Those records are known as “caucus math worksheets.” The party only corrected discrepancies between the data as recorded on the worksheets and what was officially reported in public releases of the results.

The party could not change even blatant miscalculations on the worksheets, according to a lawyer for the party, because they were a legal record and altering them would be a crime.

“The incorrect math on the Caucus Math Worksheets must not be changed to ensure the integrity of the process,” wrote the party lawyer, Shayla McCormally, according to an email sent by Troy Price, the chairman of the party, to its central committee members. The lawyer said correcting the math would introduce “personal opinion” into the official record of results.

Thanks to greater transparency in reporting the caucus results this year, outsiders were able to identify internal inconsistencies. The New York Times reported last week that some precincts, for example, had awarded more delegates to candidates than they were allotted.

In addition, caucus “captains” for individual candidates photographed the worksheets in their precincts and shared them internally with their campaigns. Those photographs provided further examples of problems. The most blatant were errors in adding up votes for candidates, which take place in two rounds, and miscalculations when using a formula that translates raw votes to “state delegate equivalents.”

But because the caucus chair and secretary of each precinct had certified the results on the worksheets, along with representatives of candidates, the documents could not be readjusted without violating election law, the state party lawyer said.

“It is the legal voting record of the caucus, like a ballot,” Ms. McCormally wrote in her opinion. “The seriousness of the record is made clear by the language at the bottom stating that any misrepresentation of the information is a crime. Therefore, any changes or tampering with the sheet could result in a claim of election interference or misconduct.”