@Mitomino points out in this comment that my understanding of what modifies what in the sentence shown below from De Bello Gallico (VI.4.3) is mistaken. I'll diagram my understanding below. Can you show me my error?
Obsidibus imperatis centum hos Haeduis custodiendos tradit.
Also, there is a theoretical question at stake here: Does this sentence have an ablative absolute that connects grammatically to the rest of the sentence?
Here's my current understanding:
Notation: When A and B are connected directly by a line, and B is higher than A, then A modifies or supplies a parameter for B (such as an object for a verb or preposition). An arrow connecting two words A⟶B means that A's grammatical form agrees with B. For an example, see this answer. The notation doesn't distinguish between predication and restriction.
Translating literally, I get a pretty natural English sentence with an absolute construction:
One hundred hostages having been levied, Caesar hands them over to the Haedui to be watched over.
Background (as I understand it—this could be wrong): The Senones had recently revolted, or at least failed to obey Caesar's command, but they had to give up their plot when the Romans showed up. They then sent legates to the Haedui, long-time allies of the Romans, to plead with Caesar for leniency on their behalf. Caesar happily granted it because, as explained in the previous sentence, he wanted to fight wars, not conduct inquisitions. The sentence at hand informs us for the first time that Caesar had taken hostages from the Senones, and also that he returned them—but to the Haedui. I gather from the verb imperatis that Caesar had not taken the hostages directly by force; he must have ordered that the Senones yield them and they complied—all of which I've tried to suggest by rendering imperatis as "levied".
So, as I understand it, obsidibus imperatis centum is grammatically disconnected from the rest of the sentence, as is normal for an absolute construction. Hos refers to obsidibus but only in the same way that a pronoun can refer to an antecedent noun in another sentence; it does not agree with obsidibus grammatically. "Them" in the English sentence works the same way.
Not shown in the diagram is that centum could modify hos: "Hostages having been levied, Caesar hands over these hundred…" I don't think this affects the analysis above, mutatis mutandis. I take this to be the sort of ambiguity that flies around all over the place in language and no one notices because either interpretation results in the same meaning.
It appears that there was some semantic misalignment regarding "grammatically disconnected". I just meant relations of modifiers to what they modify and objects to words that take objects—the kinds of relations shown in the diagram. I meant to exclude the relation of pronoun to antecedent or two nouns designating the same thing.
As I understand the concept of absolute construction (at least in Latin and English), it is defined as a phrase that, when diagrammed in a sentence as above, has no lines connecting it with any words in the main clause—"grammatically independent of the main clause" as it's more commonly put. Is that right, or is there some basis to doubt it?
Cerberus has pointed out that there is a stylistic "rule", i.e. a guideline regarding elegance, not to refer in the main clause to any nouns in the ablative absolute. Did the stylistic rule cause semantic confusion? (I understand a definition not to be a "rule" but simply a way of distinguishing a topic of interest.)
The answers have given me plenty to think about regarding how predication happens in this sentence and in Latin generally. I'll try posting more about that in other questions.