I'm with Ronk

Terak is makig what seems like an odd distinction. Here’s the puzzle, filtered for 8s for clarity:

Figure A

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`*-----------------------------------------------* `

|-8 . . | . -8 . | 8 . . |

| . 8 . | . . . | . . 8 |

| . 8 . | . . +8 | 8 . . |

|---------------+---------------+---------------|

|+8 . . | . . -8 | . . . |

| . . . | . . . | 8 . 8 |

| . . -8 | . +8 . | . . . |

|---------------+---------------+---------------|

| . 8 8 | . . . | . 8 . |

| . . . | 8 . . | . . . |

| . . 8 | . . . | . 8 . |

*-----------------------------------------------*

No other 8’s are conjugates with these 7. Because two 8’s have the same symbol in the top row, we know that the PLUS signs are 8s and the MINUS signs are not. Your claim is that this is a contradiction -- a claim which I do not agree -- but I won’t argue that point. Instead, take a look a the following grid which has one change in brackets:

Figure B

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`*-----------------------------------------------* `

| 8 . . | . -8 . | 8 . . |

| . 8 . | . . . | . . 8 |

| . 8 . | . . +8 | 8 . . |

|---------------+---------------+---------------|

|+8 . . | . . -8 | . . . |

| . . . | . . . | 8 . 8 |

| . . -8 | . +8 . | . . . |

|---------------+---------------+---------------|

| . 8 8 | . . . | . 8 . |

| . . . | 8 . . | . . . |

|[8] . 8 | . . . | . 8 . |

*-----------------------------------------------*

Because of the additional 8 at r9c1, the 8 at r1c1 cannot be labeled. We can still eliminate 8 from this cell, as it can ‘see’ cells of both signs. Suddenly, this deduction is ‘fair’ and clearly requires no contradiction.

In Figure A, the solver is free to refrain from labeling r1c1 and simple excude it once r1c5 and r4c1 are fixed. This is always the case. Just as you update your candidates after entering a digit, you could make exclusions as soon they become available and then continue coloring. You never need to label two cells in one group with the same color. However, it's much easier to show it that way when posting a solution.

The distinction between contradition and other types of deduction is arbitrary:

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`[12][23]`

[13][34]

We could say:

R1c1=1 -> r2c1=3 -> r2c2=4

R1c1=2 -> r1c2=3 -> r2c2=4

Therefore r2c2=4

… and call it a “forcing chain”

Or we could say:

R2c2=3 -> r1c2=2 -> r1c1=1

R2c2=3 -> r2c1=1 -> r1c1=2

Therefore, r2c2<>3

… and call it a “proof by contradiction”

Or we could say:

“That’s an xy-wing -- r2c2 cannot be 3.”

Coloring is not the pattern -- it is an efficient *method* for finding a *pattern*. I don’t see why we would handicap ourselves.