Fig. 3: Astronomical forcing and geological records between 337–300.6 Ma.

a Our refined Carboniferous chronostratigraphy with numerical ages for the basal Serpukhovian and Bashkirian, and ages for the basal Moscovian, Kasimovian and Gzhelian are after Global Time Scale (GTS) 2020²⁷. b Glacial frequency⁷⁴. LPIA—Late Paleozoic Ice Age; c Tropical forests including dryland biomes (DB) and wetland biomes (WB)¹⁴. WB 1—lycopsid-dominated forest; WB 2—lycopsids/cordaitalean co-dominated forest; WB 3—lycopsid-dominated forest, with an understory of marattialean tree ferns; WB 4—marattialean tree fern-dominated forest; DB 1—canopy cordaitalean-dominated forest; DB 2—walchian conifer-dominated open woodland. d Compiled atmospheric CO₂ record⁸. e Astronomically calibrated carbonate δ¹³C (δ¹³C_carb) series from Narao section. f Astronomically-calibrated gamma ray (GR) series from Narao section and its low-pass filter output (1.5 Myr⁻¹). KGB—Kasimovian/Gzhelian boundary. g Amplitude modulation (AM) of orbital eccentricity obtained from our GR series. AM (orange bold curve) of the ~100-kyr short eccentricity band (9 ± 2 Myr⁻¹) and its 2.4-Myr filter output (0.42 ± 0.08 Myr⁻¹). h AM of obliquity obtained from our GR series. AM (blue bold curve) of the ~31-kyr obliquity band (32.7 ± 1.8 Myr⁻¹) and its 1.2-Myr filtering output (0.85 ± 0.12 Myr⁻¹). i Onlap (transgression)–offlap (regression) history from the Donets Basin³³, adjusted to the GTS2020²⁷. Glaciation events are indicated by the glacio-eustatic sea-level lowstands³³. Warming intervals from refs. ^8,38. j Evolution of phase-relationship between GR and δ¹³C_carb on 405-kyr (purple area) and 95–132-kyr (blue area) eccentricity time scales (4-Myr-analysis window width and 0.25-Myr steps). CL—confidence level. k Two intervals (i.e., 330.35–328.7 Ma and 306.8–305.2 Ma) demonstrating the inphase and anti-phase behaviors of two proxies on 405-kyr band. 405-kyr eccentricity signals (red curves) were obtained using a passband of 2.46 ± 0.15 Myr⁻¹ on each data series.