Those assumptions are technically not even in scope of our “hard science”, but if one of those assumptions got “proven true” through whatever means (possible oxymoron) it would have major implications as much of pre-existing hard science would suddenly become either markedly less or markedly more consequential and/or new fields may be created.

Those assumptions describe fundamental traits of a system which humans are ill-equipped to live not having a model of; some (many?) people believe advances in science support one of them (e.g., material monism).