SO(2) playground

Drag the two basis-vector tips to build the 2×2 transform. det > 0 preserves handedness (rotation-like); det < 0 reverses it (a mirror). That sign is the whole same/mirror bit.

shape 

    


    

      

        
Transform

        
+1.000

        

        

        
rigid (isometry)?

        

      


      

        
What each oracle rung sees

        

          
          
        

        

      


      

        
Rungs grading a sample candidate

        

        
candidate answers
          
          

        

      


      

        
Experiment baseline · best-of-N (60 items)

        
        
Tight (exact) climbs to 1.00 under best-of-N; the loose graders plateau ~0.80–0.85 (fluency even dips). Haiku-4.5, SO(2), 60 items.
Stability · self-consistency 0.88 (58% of items unanimous across 8 samples) — the sample spread best-of-N selects from.