```python
def new_canvas(rows: int, cols: int) -> dict:
    for side in (rows, cols):
        if isinstance(side, bool) or not isinstance(side, int) or side < 1:
            raise ValueError("canvas dimensions must be positive integers")
    cells = [[0] * cols for _ in range(rows)]
    return {"rows": rows, "cols": cols, "cells": cells}


def stamp_rect(canvas: dict, rect: list) -> int:
    if not isinstance(rect, list) or len(rect) != 4:
        raise ValueError("rect must be a list of exactly four integers")
    if any(not isinstance(v, int) or isinstance(v, bool) for v in rect):
        raise ValueError("rect elements must be integers")
    
    top, left, bottom, right = rect
    
    if top >= bottom or left >= right:
        raise ValueError("rect must cover at least one cell (top < bottom and left < right)")
    
    rows = canvas["rows"]
    cols = canvas["cols"]
    cells = canvas["cells"]
    
    if top < 0 or bottom > rows or left < 0 or right > cols:
        raise ValueError("rect extends beyond canvas boundaries")
    
    inked = 0
    for r in range(top, bottom):
        for c in range(left, right):
            if cells[r][c] == 0:
                cells[r][c] = 1
                inked += 1
    return inked


def ink_total(canvas: dict) -> int:
    total = 0
    for row in canvas["cells"]:
        total += sum(row)
    return total
```