WASHINGTON — Representative Jason Crow, Democrat of Colorado, kept the pen he was prepared to brandish as a weapon if the rioters who stormed the Capitol in the name of Donald J. Trump made it to where he was in the House chamber last Jan. 6.

Senator Amy Klobuchar of Minnesota, the top Democrat on the Rules Committee, framed an official tally certifying President Biden’s electoral victory, along with a pen used to sign it, after the tear gas had cleared following the assault.

And upon request, Representative Andy Kim, Democrat of New Jersey, donated to the Smithsonian the blue J. Crew suit he wore during the attack, though he kept a broken golden eagle he gingerly removed from the debris while picking up trash in the Rotunda after the mayhem.

“They’re artifacts of the day and what happened,” Mr. Crow said in a recent interview. “I think it’s important for my family to be able to have those things as part of the ability to tell that story in the future.”

In the days after the attack, many who lived through it clung to tangible relics of the day — from panicked text messages they sent their families to the crumpled escape hoods they hurriedly unwrapped inside the House chamber — assembling their own makeshift memorials to one of the most destructive events in the history of the building.

But one year later, lawmakers and historians are still debating how Congress itself should memorialize the riot at the Capitol, which is both a working legislative body that came under attack and a living museum of American history. They are grappling with the thorny question of how, if at all, to officially mark an assault whose victims cannot agree on the basic facts of what happened.

The National Museum of American History, a branch of the Smithsonian, collected protest signs, posters and banners from the assault. Some of the debris and damaged items from the Capitol complex were handed over to the Justice Department. And a spokeswoman for the Architect of the Capitol, which oversees the building and its grounds, said the agency was examining options to display a collection once prosecutorial work against those who breached the building had concluded.

Some lawmakers are pressing for a far more detailed accounting of the day. House Democrats have introduced legislation that would require a permanent exhibit in the Capitol. A similar resolution was used to install a plaque that pays tribute to two Capitol Police officers killed defending the building from a gunman in 1998.

“It’s going to have to be told, and we have to make sure that we’re preserving that, because ultimately, what it shows is that democracy can be fragile if people don’t reinvigorate it and fight for it,” said Mr. Crow, a sponsor of the bill. “You have to make sure we’re telling that story to ensure that we have the resolve to do what’s necessary to preserve our democracy.”

Multiple lawmakers have called for the preservation of damaged items, particularly a cracked window in the Rotunda doors that open onto the plaza. That window has since been replaced, but it is unclear whether the shattered pane was kept.

“Hopefully, they will preserve some of what happened here so that the people can come and see it and remember what happened,” said Senator Mitt Romney, Republican of Utah, who broke with his party to support forming a bipartisan commission to investigate the attack.

But Republicans blocked that inquiry, and most of them have spent the past year downplaying or denying the significance of the assault, making it unlikely that they would back legislation to memorialize it.

Some Republicans argue that they have already paid appropriate tribute to what happened by supporting legislation that awarded the Congressional Gold Medal to the officers who responded. That measure ensures that medals will be displayed at the headquarters of the Capitol Police and the Metropolitan Police Department, one at the Smithsonian and one at the Capitol. A plaque at the Capitol will list all the law enforcement agencies involved in protecting the building.

Democrats plan to spend the anniversary on Thursday hosting a running series of memorials, reflecting on what they experienced and holding a vigil on the Capitol steps. With the exception of two hard-right lawmakers who plan to protest the treatment of the rioters, there is little indication that most Republicans plan to be involved in such public markings of the day.

The Capitol, of course, is filled with reminders of what happened. Riot shields are propped outside entrances to the building, and metal detectors have been installed outside the House chamber. Capitol Police officers still wrap black mourning bands around their badges to pay tribute to the colleagues they lost in connection with the riot.

But there is no official site or monument in the Capitol dedicated to explaining what happened, or reflecting on the wounds inflicted on the institution and American democracy itself on Jan. 6.

“I’ve still lacked the words to be able to describe to my kids what happened that day,” Mr. Kim said in an interview. “When we go through collective trauma, it’s often helpful to have some kind of collective outlet in which one can reflect on this and think through this. I find it to be just a missed opportunity for us to pay tribute to this building.”

For all of its grandeur, the Capitol is far more functional than a traditional museum. Most of its artifacts are on display, and several — from the gavels to the desks — are used on a daily basis. Many of the building’s tragedies and conflicts are not prominent for the casual visitor. The 1814 siege, when the British burned the Capitol, is marked by a ceiling painting in a first-floor hallway. A drawer in the Republican leadership desk remains damaged by bullets fired by Puerto Rican nationalists in the House chamber in 1954.

Even the acknowledgment of how the Capitol was built — a single block of sandstone to commemorate the work of enslaved African Americans — came over a decade after evidence of their work was unearthed. On rare occasions, Congress has approved individual plaques, including the one honoring the officers killed in 1998.

After the riot, three curator offices responsible for caring for the furnishings, paint and architecture of the Capitol quickly pivoted from their usual preservation work and the pandemic challenge of keeping hand sanitizer fingerprints off the historic furnishings to dealing with the devastation wrought by the rioters. They pooled resources to assess the damage, taking note of the pH balance left by fire extinguisher residue that could permanently harm sculptures and paintings, and swept away the rubble.

Farar Elliott, the House curator, told a House panel in February that millions of dollars would be needed to address the damage, including treating and cleaning the objects in the Capitol’s historic collection.

“And then, after that, take stock of what are the artifacts that tell the story of the people’s house right up through today,” she said.

Among the unanswered questions about how that story will be told is what Capitol tour guides will be instructed to say about Jan. 6. While guides undergo extensive training, there is no formal script, allowing them discretion in what they tell visitors as they guide them through the Rotunda, the Old Senate Chamber, Statuary Hall and other parts of the building.

“That’s the thing about public history — the audience is always going to play a major part,” said Lauren Rever, who worked as a visitor guide in the Capitol from August 2018 to December 2019. “We can try to predict, we can try to plan, but you never exactly know how that’s going to go. Right now, that’s what makes it a little scary.”