## 2 Materials and Methods
### Gas Chromatography-Mass Spectrometry  
Paint fragments and wooden specimens were examined by Gas Chromatography (GC) using a 6890N instrument (Agilent Technologies, Waldbrunn, Germany) coupled with and a 5973-inset mass selective detector (Agilent Technologies, Waldbrunn, Germany). When possible, the multi-layered paint samples were manually separated, resulting in paint specimens with an average weight of 388 \(\upmu\)g, whereas the wooden specimens weighed between 207 and 515 \(\upmu\)g (Cahn Micro balance). GC-MS testing configuration and parameters are described in detail in [23], and are compiled in Supplementary Materials (Table S15). Specifically, the derivatization process described for identifying oils and resins, (Meth Prep II Protocol) and proteins (Amino Acid Protocol) from a single sample were followed.  
Drying oils are identified in paint samples based on the concentration of palmitic (C\({}_{160}\)), stearic (C\({}_{180}\)), and azelaic (C\({}_{9}\)). Limited types of vegetable drying oils were available, thus fatty acid ratios were selected as a viable option for identification. However, fatty acids can be derived from various sources other than oils, such as animal glue and egg yolk. A commonly accepted approach for identifying a specific drying oil is by expressing the ratio of palmitic to stearic acid (C\({}_{160}\)/C\({}_{180}\)) [36]. Nevertheless, as C\({}_{16}\) and C\({}_{18}\) are directly correlated, the ratio is considered to be unchanging. Generally, the C\({}_{160}\)/C\({}_{180}\) ratio is a well-known value used in conservation science and has been established as the marker for different drying oils and egg (Table 3). However, when a mixture of drying oils, or egg and non-drying oils are both present, the interpretation of fatty acid profiles can be complicated.  
Additionally, the azelaic acid to palmitic acid ratio (C\({}_{9}\)/C\({}_{16}\)) can be used to signify the presence of drying oils as opposed to egg lipids [21]. A C\({}_{9}\)/C\({}_{16}\) ratio around 1, or higher, indicates the presence of a drying oil, whereas values between 0.2 and 0.5 indicate egg yolk or semi-drying oils that only partially oxidize (e.g., sesame or grapeseed oil). Lipids such as fats, grease, and non-drying oils (e.g., castor or olive oil) have very low C\({}_{9}\)/C\({}_{16}\) values (less than 0.2). Here, proteins are identified through a comparative method, in which the specimen's amino acids were compared to those of reference material [24; 25]. A match is then established using correlation coefficients in which an identical match would result in a coefficient equal to 1.0. However, a correlation coefficient of 0.93 is often deemed as acceptable [23].  
For this study, the percentage of protein was estimated using the sum of the weight percentages from the detected amino acids (mg/mg of amino acids in specimen). Stable amino acids were selectively analyzed, with this protocol yielding an underestimation of the per cent protein in the sample. L-norleucine was used as the internal standard and a blank (i.e., empty vial) was analyzed to monitor contamination during the analysis. For positively identifying the presence of fatty acids in the present study, a lower limit of two to three-times greater than the blank value was used. Here, fatty acid contamination from the glassware, or introduced by human contact, was observed at 1.65 and 2.35 ppm for palmitic and stearic acid, respectively (C\({}_{16}\)/C\({}_{18:0}\) ratio of 0.70).