The Mueller report, holding itself to the higher standard, concluded that it did not find proof beyond a reasonable doubt of criminal conspiracy with Russia. It also offered an explanation: Lies by individuals associated with the Trump campaign “materially impaired the investigation of Russian election interference.” Witnesses deleted emails and used applications with encryption or deletion functions, which also thwarted fact-finding. Part II of the report on obstruction explains why Part I may have fallen short of such a high burden.

Mr. Barr had the analysis backward in his summary letter. The failure to prove an underlying crime does not mean there was no obstruction. The obstruction meant that it became impossible to know whether there was a conspiracy beyond a reasonable doubt — and it impeded the Russian investigation. Mr. Barr then used that doubt to question whether there was the corrupt intent required by obstruction statutes. To the contrary, the preponderance of conspiracy evidence confirms the corrupt intent.

The report’s core question of whether the Trump campaign “conspired” or “coordinated” with the Russian government is a difficult legal question for any prosecutor. Criminal campaign finance charges — as opposed to civil — require proof that “a violation must have been committed knowingly and willfully,” that the defendant knew he was breaking the law, which is notoriously hard to prove. The “reasonable doubt” problem rightly prevents indictments here, but a preponderance standard is sufficient for an interpretation for public debate based on more-likely-than-not facts.

Even without knowing what is redacted, the report offers “substantial and credible information” of the Trump campaign conspiring or coordinating with the Russian government. Under federal criminal law, “conspiracy” does not require direct proof or explicit words of agreement. It can be proven by action and circumstantial evidence from which the agreement may be inferred. And on campaign “coordination,” the Mueller report made a significant omission or oversight on this question when it stated that “‘coordination’ does not have a settled definition in federal criminal law. We understood coordination to require an agreement — tacit or express.”

As the election law expert Paul Seamus Ryan noted, Congress in its 2002 campaign finance law rejected that view: Federal law “shall not require agreement or formal collaboration to establish coordination.” The federal regulations followed this command: “Coordinated means made in cooperation, consultation or concert with, or at the request or suggestion of, a candidate,” with no need to show any kind of agreement. Expenditures for coordinated communications are considered in-kind contributions, and foreign contributions — public or private — are illegal. In fact, the Federal Election Commission is reviewing a complaint along these lines.

The report states that Rick Gates, a campaign deputy, suspected that Mr. Manafort’s Russian associate, Konstantin Kilimnik, was a “spy,” a view that he shared with Mr. Manafort (and others). For months, Mr. Manafort informed Mr. Kilimnik about the campaign through internal polling data, even pointing out that Wisconsin, Pennsylvania, Michigan and Minnesota were target states. The Mueller report did not conclude their motives were criminal beyond a reasonable doubt, but by a preponderance in context, the motives were clearly campaign related and likely a coordination with Russia.

Despite being heavily redacted, the report seems to add context to Roger Stone's indictment, implicitly suggesting that Mr. Trump may have directed officials to contact Roger Stone about WikiLeaks, and may have been in contact with Mr. Stone about WikiLeaks. It may not be proven beyond a reasonable doubt that they knew WikiLeaks was an extension of Russian hacking and a Russian campaign, but it is more likely than not a kind of indirect coordination with a foreign government prohibited by law. And Donald Trump Jr.’s continuing contacts with WikiLeaks in September and October 2016, long after the Trump Tower meeting and the July events made its connection to a Russian campaign clear, also were likely a coordination, even if not knowingly proven beyond a reasonable doubt.