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The garden fence, a conspicuously displayed boundary line, often no more than a token barrier, is the outer territorial limits, separating the private world of the family from the public world beyond.

About the 'separating' above, is it reduced adverbial clause, or a modifier of 'the outer territorial limits'?
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It's an alternative expression for "which separate". So (looking it up) it's a reduced adverbial clause. I would have made "limits" singular, as it says there is only one fence.
So does this also work?

Separating the private world of the family from the public world beyond, the garden fence, a conspicuously displayed boundary line, often no more than a token barrier, is the outer territorial limits.
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It doesn't look like a clause to me, not even a reduced one. It's a participle phrase. If I had to label it more specifically, I would say adverbial.
Aspara GusIt doesn't look like a clause to me, not even a reduced one. It's a participle phrase. If I had to label it more specifically, I would say adverbial.
So you don't think it's a modifier of 'limits', AG?
"Separating the private world of the family from the public world beyond, the garden fence, a conspicuously displayed boundary line, often no more than a token barrier, is the outer territorial limits."
It's far too long for a sentence with so many concepts joined together.This is what I think of as speed bump writing. It holds up your reading, because you have to untangle it in your mind to get the meaning, before you can move on. I would not continue reading such writing if it went on much more. It takes too much effort and life it too short. I would have written:
"The garden fence is a conspicuously displayed boundary line, but often no more than a token barrier. It indicates [or similar word] the outer territorial limit and separates the private world of the family from the public world beyond."
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TakaSo you don't think it's a modifier of 'limits', AG?
I'm not sure. Which word or phrase it modifies depends on its position in the sentence, I would think.

Separating the private world of the family from the public world beyond, the garden fence, a conspicuously displayed boundary line, often no more than a token barrier, is the outer territorial limits.

The garden fence, a conspicuously displayed boundary line, often no more than a token barrier, is the outer territorial limits, separating the private world of the family from the public world beyond.