Europe recorded only about 4 or 5 of the 11 comets China recorded in the 11th century

Chinese comets in Williams 1871 for 1000 to 1100: 1003, 1014, 1018, 1035, 1036, 1049, 1056, 1066, 1075, 1080, 1097. Pingre 1783 cites European records for 1003-04 (a long comet 'like a great beam'), 1018 (Hepidannus and others), 1066 (Halley's comet) and 1097 (Florence of Worcester and others), and a Byzantine one for 1035 (Cedrenus: 'a column of fire in the east'); for 1049, 1075 and 1080 he has only the Chinese record, and none found for 1014, 1036 and 1056. So medieval Europe missed more than half of the sky events China logged, and its silence about the 1054 star is roughly what that rate predicts. Caveat: neither catalogue is complete and the scan has errors.