vertical coherence and cohesion

Depending on the context of your text, I recommend translating the whole sentence this way:

让教育课程具备横向统整与纵贯衔接 --> to ensure the components of the curriculum be horizontally synthesized and vertically integrated

I would say Mainland Chinese writing style (particularly of government or state-funded enterprises) often sounds rhetorical and may not be translated with the same rhetoric nature in the target language esp. English.

A literal translation.

（educational）system pipelined

供参考

vertically converged

衔接 is a perfect match of "converge". See below:

Converge | Define Converge at Dictionary.com
www.dictionary.com/browse/converge
翻译此页
Converge definition, to tend to meet in a point or line; incline toward each other, as lines that are not parallel. See more.
‎Convergence · ‎Convergence excess · ‎Convergence zone

There is this definition, which sounds like it could be similar:
A vertical curriculum links knowledge from one lesson to the next across a program of study, while a horizontal curriculum integrates knowledge across different classes or disciplines.

I think perhaps the Chinese uses 统整 and 衔接 more for balance, and you could collapse it into one word, and say 'horizontally and vertically integrated'.


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Note added at 6 days (2017-04-10 23:48:36 GMT)
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I started writing an entry than changed it afterwards to this one, forgetting that it was also above. So I should have agreed with the answer above, but I didn't! Sorry.