This supplementary material provides detailed information and supporting data for the study on Earth's planetary boundaries. It includes supplementary information, figures, tables, and references. The key points covered are: 1. **Reference Baseline**: The study uses Holocene conditions as a reference point, defined as the last 11,700 years of Earth's history, to assess the stability and variability of Earth's climate system. Holocene-like conditions are those that remain within the inter-glacial state, not exceeding thresholds that could irreversibly shift the Earth system away from Pleistocene inter-glacial conditions. 2. **Biosphere Integrity**: The importance of genetic diversity in species is highlighted, with recent advancements in whole-genome sequencing and macrogenetics providing new tools to capture global genetic variability. The functional integrity of the biosphere is measured by human appropriation of net primary production (HANPP) compared to Holocene values. 3. **Climate Change**: Control variables for atmospheric CO2 concentration and total effective anthropogenic radiative forcing are retained, with boundary levels set at 350 ppm and 1 W m-2, respectively. The upper end of the zone of increasing risk is set at 450 ppm for CO2 and 1.5 W m-2 for radiative forcing. 4. **Ozone Depletion**: Transgression and current ozone values are estimated from daily measurements, with the current value calculated as a five-year median for 2016-2021. 5. **Freshwater Change**: The boundary for freshwater change is defined based on the variability within the pre-industrial period, with local deviations in blue and green water (streamflow and soil moisture) used to set the global boundary conditions. The current state of freshwater deviations exceeds these boundaries, indicating a substantial exceedance of the boundary. 6. **Aerosol Loading**: The impact of aerosols on the Earth system is discussed, including their effects on climate and the biosphere. The area-weighted hemispheric difference in aerosol optical depth (Δτ) is used to assess aerosol impacts. 7. **Ocean Acidification**: The current global averaged saturation state of aragonite (Ω) is estimated, showing a significant decrease from pre-industrial levels. 8. **Land System Change**: The boundary for land system change retains the same general approach, with improved methodology for estimating remaining forest areas. The boundaries for tropical, temperate, and boreal forests are defined, and the current status of these boundaries is discussed. 9. **Model Evaluation and Results**: The performance of the coupled Earth system model (CM2Mc-LPJmL) is evaluated, and model results are presented to support the placement of the climate and land system change boundaries. The impact of transgressing these boundaries on terrestrial carbon stocks and climate is analyzed. The supplementary material provides a comprehensive overview of the methods, data, and results used to support the study's findingsThis supplementary material provides detailed information and supporting data for the study on Earth's planetary boundaries. It includes supplementary information, figures, tables, and references. The key points covered are: 1. **Reference Baseline**: The study uses Holocene conditions as a reference point, defined as the last 11,700 years of Earth's history, to assess the stability and variability of Earth's climate system. Holocene-like conditions are those that remain within the inter-glacial state, not exceeding thresholds that could irreversibly shift the Earth system away from Pleistocene inter-glacial conditions. 2. **Biosphere Integrity**: The importance of genetic diversity in species is highlighted, with recent advancements in whole-genome sequencing and macrogenetics providing new tools to capture global genetic variability. The functional integrity of the biosphere is measured by human appropriation of net primary production (HANPP) compared to Holocene values. 3. **Climate Change**: Control variables for atmospheric CO2 concentration and total effective anthropogenic radiative forcing are retained, with boundary levels set at 350 ppm and 1 W m-2, respectively. The upper end of the zone of increasing risk is set at 450 ppm for CO2 and 1.5 W m-2 for radiative forcing. 4. **Ozone Depletion**: Transgression and current ozone values are estimated from daily measurements, with the current value calculated as a five-year median for 2016-2021. 5. **Freshwater Change**: The boundary for freshwater change is defined based on the variability within the pre-industrial period, with local deviations in blue and green water (streamflow and soil moisture) used to set the global boundary conditions. The current state of freshwater deviations exceeds these boundaries, indicating a substantial exceedance of the boundary. 6. **Aerosol Loading**: The impact of aerosols on the Earth system is discussed, including their effects on climate and the biosphere. The area-weighted hemispheric difference in aerosol optical depth (Δτ) is used to assess aerosol impacts. 7. **Ocean Acidification**: The current global averaged saturation state of aragonite (Ω) is estimated, showing a significant decrease from pre-industrial levels. 8. **Land System Change**: The boundary for land system change retains the same general approach, with improved methodology for estimating remaining forest areas. The boundaries for tropical, temperate, and boreal forests are defined, and the current status of these boundaries is discussed. 9. **Model Evaluation and Results**: The performance of the coupled Earth system model (CM2Mc-LPJmL) is evaluated, and model results are presented to support the placement of the climate and land system change boundaries. The impact of transgressing these boundaries on terrestrial carbon stocks and climate is analyzed. The supplementary material provides a comprehensive overview of the methods, data, and results used to support the study's findings