« A.U.C. 653 = 101 B.C. »
There is a probable synchronism in this year. Plutarch, Marius 26.4 can be read as telling us that Marius fought against the Cimbri "after the summer solstice, which the Romans place on a.d. III Kal. Sex." The information is said to come from Sulla's memoirs, so must be regarded as contemporary. However, the reading is disputed by Brind'Amour, Le calendrier romain 126, who argues that a.d. III Kal. Sex. is the date of battle, not of the solstice. He points out that the Greek for "which" is written differently in some MSS, and argues that the variant reading allows the phrase to be reconstructed as "the battle took place after the summer solstice, according to the Romans on a.d. III Kal. Sex." Brind'Amour further notes that Plutarch, Marius 26.2 records that Catulus vowed to consecrate "the fortune of that day"; and indeed the Fasti Pinciani and Fasti Alifani record a sacrifice to the fortuna huiusque diei in campo on a.d. III Kal. Sex.
The argument about variant readings in the MSS seems doubtful to me, but the fact that the date is the date of the sacrifice in the Fasti Pinciani and Fasti Alifani does support the view that a.d. III Kal. Sex. was the date of the battle, not of the solstice. So we can only conclude that this date fell in high summer, i.e. was approximately aligned with Julian July or possibly August; but in any case was after the summer solstice, June 26.
Since there are few synchronisms in these decades, variant models are certainly possible. On the reconstruction modelled here, a.d. III Kal. Sex. A.U.C. 653 = 3 July 101, which is the closest reconstruction in line with this requirement. A looser alignment to the solstice, a.d. III Kal. Sex. A.U.C. 653 = 26 July 101, is achieved by moving one of the intercalations currently placed after 101 to between A.U.C. 641 = 112 and 101. This would reduce variation in the density of intercalations between A.U.C. 641 = 112 and A.U.C. 668 = 86, which is currently modelled as one in three between A.U.C. 641 = 112 and 101 and one in two between 101 and A.U.C. 668 = 86. However, this date is the heliacal rising of Sirius, which is often noted as a calendrical marker in classical sources. If Plutarch has correctly reported Sulla's text, Sulla's decision to mark the date by the solstice suggests that the tighter synchronism is more correct.
For an argument that this year was regular, see discussion here.
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