Author here. This started as a literature review and turned into something stranger.
We found the same mathematical structure — operator kernels with specific symmetry properties — appearing independently in physics (phase transitions), finance (market crashes), ecology (extinction cascades), neuroscience (neural criticality), and network science (cascade failures).
Each field derived it from first principles. Each named it differently. Minimal cross-citation. The paper traces the convergent discovery and asks: if the same structure keeps emerging, what does that tell us about how we organize knowledge? Freethemath.org is our summary for non-specialists.
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