## 2 Materials and Methods
Measuring conditions were: Cobalt K\(\alpha\) radiation, 40 kV and 40 mA power, angular range 3-85\({}^{\circ}\) 20, virtual steps of 0.02\({}^{\circ}\) 20. Because of the very small amount of material extracted from the objects, the signal was optimized by using a rotating zero-background sample holder. The diffraction spectra were analyzed using the X'Pert HighScore Plus software 3.0 of PANalytical. Micro-Raman analyses were performed with a DXR Thermo Scientific instrument, equipped with a 532 nm laser and a 50\(\times\) LWD (Long Working Distance) objective. The working condition selected for the analyses is acquisition time 3 s, 32 scans, 5 mW and a 25 um pinhole. The spectra were processed with the Omnic 9 software (Thermo Scientific, Waltham, MA, USA) and compared with reference spectra recovered from the online RRUFF database ([[http://rruff.info](http://rruff.info)]([http://rruff.info](http://rruff.info))) and from our internal database of minerals and pigments. Figure 1: Representative shapes of the investigated objects from Villa del Foro: (**a**) washer-like disc, with indented borders (VF91.157/E1); (**b**) small ceramic sphere with a red colored surface (VFRS11); (**c**) cubic dive with no inscriptions and red-pigmented surface (VF14.SP384D); (**d**) cubic dive with numbers or other signs (VF90.1549/E32). The scale bars are (**a,b**) 2 mm, and (**c,d**) 4 mm. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Id.** & **Catalog \(n\).** & **Location** & **Material** & **Description** & **Dimensions (cm)** & **Weight (g)** \\ \hline \hline \multicolumn{6}{c}{**Washer-like discs**} \\ \hline
1 & VFS6.1000.12 & area A, SSE10 g/g, US 1000 & fired ceramics & Irregular clay disc, with rough needed edge & \(\circ\) max 2.7; \(\circ\) min 2.4; \(\circ\) h. 0.8 & 5.50 \\
2 & VFS6.1210.1076 & area B, US 1210 & fired ceramics & Roughly modeled clay disc, irregular circle shape, flat section & \(\circ\) max 2.9; \(\circ\) min 2.8; \(\circ\) 0.6 & 6.52 \\
3 & VFS6.1210.917 & area B, S6E10, US 1210 & fired ceramics & Rough day incomplete semi-circle, flat section, nail marks on & \(\circ\) max 5.8; \(\circ\) min 3.7; 1.1 & 23.46 \\
4 & VFS8.1501.E39 & area E, US 1501 & fired ceramics & Irregular clay disc, flat asymmetric section & \(\circ\) max 2.9; \(\circ\) min 2.5; \(\circ\) h. 0.9 & 6.99 \\
5 & VFP1.157.E41 & area E, US 1571 & fired ceramics & Flat circular clay disc, with one slightly concave surface, vertical & \(\circ\) max 2.9; \(\circ\) min 19.1 & 19.50 \\
6 & VFSP244 & stray find & fired ceramics & Irregular flat clay disc & \(\circ\) max 2.9; \(\circ\) min 2.8; \(\circ\) 0.8 & 5.68 \\
7 & VFSP251 & stray find & fired ceramics & Irregular clay oval disc, carved out of a pot fragment & \(\circ\) max 6.4; \(\circ\) min 5.5; h. 1 & 49.90 \\
8 & VFSP187 & stray find & fired ceramics & Roughly modelled fragmented clay em-sphere & \(\circ\) max 1.8; \(\circ\) min 16.3; 1.4 & 3.82 \\
9 & VFP0.1514.E40 & area E, US 1514, [US 1530] & fired ceramics & Irregular clay circular disc with eleven engraved lines on a side & \(\circ\) max 5.6; \(\circ\) min 5.4; \(\circ\) h. 0.7 & 5.50 \\ \hline \multicolumn{6}{c}{**Spheres**} \\ \hline
10 & VFS9.1210-VIII.B24 & area B, US 1210 VIII. fig. & fired ceramics & Irregular clay sphere & \(\circ\) max 1.9; \(\circ\) min 1.7 (\(\circ\) mean 1.80) & 6.02 \\
11 & VFSP0.1549.E31 & area E, US 1549 [US 1531] & fired ceramics & Irregular clay sphere & \(\circ\) max 1.4; \(\circ\) min 1.3 (\(\circ\) mean 1.35) & 2.98 \\
12 & VFSP111 & area, c, surface find & fired ceramics & Irregular clay sphere, surface pigmented in red & \(\circ\) max 1.4; \(\circ\) min 1.4 (\(\circ\) mean 1.40) & 2.81 \\
13 & VFSP247 & part. 199 & fired ceramics & Irregular clay sphere & \(\circ\) max 1.9; \(\circ\) min 1.7 (\(\circ\) mean 1.80) & 4.86 \\
14 & VFP1457835D & stray find & fired ceramics & Irregular clay sphere & \(\circ\) max 1.4; \(\circ\) min 1.2 (\(\circ\) mean 1.30) & 1.94 \\ \hline \end{tabular}
\end{table} 
Table 1: List of investigated materials from Villa del Foro (Alessandria, Italy).