No, there is not a “standard dictionary”, and there cannot be. No dictionary “defines” conclusively what a word “means” or how it may be used. At most, it provides a list of approximate paraphrases reflecting how it is used in various contexts.
Those paraphrases are not in any sense official: they are attempts at an explanation by expert editors, just like the answers you get here on ELL.
When you look up an unfamiliar word in a dictionary what you hope to find is a meaning which makes sense in the context in which you have encountered the word. Consequently, the dictionary you should prefer is one which provides
- the most different definitions . . . That will give you the best chance of finding a definition which makes sense in your context.
- the most different contexts—examples of use in brief citations . . . That will give you the best chance of finding a context which you recognize as similar to your context.
The largest and most complete dictionary of English, in both of these dimensions, is the Oxford English Dictionary. But this is probably more dictionary than you actually want, since it is specifically intended to cover not only a word’s contemporary use but its use through recorded history. In any case, the most recent edition, and the one most useful to you, is available only through a fairly expensive online subscription. Many libraries and universities provide access to their own members.
All of the free online dictionaries you name provide reasonably full definitions. In my experience, the dictionary which regularly provides the most citations is OALD—the Oxford Advanced Learner’s Dictionary.
But there is no reason you should confine yourself to just one dictionary. Treat “the dictionary” like ELL: consult multiple dictionaries to get multiple answers, and “accept” the one which best suits your immediate needs.
Both Oxford Dictionaries Online and Cambridge Dictionaries Online provide access to multiple works, including dictionaries directed specifically toward the needs of learners and dictionaries directed specifically toward US and British usage. OneLook.com speeds your lookups by providing in a single report links to entries for a given headword in many dictionaries.
For even more citations you may consult a corpus, a large body of indexed texts. Google Books is the largest extant corpus; several smaller, but more usefully categorized corpora are available at Brigham Young University.
But neither a single dictionary or corpus, nor all dictionaries and corpora in concert, will provide you mastery of all of a word’s meanings and uses. Meanings and uses are not static, but constantly evolving, faster than dictionaries can keep up. Nobody really knows “what a ‘word’ means”.
Best Answer
Both involve the same metaphor of cutting across existing natural lines of cleavage, as when we speak of cutting across the grain of wood or meat:
The flank steak image is from theenchantedcook.blogspot.com, the saw image is from cmtutensili.com.
When we speak of issues or votes cutting across party lines we understand 'party lines' to be the 'lines' which divide the parties. On most issues people's attitudes follow party lines:
Note that the 'party lines' we speak of here are not the same thing as 'the party line': the official position a party takes on a particular issue and its rhetorical 'line' of argument for supporting it. When an issue cuts across party lines it is not (necessarily) contrary to the parties' positions on the issue; it is 'contrary to' the usual lines of division between parties.
But some issues divide differently: they cut across party lines: