Sextuple Adjacency Sudoku

Consecutive adjacency Sudoku are hard for humans to solve.  Computers are quite quick about it, but things fit together overall in a way that isn't pleasing for most people to attempt by hand.  Recently, I had the idea to include diagonal adjacency, something I've never seen tried before.  This is the result, and I think it makes for a good puzzle (for humans.)

The rules are simple.  A horizontal line connects cells which are horizontally, diagonally, or vertically adjacent, if and only if, they contain consecutive numbers.  We also require the center square of the center cage to be less than five.  Together with the other usual Sudoku rules, this is all that is needed to reach a unique solution.

Here is a sample three by three cage, with one way to fill in the cells consistent with the given clues.

Here is our puzzle.

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Solution