Reducing the psalms to a possible structural summary

My summaries are terribly brief compared with the complexity of the Psalms - but do they help to grasp the whole? Might they have been reflective of organizational principles at the time of their collection? I do not have enough information to assess that but here's the simplest set of interacting sections I have come up with yet.

Introduction and conclusion 1, 2, 149

   The formation of those to whom mercy in covenant has been shown

   The David outer circle 3-41, ... 138-145

      Personal dialogue, Judgment, Humanity's place, Acrostics (themselves a circle in Books 1 and 5 only)

      Books 2 and 3 a first contained cell (God as Elohim 42-86)
      The Korah inner circle Korah 42-49, 84,5,7,8,9

         Exile and Corporate lament 44 ... 137

         The Asaph inner circle 50, 73-83
             The harvest 65-67
             The history 78 ... 136
             The David inner circle and its outlier doubles 51-65, 68-70 ... 108
                 The miktamim and psalms to the tune Do not destroy and their outliers 16, 56-60, 75
      Books 4 and 5 up to Psalm 135 constitute second and third cells
         Book 4
             Moses 90
                Rebellion 95
                The LORD as king 96-99
            103-106 recapitulating the history of creation and redemption
        Book 5
            107 The human condition and the divine response
            Psalms 108 to 118, The work that is to do for Israel and all the nations
            Psalm 119, The testimony observed
            The psalms of ascent and 'arrival' - 120-134, 135
         The final cadences - for all who fear God
         136 creation and redemption
      137 - exile
   138-145 Davidic reminder and last Acrostic
146-150 the Hallel including the concluding statement in 149 re those to whom mercy in covenant has been shown