## 2 Materials and Methods  
### Materials  
The materials used for the manufacture of the mock-ups are presented in Table 1. Specifications provided by the supplier are compared with those obtained from the preliminary characterisation of the materials conducted by the authors. In the preparation of the mortar, a calcite line paste, stored under water for more than 20 years, was used as the binder. This lime is composed mainly of portlandite (Ca(OH)\({}_{2}\)), and small amounts of calcite (CaCO\({}_{3}\)) due to partial carbonation during handling. The lime paste was mixed with three aggregates with different particle sizes: (i) coarse silica; (ii) fine silica; and (iii) Carrara marble powder. Coarse and fine silica aggregates, composed of quartz (SiO\({}_{2}\)), sodium/potassium feldspars, and rutile (TiO\({}_{2}\)), were supplied by a local hardware store (Granada, Spain). The marble powder, which had irregular particles in terms of size and shape, was composed of calcite, quartz, and dolomite (CaMg(CO\({}_{3}\))\({}_{2}\)) and was supplied by CTS S.L. (Madrid, Spain). The following pigments were selected for the study: Egyptian blue (EG-B), lapis lazuli (LA-B), ultramarine blue (UL-B), green earth (GE-G), mars red (MAR-R), chromium green (CHR-G), cinnabar (CIN-R), vermilion (VER-R), and verdigris (VER-G). They were all supplied by Kremer Pigments GmbH & Co. KG (Aichstetten, Germany). The origin and main characteristics of these pigments are shown in Table 1.  
Chromatic reintegrations were carried out using Nano Estel(r) [23], also supplied by CTS S.L. (Madrid, Spain), as the binder (NE). This product consists of an aqueous colloidal dispersion of SiO\({}_{2}\) nanoparticles (around 10-20 nm), with alkaline pH (9.8-10.4). It is a non-toxic and non-flammable product, which lowers the risk factors for the restorer and the artwork. The nano-size silica particles bind together forming a silica gel, similar to that obtained with ethyl-silicate consolidants [23]. The ambient temperature must be between 5 \({}^{\circ}\)C and 35 \({}^{\circ}\)C, as must be the temperature of the surface to which the product is applied. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Supplier’s Code** & **Authors Code** & **Supplier’s** & **Authors** & **Supplier’s Composition** & **Authors Mineralized Composition by XRD** & **Authors Chemical Composition by XRF** & **Completion by XRF** \\ \hline \multirow{2}{*}{Calctic line paste} & \multirow{2}{*}{CLP} & \multirow{2}{*}{-} & - & Calcium hydroxide, & Portlanding, Ca(OH)\({}_{2}\) & - \\  & & & Ca(OH)\({}_{2}\) & & Ca(OH)\({}_{2}\) & Ca(CO)\({}_{2}\) & - \\ \hline \multirow{2}{*}{Silca E1 JP} & \multirow{2}{*}{C-SI} & \multirow{2}{*}{1-2 mm} & \multirow{2}{*}{R: 1.6-4 mm} & & Quartz, SO\({}_{2}\) & Si (97.99\(\pm\)) and Al (1.22\(\pm\)) \\  & & & & Static, TO\({}_{2}\) & Retite, TO\({}_{2}\) & +\(\times\) Fe, Mg, Ca, Na, K, Ti, P, and S \\  & & & & Al(h)\({}_{2}\) & Na(h)\({}_{2}\) & \\ \hline \multirow{2}{*}{Silca E1 A003 EP JP} & \multirow{2}{*}{F-SI} & \multirow{2}{*}{0.4-0.8 mm} & \multirow{2}{*}{R: 0.125-16 mm} & & Quartz, SO\({}_{2}\) & \\  & & & & Raitle, TO\({}_{2}\) & & St (91.03\(\pm\)), Al (2.25\(\pm\)), and K (2.21\(\pm\)) \\  & & & & Anerholose, (Na)\({}_{2}\)AsAsIn\({}_{0}\)O & +\(\times\)17\({}_{6}\), Fe, Mg, Ca, Na, Ti, P, and S \\  & & & & & Microline, KAsAsAsIn\({}_{0}\), & \\  & & & & & & & \\ \hline \multirow{2}{*}{Baroo Carrana MK 000} & \multirow{2}{*}{MRB-P} & \multirow{2}{*}{0.0-0.7 mm} & \multirow{2}{*}{R: 0.0-0.5 mm} & & Calcium, CO\({}_{2}\) & Ca(55.59\(\pm\)) and Mg, (0.89\(\pm\)) \\  & & & & & & & \\  & & & & & & & \\  & & & & & & & \\  & &