Beautiful logic work!
Setup. The grid is N×N. You must fill every cell with a digit from 1 to N.
The Run Rule. Whenever two same-digit cells are orthogonally adjacent, they form a single connected run. The run must contain exactly that many cells — so a run of three 3s is exactly three orthogonally connected cells, a run of two 2s is exactly two adjacent cells, etc.
No merge. Two separate runs of the same digit must not touch (otherwise they would merge into a longer invalid run).
Strategy. Look for 1s first — they must be isolated, so wherever a 1 is given, its 4 neighbors cannot be 1s. Look for the biggest digit N — the run of N must use exactly N cells (often half the grid), which heavily constrains the remaining cells.