, all partisan fury, sniveling self-pity, and distortion of the truth, set the tone for the afternoon. Exhibiting petulant disdain for Democratic members of the committee, he came off as nothing so much as the entitled adolescent he memorialized in a summerful of calendar entries, unable to believe his parents are about to ground him for the weekend. He raged at the prospect of being deprived of a job he apparently assumed was his by dint of mere pedigree. At times he seemed barely in control of his anger; perhaps he truly cannot remember doing what he has been accused of. Nevertheless, his reaction to questions about his drinking habits from Minnesota Senator Amy Klobuchar—“What about you, Senator? Do you ever black out?”—was not just disrespectful but disturbing, and his apology for it devoid of real contrition. Though he loudly proclaimed his innocence, he repeatedly declined to say whether he would support additional investigation by the FBI into the allegations against him. Kavanaugh’s belligerence had a contagious effect on Republican members, stirring Lindsey Graham to preposterous expressions of indignation on the nominee’s behalf. Rachel Mitchell, the Arizona sex-crimes prosecutor Republican senators chose to question Ford in their place, was sidelined soon after Kavanaugh was sworn in; to him, they preferred to speak man to man, fanning his anger with their own.

There were reasons to oppose Kavanaugh’s elevation to the Supreme Court even before allegations of misconduct came to light. His record suggests hostility toward voting rights and affirmative action, and his originalist stance on Constitutional interpretation seems fully in line with conservative aims to dismantle government programs and further deregulate the economy. His writings suggest an expansive view of executive power—troubling especially now, given the current president’s musings on self-pardon and threats to end the investigation into Russian interference with the 2016 election. Kavanaugh’s time as a Republican party operative—from his role in drafting the 1998 Starr Report, which laid out grounds for impeaching President Bill Clinton, to helping stop the Florida recount in the 2000 presidential election—raises legitimate questions about his impartiality. He seems to have been less than fully truthful in sworn testimony about his knowledge of documents stolen from Democrats when he worked in the George W. Bush administration.

The classmate, Chad Ludington, who said he frequently socialized with Judge Kavanaugh as a student, said in a statement that the judge had been untruthful in testimony to the Senate Judiciary Committee when he had denied any possibility that he had ever blacked out from drinking.

Mr. Ludington said that Judge Kavanaugh had played down “the degree and frequency” of his drinking, and that the judge had often become “belligerent and aggressive” while intoxicated. Other former classmates have made similar claims.

“It is truth that is at stake, and I believe that the ability to speak the truth, even when it does not reflect well upon oneself, is a paramount quality we seek in our nation’s most powerful judges,” Mr. Ludington said, adding that he planned to “take my information to the F.B.I.”

Mr. Ludington, a professor at North Carolina State University who appears to have made small political contributions to Democratic candidates, said to The New York Times on Sunday that he had been told by the F.B.I.’s Washington, D.C., field office that he should go to the bureau’s Raleigh, N.C., office on Monday morning. He said he intended to do that, so he could “tell the full details of my story.”

It is illegal to lie to Congress. But it was unclear whether the F.B.I. would add Mr. Ludington’s accusations to the newly reopened background investigation into allegations of sexual misconduct against Judge Kavanaugh, which has been limited in scope and time by the White House and Senate Republicans.

The White House had no immediate comment about Mr. Ludington’s accusations.

Even before Mr. Ludington’s statement, Democrats in Washington reacted with anger on Sunday as the narrow scope of the new F.B.I. background inquiry became clear, warning that it threatened to become a sham…

Democrats have cast the initial list of those to be interviewed as falling short of a full examination of the allegations. The four witnesses are Mark Judge and P.J. Smyth, high school friends of Judge Kavanaugh’s; Leland Keyser, a high school friend of one of Judge Kavanaugh’s accusers, Christine Blasey Ford; and Deborah Ramirez, another of the judge’s accusers.

A lawyer for Dr. Blasey, who riveted the nation on Thursday as she recounted before the Judiciary Committee what she said was a rape attempt by a drunken Judge Kavanaugh when they were in high school, said on Sunday that she had not been contacted by the F.B.I.

Judge Kavanaugh portrayed himself in his testimony as enjoying a beer or two as a high school and college student, but not as someone who often drank to excess during those years. “I drank beer with my friends,” he said. “Almost everyone did. Sometimes I had too many beers. Sometimes others did. I liked beer. I still like beer. But I did not drink beer to the point of blacking out,” he said.

This is disputed.

His statements are at odds with how some of his classmates remembered him. In interviews before his testimony, nearly a dozen college classmates of Judge Kavanaugh’s said they recalled him indulging in heavy drinking, some saying it went beyond normal consumption. (To be sure, a smaller number of classmates said his drinking was unexceptional.)

Reached after the hearing, Lynne Brookes, an undergraduate classmate of Judge Kavanaugh’s at Yale University, said she believed he had “grossly misrepresented and mischaracterized his drinking.”

“He frequently drank to excess,” she said. “I know because I frequently drank to excess with him.”

Ms. Brookes was roommates with Deborah Ramirez, who told The New Yorker that Judge Kavanaugh exposed himself to her during a drinking game while they were students.

Like Judge Kavanaugh, Ms. Brookes, a Republican, was an athlete who went to a prestigious graduate school after Yale. She disputed the implication in his testimony that he could not have overindulged because he was too busy studying and competing in athletics. “It is completely possible to do both,” she said.

Another Yale classmate, Elizabeth Swisher, now a Seattle physician, said: “I drank a lot. Brett drank more.”

“I definitely saw him on multiple occasions stumbling drunk where he could not have rational control over his actions or clear recollection of them,” said Daniel Lavan, who lived in Mr. Kavanaugh’s dorm freshman year. “His depiction of himself is inaccurate.”

Judge Kavanaugh disputed such accounts, saying they did not point to specific instances. But his own recollections have offered clues about his drinking. His high school yearbook, for example, refers to him as the treasurer of the Keg City Club, noting “100 Kegs or Bust.” Multiple high school classmates, in interviews, described Judge Kavanaugh as a heavy and frequent drinker.

As an undergrad, he was affiliated with two organizations known for hard partying, including the fraternity Delta Kappa Epsilon.

He also recounted his own drinking exploits in speeches. In a 2014 address to Yale Law students, he recalled a night of “group chugs” in Boston that ended with his group “falling out of the bus onto the front steps of Yale Law School at about 4:45 a.m.”

A Display of Affection

A substantial portion of Judge Kavanaugh’s testimony was devoted to discussing his 1983 senior yearbook. In one entry, he described himself as a “Renate Alumnius,” referring to Renate Schroeder, now Renate Dolphin, who attended a nearby Catholic school. A number of his football teammates had similar entries. Judge Kavanagh said: “That yearbook reference was clumsily intended to show affection, and that she was one of us. But in this circus, the media’s interpreted the term is related to sex. It was not related to sex.”

This is disputed.

Four of Judge Kavanaugh’s former schoolmates, including Sean Hagan, said the notion that the phrase was meant affectionately did not ring true. They said that Judge Kavanaugh and his friends often made disrespectful sexual comments about Ms. Dolphin, and that the understanding at the time was that the many yearbook references to her were boasts about sexual conquests.

On Monday, Judge Kavanaugh’s lawyer told The Times that the “Renate Alumnius” note referred to a school event that he and Ms. Dolphin attended, after which they “shared a brief kiss good night.” Ms. Dolphin responded that they had never kissed.

On Thursday, Judge Kavanaugh steered away from the idea that the yearbook reference had any sexual connotations. “We never had any sexual interaction,” he said.

After his testimony ended, Mr. Hagan wrote on Facebook: “So angry. So disgusted. So sad. Integrity? Character? Honesty?”

Yearbook Lingo

Judge Kavanaugh’s yearbook page included the entries “Judge — Have You Boofed Yet?” and “Devil’s Triangle.” On Thursday, he said that “boofed” meant “flatulence” and that “Devil’s Triangle” was a drinking game in which three glasses were arranged in a triangle.

This is disputed.

“Boofed” in the 1980s was a term that often referred to anal sex, and that is how Judge Kavanaugh’s classmates said they interpreted his comment. They said they had never heard it used to refer to flatulence.

Similarly, they said that they had never heard of a drinking game called Devil’s Triangle, but that the phrase was regularly used to describe sex between two men and a woman. “The explanation of Devil’s Triangle does not hold water for me,” said William Fishburne, who managed the football team during Judge Kavanaugh’s senior year.

“Our senior yearbook pages were a place to have a little bit of fun with commemorating inside jokes,” said Bill Barbot, who overlapped with Judge Kavanaugh at Georgetown Prep, an all-boys Catholic school. “However, the spin that Brett was putting on it was a complete overstatement of the innocence with which they were intended.”

His Social Circle

Asked about the intersection of his and Ms. Blasey’s friend groups, Judge Kavanaugh said: “When my friends and I spent time together at parties on weekends, it was usually with friends from nearby Catholic all-girls high schools — Stone Ridge, Holy Child, Visitation, Immaculata, Holy Cross. Dr. Blasey did not attend one of those schools. She attended an independent private school named Holton-Arms, and she was a year behind me.”

This is disputed.

Judge Kavanaugh’s implication is that students at Holton-Arms, an all-girls school, didn’t mingle much those who attended Georgetown Prep. Two of Judge Kavanaugh’s former schoolmates said on Friday that this was not true and that Holton-Arms students were routinely present at parties with Georgetown Prep boys.