To put soil sequestration in practice, the key is soil microbes and the interactions among them.
Soil is alive! Soil is more than just a space or inert medium to physically hold the roots for plants. It is full of microorganisms such as bacteria, fungi, algae, protozoa, nematodes, and many other creatures. In a teaspoon of healthy soil, there are more individual microbes than human population on earth!
Second, soil microbes and plants live in mutualism: Plants photosynthesize and make carbohydrates not only for their own growth, but also exude through their roots a significant amount of these carbohydrates into the soil to feed microbes who help the plants to grow in exchange. 
Microbes are fueled by carbon in soil in the form of organic matter and root exudates. To stabilize carbon in soil and protect it from decomposition, HUMUS has to be formed (i.e. humification). However, building long-term soil carbon does not equate to merely adding organic matter to your soil. Organic matter without proper protection from decomposition is oxidized and the carbon within is released to the air as carbon dioxide. To build long-term soil carbon, it is essential to ensure good soil structure and soil aggregation that offer physical protection for organic matter from rapid decomposition, and such structure can only be built by a thriving soil food web with abundant fungi. 
The great diversity and quantity of soil organisms make up the soil food web when they eat and grow. The food web diagram shows a series of conversions (represented by arrows) of energy and nutrients as one organism eats another. 
Soil food web is the knowledge supporting regenerative farming practices based on solid science with years of observation of soil life via microscope and practices. The websites below are recommended for those who would like to learn the important role of soil food web in the nature:
Benefits of healthy soil food web: 
Reclaiming soil health in biological perspective of getting a wide diversity of microbes is the major task for regenerative farmers. There is a lot more to dig deeper in soil science internationally, please stay tune with the above mentioned leading associations and scientists for the updated and thorough explanation of regenerative farming!
 Hoorman JJ, Islam R, (2010) Understanding soil Microbes and Nutrient Recycling, Ohio State University Fact Sheet, SAG-16-10
 Jones C, (2015) Save Our Soils, Acres USA, retrieved from: http://www.amazingcarbon.com/PDF/Jones_ACRES_USA%20(March2015).pdf
 Meléndrez M, (2014) The Journey to Better Soil Health, unpublished paper presented to the First International Humus Expert’s Meeting, Kaindorf, Austria, January 22 and 23, 2014
 USDA, Soil Food Web Diagram: https://www.nrcs.usda.gov/wps/portal/nrcs/detailfull/soils/health/biology/?cid=nrcs142p2_053868
 Benefits of the Soil Foodweb: https://www.permaculturenews.org/files/CompostTeaSpraysBenefitsLivingProof.pdf