Accepted answer
At 4 °C the question is which route is fastest, not whether fibrillation happens — and the routes do not share an activation energy, so their ranking changes with temperature. 4 °C is the condition the rule of thumb is anchored to, so it is the baseline rather than a multiplier: everything else in this thread is quoted relative to it. That multiplier is an average over every route at once, which is exactly why it cannot tell you which one wins. Ordered beta-sheet assembly, effectively irreversible, and its endpoint is opalescence you can see rather than a peak you can integrate. So the way to answer it for your vial is to pick the method that sees fibrillation specifically and run it against a control held cold, rather than to infer a mechanism from a purity number that averages all of them.
Answer first: the degradation pathways worth knowing are hydrolysis, deamidation, oxidation, aggregation and adsorption, and each has a different trigger and a different mitigation.
Light exposure matters for tryptophan-containing sequences and for anything with a chromophore. Amber vials and a closed box are free mitigations.
In practice, oxidation targets methionine, cysteine and tryptophan, adding sixteen daltons per oxygen. It is catalysed by trace metals and promoted by dissolved oxygen and by light.
Aggregation at air-liquid interfaces is established from surface-tension and particle-count studies and is the basis for anti-agitation handling guidance.
At dilute concentrations, suspect adsorption before you suspect chemistry.