## 2 Materials and Methods  
The experiment was conducted at the Teaching, Research, and Extension Farm (FEPE)--Plant Production Sector, belonging to the Faculty of Engineering of Ilha Solteira (FEIS)/Sao Paulo State University (UNESP), located in the municipality of Selvriia/ Mato Grosso do Sul (Scheme 1), with geographic coordinates 20\({}^{\circ}\)20\({}^{\prime}\)45\({}^{\prime\prime}\) S and 51\({}^{\circ}\)24\({}^{\prime}\)25\({}^{\prime\prime}\) W and an altitude of 350 m.  
**Scheme 1. ** Location of the experimental area. The relief of the area is characterized as moderately flat, with soil classified as a typical Dystrophic Red Oxisol [11], with a clayey texture, updated according to the Brazilian Soil Classification System [12]. The climate type is Aw, according to [PERSON]'s classification [13], described as humid tropical with a rainy season in summer and a dry season in winter. The average annual precipitation is 1370 mm and the average temperature is 23.5 \({}^{\circ}\)C [14]. During the experiment, climatic data were collected from the meteorological station installed at FEIS (Figure 1). The experimental area has a history of annual crop cultivation under no-tillage (NT) for 20 years. Before the current study, the following crops were grown in rotation (Scheme 2). The experimental design was a randomized complete block design (RCBD), in a \(5\times 2\) factorial scheme; treatments combined five P\({}_{2}\)O\({}_{5}\) doses (0, 30, 60, 120, and 240 kg ha\({}^{-1}\)) with two inoculation levels (with/without _A. brasilense_), using plots with 0 kg ha\({}^{-1}\) of P\({}_{2}\)O\({}_{5}\) and no inoculation as controls. Fertilization was applied using monoammonium phosphate (MAP\(-\)11% N, 52% P\({}_{2}\)O\({}_{5}\)), aiming to evaluate phosphorus complexation in assimilable forms. The recommended dose, based on an initial soil analysis conducted in 2013 (Bulletin 100), was 60 kg ha\({}^{-1}\) of P\({}_{2}\)O\({}_{5}\). The other rates were established as half (30 kg ha\({}^{-1}\)), double (120 kg ha\({}^{-1}\)), quadruple (240 kg ha\({}^{-1}\)), and zero of the recommended dose. To ensure that nitrogen was not a limiting or confounding factor in the evaluation of phosphorus effects, the amount of N provided by MAP was calculated for each P\({}_{2}\)O\({}_{5}\) dose, and complementary N was applied using urea (46% N) so that all treatments received a uniform nitrogen supply of 50.77 kg ha\({}^{-1}\). The urea rates applied to each treatment were 110.37, 96.57, 82.78, 55.20, and 0 kg ha\({}^{-1}\) for 0, 30, 60, 120, and 240 kg ha\({}^{-1}\) of P\({}_{2}\)O\({}_{5}\), respectively. Phosphorus application was broadcast without incorporation during black oat sowing in 2013 and reapplied in 2020, together with the inoculation (or not) of the grain-producing grasses in the crop rotation (Scheme 2) with _A. brasilense_. There were four replications per treatment. Each experimental unit (plot) was 3.2 m wide and 10 m long, covering an area of 32 m\({}^{2}\). The experiment had four blocks for each area (inoculated and non-inoculated), with five P\({}_{2}\)O\({}_{5}\) rates per block, totaling an experimental area of 1280 m\({}^{2}\)  
Figure 1: Monthly averages of precipitation and minimum, average, and maximum temperatures for the research period, March 2022 to November 2023, Selvriia/MS. Source: adapted by the author from data from the irrigation and drainage laboratory meteorological station at FE/Unesp-Ilha Soleira. excluding the buffer zone surrounding the entire experimental area, which was established to prevent interference from adjacent plots and ensure the integrity of treatment effects. Before the implementation of the experiment and surface liming, a chemical analysis of the soil was conducted in the 0.00-0.20 m layer. The results indicated an acidic pH (CaCl\({}_{2}\)) of 5.0, organic matter content of 25 g dm\({}^{-3}\), and available phosphorus (P, resin method) of 22 mg dm\({}^{-3}\).