Synthesis of cultural evidence: Paul preserves gender-role meaning of coverings against both rich women and Roman ritual practices

1 Corinthians 11 itself is historical evidence: it implies a general rule in all churches that women cover and men don't. The passage starts with praise (most are doing it) and ends with concern about a few dissenters. After this section (v.17), Paul shifts to things most Corinthians are doing wrong (communion practices). Paul opts for the rule preserving gender relationships: men should be men, women should be women, including authority differences connected to gender, most clearly in marriage.