Understanding the cognitive and emotional perceptions of people who commit suicide is one of the most sensitive scientific challenges. There are circumstances where people feel the need to leave something written, an artifact where they express themselves, registering their last words and feelings. These suicide notes are of utmost importance for better understanding the psychology of suicidal ideation. This work gives structure to the linguistic content of suicide notes, revealing interconnections between cognitive and emotional states of people who committed suicide. We build upon cognitive network science, psycholinguistics and semantic frame theory to introduce a network representation of the mindset expressed in suicide notes. Our cognitive network representation enables the quantitative analysis of the language in suicide notes through structural balance theory, semantic prominence and emotional profiling. Our results indicate that the emotional syntax connecting positively- and negatively-valenced terms gives rise to a degree of structural balance that is significantly higher than null models where the affective structure was randomized. We show that suicide notes are affectively compartmentalized such that positive concepts tend to cluster together and dominate the overall network structure. A key positive concept is "love", which integrates information relating the self to others in ways that are semantically prominent across suicide notes. The emotions populating the semantic frame of "love" combine joy and trust with anticipation and sadness, which connects with psychological theories about meaning-making and narrative psychology. Our results open new ways for understanding the structure of genuine suicide notes informing future research for suicide prevention.