Band names, movie names, noun adjuncts, and substantives.

It is possible that someone recognized:

If you look up at the movie and think this might be the computer animated story of a redheaded girl/woman with punk pigtails who participates in seedy robot fights...

As the beginning of the movie Big Hero 6.  I have sort of seen the movie now, but not with sound, and so do not feel qualified to talk about it.  Though it definitely wasn't about the redheaded girl/woman (it can be hard to tell with computer animation and a middling age) with punk pigtails who participates in seedy robot fights.  Pretty sure she never appears in another scene.

When the movie came out and I was hearing the name a lot I initially said, "I haven't seen one through five."  Only to find out that that wasn't what the "6" is all about.  There are six of them, you see.

This, in turn, confused me.  Then it should be "Six Big Heroes" and even if you switched the adjective to the predicate position and dropped the copula (which would be hideously bad grammar) it would be "Big Heroes, Six"

While I was talking about this (back then, not just now) Lonespark said that I was making an overly large deal about there not being a "The" at the front and it threw me for a loop.  I initially had no idea what she was talking about and, for reasons I don't remember now, was not able to get clarification because the phone call had to end.

What finally came to my rescue was "The Dave Clark Five".  It has the same form as, "The Big Hero Six," and is a perfectly acceptable thing to say.  So, what is it that makes "The Dave Clark Five" or "The Big Hero Six" perfectly acceptable while "Big Hero Six" throws up a red flag?

First off, the nouns have switched function.  They're adjuncts.  They're adjective-like but not adjectives.  The major difference is that adjuncts come after adjectives.  You can say "The New Dave Clark Five," but not, "The Dave Clark New Five," (the closest you can manage is "Dave Clark's New Five," but in that case "Dave Clark's" is acting as a determiner and thus displacing "The".)

Other than word order, Noun adjuncts function pretty much exactly like adjectives.  They can modify nouns (in "The college student" 'college' is a noun adjunct and functions just like the adjective in "The bright student,") and adjectives (in "the puke green car" 'puke' is a noun adjunct modifying 'green' like 'bright' modifies 'green' in "the bright green student",)

Since Dave Clark is relegated to adjunct we know it can't be the main noun of the noun phrase.  Now it's vaguely important that noun adjuncts don't take determiners.  "The college student" is "The student," first, and "college" as a description of what kind of student, never "Student" first and "The college" as what kind of student.  You can't use an adjunct to say "The student who goes to my college" because "My college student" will always mean "my student" not "My college".

Non-determiners are trickier.  Adjuncts can have adjectives (and even adjuncts of their own.)  Since adjuncts come after both adjectives that modify the noun they modify and ones that modify themselves, it can be unclear which type of adjective a word is.  Thus, "The Big Hero Six" could be "The Big Six" modified by "Hero" or "The Six" modified by "Big Hero." There is no way to tell.

I'm assuming, "Big Hero" is a unit since The Six actually come in various sizes.

But that's not important.  We've covered adjuncts, but that doesn't tell us why "The Big Hero Six" is standard grammar while, "Big Hero Six" is either non-standard or implies that there exist Big Heroes one through five.

Which brings us to another thing.  "Six" can be a noun, but when it is it refers exclusively to the number six.  Why was six afraid of seven?"  You don't need to modify it because there is only one six.

Usually, though, "six" is an adjective.  "The six stages of morality."  (Six modifies stages.)  "I have six apples."  (Six modifies apples.)

Just as a noun can be used like an adjective as an adjunct, though, an adjective can be used like a noun as a substantive.  My first inclination was to call this articular (an articular infinitive is a Greek verb that is made to act like a noun by sticking an article in front of it) but it works with more than just articles.  For example:

These six, my six, some six, whichever six, her six, et cetera

Instead what it needs is a determiner, which is a broader class.  But the thing is that it needs a determiner.

Old and new are adjectives that act as nouns in, "Out with the old, in with the new."  You can swap out the "the" for another determiner:

Out with these old, in with those new.
Out with an old, in with a new.
Out with your old, in with your new.
Out with some old, in with some new.
Out with no old, in with no new.

but what you can't do is drop the determiner entirely:

Out with old, in with new.

Without a determiner the adjective is just an adjective, not a substantive.  "The dispossessed" is a group that has been screwed over, "Dispossessed," is impossible to interpret without seeing the noun to which it is attached.

Thus "The five" of "The Dave Clark Five" functions as a noun but the word "six," in "Big Hero Six" does not.

All of that said, one could theorize that the name of the movie is perfectly accurate and does in fact refer to the sixth big hero.  Not the sixth "Big Hero" movie, but the sixth member of the squad.  Certainly one can divide the six members such that Big Heroes one through five are homogeneous and number six is different.

Anyway: grammar.

[Added:]

Well after finishing writing, it occurred to me that a really good example of a substantive in action is, "Make new friends, but keep the old."  "The old" stands for "old friends" or, one could argue, "the old ones," with "ones" standing in for "friends", but either way, even though structure makes it completely clear you're talking about friends, you still need a determiner on the adjective "old".

"Make new friends, but keep old," doesn't work.  It's not a proper sentence.  The first part has the form of half of a compound sentence, but the second part doesn't actually mean anything.