The formulation of a claim rests at the core of argument mining. To demarcate between a claim and a non-claim is arduous for both humans and machines, owing to latent linguistic variance between the two and the inadequacy of extensive definition-based formalization. Furthermore, the increase in the usage of online social media has resulted in an explosion of unsolicited information on the web presented as informal text. To account for the aforementioned, in this paper, we proposed DESYR. It is a framework that intends on annulling the said issues for informal web-based text by leveraging a combination of hierarchical representation learning (dependency-inspired Poincare embedding), definition-based alignment, and feature projection. We do away with fine-tuning computer-heavy language models in favor of fabricating a more domain-centric but lighter approach. Experimental results indicate that DESYR builds upon the state-of-the-art system across four benchmark claim datasets, most of which were constructed with informal texts. We see an increase of 3 claim-F1 points on the LESA-Twitter dataset, an increase of 1 claim-F1 point and 9 macro-F1 points on the Online Comments(OC) dataset, an increase of 24 claim-F1 points and 17 macro-F1 points on the Web Discourse(WD) dataset, and an increase of 8 claim-F1 points and 5 macro-F1 points on the Micro Texts(MT) dataset. We also perform an extensive analysis of the results. We make a 100-D pre-trained version of our Poincare-variant along with the source code.