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              Abstract
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 We study the Gram determinant and construct bases of hom spaces for the
 one-dimensional topological theory of decorated unoriented one-dimensional
 cobordisms, as recently defined by Khovanov, when the pair of generating functions is
 linear.
  
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              Keywords
              
                topological quantum field theory, cobordism, universal
                construction, string diagrams, defects, evaluations, linear
                generating functions
               
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              Mathematical Subject Classification
              
                Primary: 18M30
               
              
                Secondary: 05A15, 57K16
               
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              Milestones
              
                Received: 19 May 2021
               
              
                Accepted: 16 September 2021
               
              
                Published: 29 July 2022
                
              
                Communicated by Józef H. Przytycki
               
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