A Winding Path: Yet Another Sudoku Variant Ruleset!

Today's Puzzle:

Uses yet another variant ruleset from Arbitary, an individual who is clearly a Sudoku variant construction machine!

Do let me know in the comments if you enjoyed the variant and wish to see some of the tougher puzzles that use it.

Link to Play Along:

A Winding Path by Arbitrary http://tinyurl.com/SudokuSleuthWindingPath

Rules:

Normal sudoku rules apply.

Consecutive Sum Lines: Within each 3x3 box, the sum of digits along a contiguous line segment is consecutive with the sum along the red line segment in any box it directly connects to. If a line re-enters a box, each contiguous segment is a separate sum which may be different in value if permitted by other rules. For example, in box 9, the sum of [R8C7, R9C7, R9C8] and the value of R7C7 may be different but each differs from the value of R8C6 by exactly 1.

i.e. Lines behave like region sum lines, but the sum increases or decreases by 1 whenever the line crosses into a box.