## 2 Materials and Methods
To evaluate soil fertility characteristics, biological attributes, enzymatic activity, and soil P fractions in the experimental units, ten simple soil samples were collected on 26 September 2023 to form a composite sample per plot for subsequent analyses at depths of 0.00 to 0.10 m and 0.10 to 0.20 m.  
After harvesting the intercropping system, the area remained fallow with Piata grass (Figure 5). On 6 October 2023, for the dry matter yield determination of Piata grass, a 1.0 \(\times\) 1.0 m sampling frame was used to collect plants within 1 m\({}^{2}\) of each plot. These plants were placed in properly labeled plastic bags and weighed on a precision balance for FM determination. Again, after this procedure, subsamples were taken, placed in paper bags, and taken to a forced-air oven at 65 \({}^{\circ}\)C for 72 h to obtain DM, which was later extrapolated to production per hectare. The Piata grass was desiccated on 13 October 2023 using the herbicide glyphosate (1560 g ha\({}^{-1}\) of active ingredient) to proceed with the next crop rotation. For soil biological attribute evaluations, the following were determined: microbial respiratory activity (MRA), according to the methodology proposed by [15] and microbial biomass carbon (MBC), according to the methodology proposed by [16], with both analyses (MRA and MBC) performed at the Soil Microbiology Laboratory of the \"Luiz de Queiroz\" College of Agriculture, University of Sao Paulo (ESALQ/USP--Piracicaba/SP). The metabolic quotient (qCO\({}_{2}\)) was calculated as the ratio between MRA and MBC, as proposed by [17], and total organic carbon (TOC) was determined using the method pro  
Figure 5: Conducting sorghum cultivation intercropped with Piata grass in a no-tillage system, influenced by the residual effect of phosphate fertilization and inoculation of previous grasses with _A. brasilense._ Selviria/MS, 2022/2023. (**A**) Immediately after the intercropping sorghum \(\times\) Piata grass harvest; (**B**) twenty days of Piata grass fallow; (**C**) forty days of Piata grass fallow. posed by [18], performed at the Soil Microbiology Laboratory of the Brazilian Agricultural Research Corporation (Embrapa Cerrados--Brasilia/DF). For soil enzymatic activity analyses, \(\beta\)-glucosidase (\(\updelta\)G), aryl sulfatase (AS), and acid phosphatase (AF) were determined using methodologies proposed by [19]. These determinations were performed at the Soil Microbiology Laboratory of the Brazilian Agricultural Research Corporation (Embrapa Cerrados--Brasilia/DF). Soil health was assessed using the four-quadrant model proposed by [20], which evaluates soil carbon modifications (loss, gain, or stability) based on the relationship between TOC and the average activity of the \(\updelta\)G and AS enzymes per unit of TOC. Soil phosphorus fractionation into labile phosphorus (Lab), moderately labile phosphorus (Mod Lab), non-labile phosphorus (N Lab), inorganic phosphorus (Pi), organic phosphorus (Po), and total phosphorus (P tot) was performed according to the methodology proposed by [21], with adaptations. Analyses were conducted at the Soil Chemistry Analysis Laboratory of the \"Luiz de Queiroz\" College of Agriculture, University of Sao Paulo (ESALQ/USP--Piracicaba/SP). Soil fertility analyses included chemical attributes such as phosphorus (P), sulfur (S), potassium (K), calcium (Ca), magnesium (Mg), potential acidity (H+Al), base sum (BS), cation exchange capacity (CEC), base saturation (V), aluminum saturation (m), organic matter content (OM), and hydrogen potential values (pH), conducted according to the methodology proposed by [22] at the Soil Fertility Laboratory of Sao Paulo State University \"[PERSON]\" (UNESP--Ilha Solteira/SP). Soil chemical analyses were expressed on a volumetric basis (mmolc dm\({}^{-3}\)), in accordance with the standard methodology adopted in Brazil [9]. This approach is widely used in Brazilian laboratories, where soil samples are processed as air-dried fine earth (TFSA), involving drying, gentle disaggregation, and sieving through a 2 mm mesh.