This supplementary material provides detailed information on the planetary boundaries framework, focusing on Earth's systems beyond the nine planetary boundaries. The study uses Holocene conditions as a reference, representing the stable state of the Earth system from 11,700 years ago to the present. The Holocene is characterized by a relatively stable climate, with global mean surface temperature oscillating only 0.5°C from pre-industrial levels. The Earth system modeling and ice-core data show that the Earth system has never exceeded a 2°C global mean surface temperature during warm inter-glacial periods, indicating its capacity to remain within inter-glacial conditions. The biosphere integrity boundary is updated to include genetic diversity, which is crucial for ecosystem resilience and productivity. The study highlights the need for better data and methods to assess genetic diversity, with new approaches like macrogenetics helping to capture global genetic variability. The biosphere function is measured by human appropriation of net primary production (HANPP), compared to Holocene values. The study estimates the Holocene mean NPP as 55.9 GtC yr⁻¹, with a standard deviation of 0.54 GtC yr⁻¹. The climate change boundary is set at 350 ppm for atmospheric CO₂ and 1 W m⁻² for radiative forcing. The ozone depletion boundary is based on current ozone values from NOAA. The freshwater change boundary is defined by the variability in pre-industrial periods, with the global boundary set at the upper limit of this variability. The study finds that the freshwater change boundary has been transgressed, with significant deviations from pre-industrial levels. The land system change boundary is defined as the area of forested land maintained, with 75% of potential forest cover remaining. The study finds that seven of the eight major forest biomes have transgressed this boundary. The ocean acidification boundary is based on the saturation state of aragonite, with the current value estimated at 2.8, indicating a significant decrease from pre-industrial levels. The study also discusses aerosol loading, which has physical and biogeochemical effects on the Earth system. The model simulations show that the CM2Mc-LPJmL model performs well, with results comparable to other models. The study finds that the climate and land system change boundaries have been passed, with the current state heading towards the upper end of the zone of increasing risk. The results suggest that maintaining the climate change boundary at 350 ppm would result in a temperature increase of about 1.3°C, below the Paris target of 1.5°C. The study also highlights the importance of land system change in stabilizing the climate, with the current state indicating a potential for further transgression.This supplementary material provides detailed information on the planetary boundaries framework, focusing on Earth's systems beyond the nine planetary boundaries. The study uses Holocene conditions as a reference, representing the stable state of the Earth system from 11,700 years ago to the present. The Holocene is characterized by a relatively stable climate, with global mean surface temperature oscillating only 0.5°C from pre-industrial levels. The Earth system modeling and ice-core data show that the Earth system has never exceeded a 2°C global mean surface temperature during warm inter-glacial periods, indicating its capacity to remain within inter-glacial conditions. The biosphere integrity boundary is updated to include genetic diversity, which is crucial for ecosystem resilience and productivity. The study highlights the need for better data and methods to assess genetic diversity, with new approaches like macrogenetics helping to capture global genetic variability. The biosphere function is measured by human appropriation of net primary production (HANPP), compared to Holocene values. The study estimates the Holocene mean NPP as 55.9 GtC yr⁻¹, with a standard deviation of 0.54 GtC yr⁻¹. The climate change boundary is set at 350 ppm for atmospheric CO₂ and 1 W m⁻² for radiative forcing. The ozone depletion boundary is based on current ozone values from NOAA. The freshwater change boundary is defined by the variability in pre-industrial periods, with the global boundary set at the upper limit of this variability. The study finds that the freshwater change boundary has been transgressed, with significant deviations from pre-industrial levels. The land system change boundary is defined as the area of forested land maintained, with 75% of potential forest cover remaining. The study finds that seven of the eight major forest biomes have transgressed this boundary. The ocean acidification boundary is based on the saturation state of aragonite, with the current value estimated at 2.8, indicating a significant decrease from pre-industrial levels. The study also discusses aerosol loading, which has physical and biogeochemical effects on the Earth system. The model simulations show that the CM2Mc-LPJmL model performs well, with results comparable to other models. The study finds that the climate and land system change boundaries have been passed, with the current state heading towards the upper end of the zone of increasing risk. The results suggest that maintaining the climate change boundary at 350 ppm would result in a temperature increase of about 1.3°C, below the Paris target of 1.5°C. The study also highlights the importance of land system change in stabilizing the climate, with the current state indicating a potential for further transgression.