Are you thinking of statistics?
The issue with things like Hydrogen classification would, I would imagine, be referred to as the “boundary condition”. Things are different at the boundary edge of the distribution.
The thing about my “rule” is…sometimes, where there’s a system operating, the first one (or first few) unit(s) of the lower bound of the ordered list will be “(the) exception(s) to the rule” to whatever process generates the ordered list.
Here’s another example…geometry.
An n-dimensional object can be constructed by an infinite sum of n-1 dimensional objects
A 3d cube can be thought of as an infinite “stack” of squares.
a 2d square is an infinite stack of line segments.
a 1d line segment is an infinite stack of points.
However, a 0 dimensional point is not made up of an infinite stack of…“something”.
It is fundamental…and is the bottom end that doesn’t obey the stated program of the system.
0 is a small number, yes?
Yes, though I know at least one very small child who would say “No!” - and prove it by drawing one that covers the entire page. 
Enola: does the fact that the Fibonacci series seems to start in such an inelegant or inadequate way seem like another example of what you’re saying, or is that different?
I cannot speak for Enola Straight, but while the Fibonacci sequence is determined by two of the numbers and a recurrence relation, it need not necessarily start anywhere specific:
…, 5, -3, 2, -1, 1, 0, 1, 1, 2, 3, 5, …
His [since Enola Gay is “her” I guess Enola Straight is “his”?] example seems more related to the fact there is a smallest natural number (0 or 1) - a boundary condition?
What if we started it
543, 1, 544, 545, 1089, …
?
I don’t get it, I thought it necessarily began 1, 1, 2…
Right, if you started with 543, 1 you would get a different sequence. That’s why I said you have to specify two of the numbers, e.g., 1, 1, or 0, 1. What I meant was that, unlike the natural numbers, you can extend the Fibonacci sequence indefinitely in both directions, so it’s turtles all the way down and no boundary condition.
But I did specify two numbers, 543 and 1. I’m genuinely confused and it’s because I don’t know what I’m talking about, but I can’t see which part it is that I’m getting wrong. If you have to specify only either 1, 1 or 0, 1 , but no other combination, then I believe that means you “necessarily start with” those numbers - not that they are printed at the left side, just that they “start” it as in “generate” it. So I think it is a boundary condition, even though it isn’t on the left side of the page.
But the beginning of the Fibonacci sequence as 1,1 is specifically what I would refer to as the “Boundary Condition”, assuming the definition is start with two numbers and go up (right?)… Similarly, that the first number in sequence is prime but its multiples are not - a boundary condition. I.e. 2 is prime, 4,6,8,10,… not. Similarly, 3 is prime. 6,9,12, etc. not. Same with any other prime.
I would think “anomaly at the beginning - first one or two” is typically a boundary condition - or more accurately, by definition the boundary condition.
Fair enough, I don’t disagree. But it is a different sort of “boundary” or initial value than the one in the OP’s example, where there is such a thing as a 1-dimensional space, or a zero-dimensional space, but no such thing as a negative-dimensional space. (Well, at least not in the usual sense.)
That’s actually a good example. You can start a Fibonacci-like sequence with any two numbers. And although such sequences will start off very different from each other, in the long run they’ll all share many properties in common. So you can have the first few terms being un-Fibonacci-like.
I believe, for clarity’s sake, I must re-state the rule:
Sometimes, the first unit(s) after the Lower Bound of an Ordered List, will…due to the smallness of numerical value…be the “exception(s) to the rule”…whatever “rule” governs the system and defines the larger, more structured units of the list.
Reminds me of the story of how different professions prove all odd number are prime.
Mathematician: “One is prime, One plus two is three is prime. Three plus two is five is prime. Five plus two is seven is prime. Therefore by induction, all odd numbers are prime.”
Physicist: “One is prime, three is prime, five is prime, seven is prime, nine - experimental error, eleven is prime… Therefore I conclude all odd numbers are prime.”
Engineer: * “One is prime, three is prime, five is prime, seven is prime, nine is prime, eleven is prime… Therefore all odd numbers are prime.”*
My parents’ physicist friends thought this was funny, but my brother the engineer was not as amused.
And mathematicians get annoyed at the claim that 1 is prime.
Hey, there’s another example: The general rule is that all integers are either prime or composite. But there are three exceptions: -1, 0, and 1 are neither.
Maybe, maybe not.
If you include -1, then there must be all the negative primes below that.
You begin at the exceptions at the lower bound…not the middle.
-1 is a low absolute value, which is the sort of bound that matters here.
But the same applies if we’re talking about just the nonnegative integers (and you don’t see much talk about negative primes, anyway).
Regarding hydrogen, the reason it’s not a super-halogen is because to fill its orbital it would have to hold on to twice the electric charge of its nucleus, which only happens with really loosely bound electrons (alkali hydrides for example).
But yeah, 1 and even worse 0 are involved in a lot of “degenerate” math.
I think a better way to state this is…
Because two and three are prime, all other primes must be of the form 6 x + 1 or 6 x - 1.
Two and three are the cause of the pattern, not exceptions to the rule.
Here is a rather trivial generalization of the law
If a given rule has a finite number of exemptions, there exist a number N such that all exemptions are less than N.
would that hold true for other products of primes? 3 and 5, for example, give 15, which + or - 1, doesn’t yield primes, but +/- 2 does. 2,3,and 5 gives 30, which +/- 1 give two primes.