It vastly depends on the actual science which standard of proof is accepted.
For maths, with a 5-sigma result you can maybe get a mention in the "curiosa" section if it's weird enough. It is certainly not considered a valid mathematical result.
For biology, a 1 sigma result is considered pretty good. And due to experimental restrictions, this is actually more strict than medicine requires.
Many science disciplines work with known-wrong theories. Civil engineering for example, works with pre-Newtonian mechanics (not even "turtle mechanics" : in the best simulations a building stands on ground, which stands on a plate which is magically suspended in a "downward" gravity field, not on a planet).
The idea of "this is the standard of proof for 'science'" is a nice one, but it doesn't exist in any reasonable sense. Only the utilitarian definition sticks : we have 100 standards of proof, and if the theory works (or gets enough money if your cynical) we'll find the standard of proof that allows us to call it science.
Furthermore, there are several inconsistencies in the science underpinning, for example, the Higgs boson discovery. We do not actually have rigorous proofs for constructing even natural numbers by the standards of first-order logic. And second order logic has paradoxes that stand unresolved (there is a lot of research to find something "more flexible" than first-order logic, but stricter than second-order that works, but this research has been going on for more than a century and there are no really good candidates, only really bad ones like the famous failure of the Choice axiom)
The standard model doesn't even contain gravity, so if you're being pedantic you could drop a pen from your desk and claim, correctly, that you've just falsified the entire standard model, or at least proven it's incompleteness.
Less pedantically in the physics itself there is the massive open question. The Higgs field only causes inertia, not gravity. Yet the measure of interaction with the Higgs field of any object we've ever measured matches exactly the value we've got for that same object's gravitic interactions. Does anyone believe this to be a coincidence ? Major open hole there.