Scientific innovations often struggle to pass through peer review and regularly fail under certain circumstances: In its theoretical aspects, science is believed to progress through criticism and falsification, but where a dominant theoretical framework is established, expert reviewers practically only allow its completeness to be questioned. Falsifications are frequently bypassed by fudge factors. Criticism, even if fatal, can be turned a blind eye. This blocks fundamental scientific progress. An article about cosmology with published reviews highlights this issue. There, a critical evaluation is suppressed despite evident contradictions in the standard approach. As a countermeasure against similar cases, a new open access medium “Well-Founded Extraordinary Science”, with published reviews, is proposed. It aims to promote epistemic progress by challenging established wisdom. It accepts only studies that go against established assumptions, theories or methods and advances innovations or ‘revolutions’ that are well-founded and parsimonious. Reviewers are guided to check each claimed deficiency and innovation, whereby their confirmation bias is bridled. It is acceptable to present criticism without elaborating innovations and innovations without elaborate criticism of the established framework.