The Japanese '4th month' date for the 1054 star is impossible; the 5th month fits
Meigetsuki (quoting an older record): the guest star appeared in the middle ten days of the 4th month of Tenki 2. Converted with the Senmyo calendar: 20 to 29 May 1054, when the star was only 2 to 7 degrees from the Sun, lost in its glare. The 5th month's middle ten days (19 to 28 June) put it 22 to 31 degrees from the Sun, well placed at dawn and a week or two before China's 4 July. Agrees with the usual reading that '4th' is a copying slip for '5th' (Stephenson and Green).