Laws of nature are hyperintensional

Are the laws of nature hyperintensional? I.e., if p and q are logically equivalent, could it be that one of them is a law of nature and the other is not?

I am inclined to think so.

Argument 1: The laws of nature in our world do not make reference to particular substances. But if p is a law of nature, then let q be the proposition that p is true and either Biden is president or Biden is not presiden. Then p and q are logically equivalent, but q is not a law as it makes reference to a particular substance.

Argument 2: The laws of nature in our world are first-order. But any first-order proposition p is logically equivalent to the second-order proposition that p is true.

Argument 3: Plausibly, the values of fundamental constants like the fine-structure constant α are a part of the laws of nature. But now imagine that it turns out that the infinitely many significant digits of α express the infinite list of all arithmetical propositions and their truth values in some specific simple encoding scheme. There are two possibilities. Supposing that it is a law of nature that the digits of α have this curious property, then after verifying this property for a sufficiently large number of digits, we could know which of the remaining arithmetical propositions are true simply by measuring α to a high degree of precision. But if the law of nature is simply the brute fact that the digits are 0.007297352569…, and it just happens that these digits encode arithmetical truths in that encoding scheme, then we wouldn’t know truths by just measuring α. (Compare: Imagine a machine where you input an arithmetical proposition, and the machine flips a coin to yield an output of “True” and “False”. Even if we are so lucky that the machine always gives the right answer, that answer wouldn’t be knowledge. It would be just luck.) This means that there is a difference between having a law that says that the digits of α are determined by the arithmetical truths according to that encoding scheme and having an infinite law that simply states the digits, even though the two laws are logically equivalent (assuming the truths of arithmetic are logically necessary; if not, replace the truths of arithmetic by any sequence of hard to know logically necessary truths).

Argument 4: Laws of nature figure in explanations, but explanation is hyperintensional. The correct explanation of why the apple fell down is not that F = Gm₁m₂/r² and either Biden is president or Biden is not president, but simply that F = Gm₁m₂/r².

Argument 5: One of our best accounts of laws of nature is the Lewis-Ramsey best-systems model. But on that model it is very natural to identify the laws of nature with the axioms of the best system, and not just with propositions equivalent to the axioms of the best system.

Final note: I wonder, though, whether there is a unique proposition that expresses any given law of nature. Is there really a fact of the matter whether the law is F = Gm₁m₂/r² or F = m₁m₂(G/r²)?